theory of teaching essay

The 6 Most Important Theories of Teaching

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• M.A., Communications and Information Management, Bay Path College
• B.A., Journalism and Design, Mount Holyoke College

The learning process has been a popular subject for theoretical analysis for decades. While some of those theories never leave the abstract realm, many of them are put into practice in classrooms on a daily basis. Teachers synthesize multiple theories, some of them decades-old, in order to improve their students' learning outcomes. The following theories of teaching represent some of the most popular and well-known in the field of education.

Multiple Intelligences

The theory of multiple intelligences , developed by Howard Gardner, posits that humans can possess eight different types of intelligence: musical-rhythmic, visual-spatial, verbal-linguistic, bodily-kinesthetic, interpersonal, intrapersonal, and naturalistic. These eight types of intelligence represent the varied ways individuals process information. 

The theory of multiple intelligence transformed the world of learning and pedagogy. Today, many teachers employ curriculums that have been developed around eight types of intelligence. Lessons are designed to include techniques that align with each individual student's learning style.

Bloom's Taxonomy

Developed in 1956 by Benjamin Bloom, Bloom’s Taxonomy is a hierarchical model of learning objectives. The model organizes individual educational tasks, such as comparing concepts and defining words, into six distinct educational categories: knowledge, comprehension, application, analysis, synthesis, and evaluation. The six categories are organized in order of complexity.

Bloom's Taxonomy gives educators a common language to communicate about learning and helps teachers establish clear learning goals for students. However, some critics contend that the taxonomy imposes an artificial sequence on learning and overlooks some crucial classroom concepts, such as behavior management. 

Zone of Proximal Development (ZPD) and Scaffolding

Lev Vygotsky developed a number of important pedagogical theories, but two of his most important classroom concepts are the Zone of Proximal Development and scaffolding .

According to Vygotsky, the Zone of Proximal Development (ZPD) is the conceptual gap between what a student is  and is   not  able to accomplish independently. Vygotsky suggested that the best way for teachers to support their students is by identifying the Zone of Proximal Development and working with them to accomplish tasks just beyond it. For example, a teacher might choose a challenging short story, just outside of what would be easily digestible for the students, for an in-class reading assignment. The teacher would then provide support and encouragement for the students to hone their reading comprehension skills throughout the lesson.

The second theory, scaffolding, is the act of adjusting the level of support provided in order to best meet each child's abilities. For example, when teaching a new math concept, a teacher would first walk the student through each step to complete the task. As the student begins to gain an understanding of the concept, the teacher would gradually reduce the support, moving away from step-by-step direction in favor of nudges and reminders until the student could complete the task entirely on her own.

Schema and Constructivism

Jean Piaget's schema theory suggests new knowledge with students' existing knowledge, the students will gain a deeper understanding of the new topic. This theory invites teachers to consider what their students already know before starting a lesson. This theory plays out in many classrooms every day when teachers begin lessons by asking their students what they already know about a particular concept. 

Piaget's theory of constructivism, which states that individuals construct meaning through action and experience, plays a major role in schools today. A constructivist classroom is one in which students learn by doing, rather than by passively absorbing knowledge. Constructivism plays out in many early childhood education programs, where children spend their days engaged in hands-on activities.

Behaviorism

Behaviorism, a set of theories laid out by B.F. Skinner, suggests that all behavior is a response to an external stimulus. In the classroom, behaviorism is the theory that students' learning and behavior will improve in response to positive reinforcement like rewards, praise, and bonuses. The behaviorist theory also asserts that negative reinforcement — in other words, punishment — will cause a child to stop undesired behavior. According to Skinner, these repeated reinforcement techniques can  shape behavior and produce improves learning outcomes.

The theory of behaviorism is frequently criticized for failing to consider students' internal mental states as well as for sometimes creating the appearance of bribery or coercion.  

Spiral Curriculum

In the theory of the spiral curriculum, Jerome Bruner contends that children are capable of comprehending surprisingly challenging topics and issues, provided that they are presented in an age-appropriate manner. Bruner suggests that teachers revisit topics annually (hence the spiral image), adding complexity and nuance every year. Achieving a spiral curriculum requires an institutional approach to education, in which the teachers at a school coordinate their curriculums and set long-term, multi-year learning goals for their students. 

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Philosophy of Education

All human societies, past and present, have had a vested interest in education; and some wits have claimed that teaching (at its best an educational activity) is the second oldest profession. While not all societies channel sufficient resources into support for educational activities and institutions, all at the very least acknowledge their centrality—and for good reasons. For one thing, it is obvious that children are born illiterate and innumerate, and ignorant of the norms and cultural achievements of the community or society into which they have been thrust; but with the help of professional teachers and the dedicated amateurs in their families and immediate environs (and with the aid, too, of educational resources made available through the media and nowadays the internet), within a few years they can read, write, calculate, and act (at least often) in culturally-appropriate ways. Some learn these skills with more facility than others, and so education also serves as a social-sorting mechanism and undoubtedly has enormous impact on the economic fate of the individual. Put more abstractly, at its best education equips individuals with the skills and substantive knowledge that allows them to define and to pursue their own goals, and also allows them to participate in the life of their community as full-fledged, autonomous citizens.

But this is to cast matters in very individualistic terms, and it is fruitful also to take a societal perspective, where the picture changes somewhat. It emerges that in pluralistic societies such as the Western democracies there are some groups that do not wholeheartedly support the development of autonomous individuals, for such folk can weaken a group from within by thinking for themselves and challenging communal norms and beliefs; from the point of view of groups whose survival is thus threatened, formal, state-provided education is not necessarily a good thing. But in other ways even these groups depend for their continuing survival on educational processes, as do the larger societies and nation-states of which they are part; for as John Dewey put it in the opening chapter of his classic work Democracy and Education (1916), in its broadest sense education is the means of the “social continuity of life” (Dewey, 1916, 3). Dewey pointed out that the “primary ineluctable facts of the birth and death of each one of the constituent members in a social group” make education a necessity, for despite this biological inevitability “the life of the group goes on” (Dewey, 3). The great social importance of education is underscored, too, by the fact that when a society is shaken by a crisis, this often is taken as a sign of educational breakdown; education, and educators, become scapegoats.

It is not surprising that such an important social domain has attracted the attention of philosophers for thousands of years, especially as there are complex issues aplenty that have great philosophical interest. Even a cursory reading of these opening paragraphs reveals that they touch on, in nascent form, some but by no means all of the issues that have spawned vigorous debate down the ages; restated more explicitly in terms familiar to philosophers of education, the issues the discussion above flitted over were: education as transmission of knowledge versus education as the fostering of inquiry and reasoning skills that are conducive to the development of autonomy (which, roughly, is the tension between education as conservative and education as progressive, and also is closely related to differing views about human “perfectibility”—issues that historically have been raised in the debate over the aims of education); the question of what this knowledge, and what these skills, ought to be—part of the domain of philosophy of the curriculum; the questions of how learning is possible, and what is it to have learned something—two sets of issues that relate to the question of the capacities and potentialities that are present at birth, and also to the process (and stages) of human development and to what degree this process is flexible and hence can be influenced or manipulated; the tension between liberal education and vocational education, and the overlapping issue of which should be given priority—education for personal development or education for citizenship (and the issue of whether or not this is a false dichotomy); the differences (if any) between education and enculturation; the distinction between educating versus teaching versus training versus indoctrination; the relation between education and maintenance of the class structure of society, and the issue of whether different classes or cultural groups can—justly—be given educational programs that differ in content or in aims; the issue of whether the rights of children, parents, and socio-cultural or ethnic groups, conflict—and if they do, the question of whose rights should be dominant; the question as to whether or not all children have a right to state-provided education, and if so, should this education respect the beliefs and customs of all groups and how on earth would this be accomplished; and a set of complex issues about the relation between education and social reform, centering upon whether education is essentially conservative, or whether it can be an (or, the ) agent of social change.

It is impressive that most of the philosophically-interesting issues touched upon above, plus additional ones not alluded to here, were addressed in one of the early masterpieces of the Western intellectual tradition—Plato's Republic . A.N. Whitehead somewhere remarked that the history of Western philosophy is nothing but a series of footnotes to Plato, and if the Meno and the Laws are added to the Republic , the same is true of the history of educational thought and of philosophy of education in particular. At various points throughout this essay the discussion shall return to Plato, and at the end there shall be a brief discussion of the two other great figures in the field—Rousseau and Dewey. But the account of the field needs to start with some features of it that are apt to cause puzzlement, or that make describing its topography difficult. These include, but are not limited to, the interactions between philosophy of education and its parent discipline.

1.1 The open nature of philosophy and philosophy of education

1.2 the different bodies of work traditionally included in the field, 1.3 paradigm wars the diversity of, and clashes between, philosophical approaches, 2.1 the early work: c.d. hardie, 2.2 the dominant years: language, and clarification of key concepts, 2.3 countervailing forces, 2.4 a new guise contemporary social, political and moral philosophy, 3.1 philosophical disputes concerning empirical education research, 3.2 the content of the curriculum, and the aims and functions of schooling, 3.3 rousseau, dewey, and the progressive movement, 4. concluding remarks, bibliography, other internet resources, related entries, 1. problems in delineating the field.

There is a large—and ever expanding—number of works designed to give guidance to the novice setting out to explore the domain of philosophy of education; most if not all of the academic publishing houses have at least one representative of this genre on their list, and the titles are mostly variants of the following archetypes: The History and Philosophy of Education , The Philosophical Foundations of Education , Philosophers on Education , Three Thousand Years of Educational Wisdom , A Guide to the Philosophy of Education , and Readings in Philosophy of Education . The overall picture that emerges from even a sampling of this collective is not pretty; the field lacks intellectual cohesion, and (from the perspective taken in this essay) there is a widespread problem concerning the rigor of the work and the depth of scholarship—although undoubtedly there are islands, but not continents, of competent philosophical discussion of difficult and socially-important issues of the kind listed earlier. On the positive side—the obverse of the lack of cohesion—there is, in the field as a whole, a degree of adventurousness in the form of openness to ideas and radical approaches, a trait that is sometimes lacking in other academic fields. This is not to claim, of course, that taken individually philosophers of education are more open-minded than their philosophical cousins!

Part of the explanation for this diffuse state-of-affairs is that, quite reasonably, most philosophers of education have the goal (reinforced by their institutional affiliation with Schools of Education and their involvement in the initial training of teachers) of contributing not to philosophy but to educational policy and practice. This shapes not only their selection of topics, but also the manner in which the discussion is pursued; and this orientation also explains why philosophers of education—to a far greater degree, it is to be suspected, than their “pure” cousins—publish not in philosophy journals but in a wide range of professionally-oriented journals (such as Educational Researcher , Harvard Educational Review , Teachers College Record , Cambridge Journal of Education, Journal of Curriculum Studies , and the like). Some individuals work directly on issues of classroom practice, others identify as much with fields such as educational policy analysis, curriculum theory, teacher education, or some particular subject-matter domain such as math or science education, as they do with philosophy of education. It is still fashionable in some quarters to decry having one's intellectual agenda shaped so strongly as this by concerns emanating from a field of practice; but as Stokes (1997) has made clear, many of the great, theoretically-fruitful research programs in natural science had their beginnings in such practical concerns—as Pasteur's grounbreaking work illustrates. It is dangerous to take the theory versus practice dichotomy too seriously.

However, there is another consequence of this institutional housing of the vast majority of philosphers of education that is worth noting—one that is not found in a comparable way in philosophers of science, for example, who almost always are located in departments of philosophy—namely, that experience as a teacher, or in some other education-related role, is a qualification to become a philosopher of education that in many cases is valued at least as much as depth of philosophical training. (The issue is not that educational experience is irrelevant—clearly it can be highly pertinent—but it is that in the tradeoff with philosophical training, philosophy often loses.) But there are still other factors at work that contribute to the field's diffuseness, that all relate in some way to the nature of the discipline of philosophy itself.

In describing the field of philosophy, and in particular the sub-field that has come to be identified as philosophy of education, one quickly runs into a difficulty not found to anything like the same degree in other disciplines. For example, although there are some internal differences in opinion, nevertheless there seems to be quite a high degree of consensus within the domain of quantum physics about which researchers are competent members of the field and which ones are not, and what work is a strong contribution (or potential contribution). The very nature of philosophy, on the other hand, is “essentially contested”; what counts as a sound philosophical work within one school of thought, or socio-cultural or academic setting, may not be so-regarded (and may even be the focus of derision) in a different one. Coupled with this is the fact that the borders of the field are not policed, so that the philosophically-untrained can cross into it freely—indeed, over the past century or more a great many individuals from across the spectrum of real and pseudo disciplines have for whatever reason exercised their right to self-identify as members of this broad and loosely defined category of “philosophers” (as a few minutes spent browsing in the relevant section of a bookstore will verify).

In essence, then, there are two senses of the term “philosopher” and its cognates: a loose but common sense in which any individual who cogitates in any manner about such issues as the meaning of life, the nature of social justice, the essence of sportsmanship, the aims of education, the foundations of the school curriculum, or relationship with the Divine, is thereby a philosopher; and there is a more technical sense referring to those who have been formally trained or have acquired competence in one or more areas such as epistemology, metaphysics, moral philosophy, logic, philosophy of science, and the like. If this bifurcation presents a problem for adequately delineating the field of philosophy, the difficulties grow tenfold or more with respect to philosophy of education.

This essay offers a description and assessment of the field as seen by a scholar rooted firmly in the formal branch of “philosophy of education”, and moreover this branch as it has developed in the English-speaking world (some of which, of course, has been inspired by Continental philosophy); but first it is necessary to say a little more about the difficulties that confront the individual who sets out, without presuppositions, to understand the topography of “philosophy of education”.

It will not take long for a person who consults several of the introductory texts alluded to earlier to encounter a number of different bodies of work (loosely bounded to be sure) that have by one source or another been regarded as part of the domain of philosophy of education; the inclusion of some of these as part of the field is largely responsible for the diffuse topography described earlier. What follows is an informal and incomplete accounting.

First, there are works of advocacy produced by those non-technical, self-identified “philosophers” described above, who often have an axe to grind; they may wish to destroy (or to save) common schooling, support or attack some innovation or reform, shore-up or destroy the capitalist mode of production, see their own religion (or none at all) gain a foothold in the public schools, strengthen the place of “the basics” in the school curriculum, and so forth. While these topics certainly can be, and have been, discussed with due care, often they have been pursued in loose but impressive language where exhortation substitutes for argumentation—and hence sometimes they are mistaken for works of philosophy of education! In the following discussion this genre shall be passed over in silence.

Second, there is a corpus of work somewhat resembling the first, but where the arguments are tighter, and where the authors usually are individuals of some distinction whose insights are thought-provoking—possibly because they have a degree of familiarity with some branch of educational activity, having been teachers (or former teachers), school principals, religious leaders, politicians, journalists, and the like. While these works frequently touch on philosophical issues, they are not pursued to any philosophical depth and can hardly be considered as contributions to the scholarship of the discipline. However, some works in this genre are among the classics of “educational thought”—a more felicitous label than “philosophy of education”; cases in point would be the essays, pamphlets and letters of Thomas Arnold (headmaster of Rugby school), John Wesley (the founder of Methodism), J.H. (Cardinal) Newman, T.H. Huxley, and the writings on progressive schooling by A.S. Neill (of Summerhill school). Some textbooks even include extracts from the writings or recorded sayings of such figures as Thomas Jefferson, Ben Franklin, and Jesus of Nazareth (for the latter three, in works spanning more than half a century, see Ulich, 1950, and Murphy, 2006). Books and extracts in this genre—which elsewhere I have called “cultured reflection on education”—are often used in teacher-training courses that march under the banner of “educational foundations”, “introduction to educational thought”, or “introduction to philosophy of education”.

Third, there are a number of educational theorists and researchers, whose field of activity is not philosophy but—for example—might be human development or learning theory, who in their technical work and sometimes in their non-technical books and reflective essays explicitly raise philosophical issues or adopt philosophical modes of argumentation—and do so in ways worthy of careful study. If philosophy (including philosophy of education) is defined so as to include analysis and reflection at an abstract or “meta-level”, which undoubtedly is a domain where many philosophers labor, then these individuals should have a place in the annals of philosophy or philosophy of education; but too often, although not always, accounts of the field ignore them. Their work might be subjected to scrutiny for being educationally important, but their conceptual or philosophical contributions are rarely focused upon. (Philosophers of the physical and biological sciences are far less prone to make this mistake about the meta-level work of reflective scientists in these domains.)

The educational theorists and researchers I have in mind as exemplars here are the behaviorist psychologist B.F. Skinner (who among other things wrote about the fate of the notions of human freedom and dignity in the light of the development of a “science of behavior”, and who developed a model of human action and also of learning that eschewed the influence of mental entities such as motives, interests, and ideas and placed the emphasis instead upon “schedules of reinforcement”); the foundational figure in modern developmental psychology with its near-fixation on stage theories, Jean Piaget (who developed in an abstract and detailed manner a “genetic epistemology” that was related to his developmental research); and the social psychologist Lev Vygotsky (who argued that the development of the human youngster was indelibly shaped by social forces, so much so that approaches which focused on the lone individual and that were biologically-oriented—he had Piaget in mind here—were quite inadequate).

Fourth, and in contrast to the group above, there is a type of work that is traditionally but undeservedly given a prominent place in the annals of philosophy of education, and which thereby generates a great deal of confusion and misunderstanding about the field. These are the books and reflective essays on educational topics that were written by mainstream philosophers, a number of whom are counted among the greatest in the history of the discipline. The catch is this: Even great philosophers do not always write philosophy! The reflections being referred-to contain little if any philosophical argumentation, and usually they were not intended to be contributions to the literature on any of the great philosophical questions. Rather, they expressed the author's views (or even prejudices) on educational rather than philosophical problems, and sometimes—as in the case of Bertrand Russell's rollicking pieces defending progressive educational practices—they explicitly were “potboilers” written to make money. (In Russell's case the royalties were used to support a progressive school he was running with his current wife.) Locke, Kant, and Hegel also are among those who produced work of this genre.

John Locke is an interesting case in point. He had been requested by a cousin and her husband—possibly in part because of his medical training—to give advice on the upbringing of their son and heir; the youngster seems to have troubled his parents, most likely because he had learning difficulties. Locke, then in exile in Europe, wrote the parents a series of letters in which alongside sensible advice about such matters as the priorities in the education of a landed gentleman, and about making learning fun for the boy, there were a few strange items such as the advice that the boy should wear leaky shoes in winter so that he would be toughened-up! The letters eventually were printed in book form under the title Some Thoughts Concerning Education (1693), and seem to have had enormous influence down the ages upon educational practice; after two centuries the book had run through some 35 English editions and well over thirty foreign editions, and it is still in print and is frequently excerpted in books of readings in philosophy of education. In stark contrast, several of Locke's major philosophical writings—the Essay Concerning Human Understanding , and the Letter on Toleration —have been overlooked by most educational theorists over the centuries, even though they have enormous relevance for educational philosophy, theory, policy, and practice. It is especially noteworthy that the former of these books was the foundation for an approach to psychology—associationism—that thrived during the nineteenth century. In addition it stimulated interest in the processes of child development and human learning; Locke's model of the way in which the “blank tablet” of the human mind became “furnished” with simple ideas that were eventually combined or abstracted in various ways to form complex ideas, suggested to some that it might be fruitful to study this process in the course of development of a young child (Cleverley and Phillips, 1986).

Fifth, and finally, there is a large body of work that clearly falls within the more technically-defined domain of philosophy of education. Three historical giants of the field are Plato, Rousseau, and Dewey, and there are a dozen or more who would be in competition for inclusion along with them; the short-list of leading authors from the second-half of the 20 th century would include Richard Peters, Paul Hirst, and Israel Scheffler, with many jostling for the next places—but the choices become cloudy as we approach the present-day, for schisms between philosophical schools have to be negotiated.

It is important to note, too, that there is a sub-category within this domain of literature that is made-up of work by philosophers who are not primarily identified as philosophers of education, and who might or might not have had much to say directly about education, but whose philosophical work has been drawn upon by others and applied very fruitfully to educational issues. (A volume edited by Amelie Rorty contains essays on the education-related thought, or relevance, of many historically-important philosophers; significantly the essays are almost entirely written by philosophers rather than by members of the philosophy of education community. This is both their strength and weakness. See Rorty, 1998.)

The discussion will turn briefly to the difficulty in picturing the topography of the field that is presented by the influence of these philosophers.

As sketched earlier, the domain of education is vast, the issues it raises are almost overwhelmingly numerous and are of great complexity, and the social significance of the field is second to none. These features make the phenomena and problems of education of great interest to a wide range of socially-concerned intellectuals, who bring with them their own favored conceptual frameworks—concepts, theories and ideologies, methods of analysis and argumentation, metaphysical and other assumptions, criteria for selecting evidence that has relevance for the problems that they consider central, and the like. No wonder educational discourse has occasionally been likened to Babel, for the differences in backgrounds and assumptions means that there is much mutual incomprehension. In the midst of the melee sit the philosophers of education.

It is no surprise, then, to find that the significant intellectual and social trends of the past few centuries, together with the significant developments in philosophy, all have had an impact on the content and methods of argument in philosophy of education—Marxism, psycho-analysis, existentialism, phenomenology, positivism, post-modernism, pragmatism, neo-liberalism, the several waves of feminism, analytic philosophy in both its ordinary language and more formal guises, are merely the tip of the iceberg. It is revealing to note some of the names that were heavily-cited in a pair of recent authoritative handbooks in the field (according to the indices of the two volumes, and in alphabetical order): Adorno, Aristotle, Derrida, Descartes, Dewey, Habermas, Hegel, Horkheimer, Kant, Locke, Lyotard, Marx, Mill, Nietzsche, Plato, Rawls, Richard Rorty, Rousseau, and Wittgenstein (Curren 2003; Blake, Smeyers, Smith, and Standish 2003). Although this list conveys something of the diversity of the field, it fails to do it complete justice, for the influence of feminist philosophers is not adequately represented.

No one individual can have mastered work done by such a range of figures, representing as they do a number of quite different frameworks or approaches; and relatedly no one person stands as emblematic of the entire field of philosophy of education, and no one type of philosophical writing serves as the norm, either. At professional meetings, peace often reigns because the adherents of the different schools go their separate ways; but occasionally there are (intellectually) violent clashes, rivaling the tumult that greeted Derrida's nomination for an honorary degree at Cambridge in 1992. It is sobering to reflect that only a few decades have passed since practitioners of analytic philosophy of education had to meet in individual hotel rooms, late at night, at annual meetings of the Philosophy of Education Society in the USA, because phenomenologists and others barred their access to the conference programs; their path to liberation was marked by discord until, eventually, the compromise of “live and let live” was worked out (Kaminsky, 1996). Of course, the situation has hardly been better in the home discipline; an essay in Time magazine in 1966 on the state of the discipline of philosophy reported that adherents of the major philosophical schools “don't even understand one another”, and added that as a result “philosophy today is bitterly segregated. Most of the major philosophy departments and scholarly journals are the exclusive property of one sect or another” ( Time , reprinted in Lucas, 1969, 32). Traditionally there has been a time-lag for developments in philosophy to migrate over into philosophy of education, but in this respect at least the two fields have been on a par.

Inevitably, however, traces of discord remain, and some groups still feel disenfranchised, but they are not quite the same groups as a few decades ago—for new intellectual paradigms have come into existence, and their adherents are struggling to have their voices heard; and clearly it is the case that—reflecting the situation in 1966—many analytically-trained philosophers of education find postmodern writings incomprehensible while scholars in the latter tradition are frequently dismissive if not contemptuous of work done by the former group. In effect, then, the passage of time has made the field more—and not less—diffuse. All this is evident in a volume published in 1995 in which the editor attempted to break-down borders by initiating dialogue between scholars with different approaches to philosophy of education; her introductory remarks are revealing:

Philosophers of education reflecting on the parameters of our field are faced not only with such perplexing and disruptive questions as: What counts as Philosophy of Education and why?; but also Who counts as a philosopher of education and why?; and What need is there for Philosophy of Education in a postmodern context? Embedded in these queries we find no less provocative ones: What knowledge, if any, can or should be privileged and why?; and Who is in a position to privilege particular discursive practices over others and why? Although such questions are disruptive, they offer the opportunity to take a fresh look at the nature and purposes of our work and, as we do, to expand the number and kinds of voices participating in the conversation. (Kohli, 1995, xiv).

There is an inward-looking tone to the questions posed here: Philosophy of education should focus upon itself, upon its own contents, methods, and practitioners. And of course there is nothing new about this; for one thing, almost forty years ago a collection of readings—with several score of entries—was published under the title What is Philosophy of Education? (Lucas, 1969). It is worth noting, too, that the same attitude is not unknown in philosophy; Simmel is reputed to have said a century or so ago that philosophy is its own first problem.

Having described the general topography of the field of philosophy of education, the focus can change to pockets of activity where from the perspective of this author interesting philosophical work is being, or has been, done—and sometimes this work has been influential in the worlds of educational policy or practice. It is appropriate to start with a discussion of the rise and partial decline—but lasting influence of—analytic philosophy of education This approach (often called “APE” by both admirers and detractors) dominated the field in the English-speaking world for several decades after the second world war, and its eventual fate throws light on the current intellectual climate.

2. Analytic philosophy of education, and its influence

Conceptual analysis, careful assessment of arguments, the rooting out of ambiguity, the drawing of clarifying distinctions—which make up part at least of the philosophical analysis package—have been respected activities within philosophy from the dawn of the field. But traditionally they stood alongside other philosophical activities; in the Republic , for example, Plato was sometimes analytic, at other times normative, and on occasion speculative/metaphysical. No doubt it somewhat over-simplifies the complex path of intellectual history to suggest that what happened in the twentieth century—early on, in the home discipline itself, and with a lag of a decade or more in philosophy of education—is that philosophical analysis came to be viewed by some scholars as being the major philosophical activity (or set of activities), or even as being the only viable or reputable activity (for metaphysics was judged to be literally vacuous, and normative philosophy was viewed as being unable to provide compelling warrants for whatever moral and ethical positions were being advocated).

So, although analytic elements in philosophy of education can be located throughout intellectual history back to the ancient world, the pioneering work in the modern period entirely in an analytic mode was the short monograph by C.D. Hardie, Truth and Fallacy in Educational Theory (1941; reissued in 1962). In his Introduction, Hardie (who had studied with C.D. Broad and I.A. Richards) made it clear that he was putting all his eggs into the ordinary-language-analysis basket:

The Cambridge analytical school, led by Moore, Broad and Wittgenstein, has attempted so to analyse propositions that it will always be apparent whether the disagreement between philosophers is one concerning matters of fact, or is one concerning the use of words, or is, as is frequently the case, a purely emotive one. It is time, I think, that a similar attitude became common in the field of educational theory. (Hardie, 1962, xix)

The first object of his analytic scrutiny in the book was the view that “a child should be educated according to Nature”; he teased apart and critiqued various things that writers through the ages could possibly have meant by this, and very little remained standing by the end of the chapter. Then some basic ideas of Herbart and Dewey were subjected to similar treatment. Hardie's hard-nosed approach can be illustrated by the following: One thing that educationists mean by “education according to Nature” (later he turns to other things they might mean) is that “the teacher should thus act like a gardener” who fosters natural growth of his plants and avoids doing anything “unnatural”(Hardie, 1962, 3). He continues:

The crucial question for such a view of education is how far does this analogy hold? There is no doubt that there is some analogy between the laws governing the physical development of the child and the laws governing the development of a plant, and hence there is some justification for the view if applied to physical education. But the educationists who hold this view are not generally very much concerned with physical education, and the view is certainly false if applied to mental education. For some of the laws that govern the mental changes which take place in a child are the laws of learning …. [which] have no analogy at all with the laws which govern the interaction between a seed and its environment. (Hardie, 1962, 4)

About a decade after the end of the Second World War the floodgates opened and a stream of work in the analytic mode appeared; the following is merely a sample. D.J. O'Connor published An Introduction to Philosophy of Education (1957) in which, among other things, he argued that the word “theory” as it is used in educational contexts is merely a courtesy title, for educational theories are nothing like what bear this title in the natural sciences; Israel Scheffler, who became the paramount philosopher of education in North America, produced a number of important works including The Language of Education (1960), that contained clarifying and influential analyses of definitions (he distinguished reportive, stipulative, and programmatic types) and the logic of slogans (often these are literally meaningless, and should be seen as truncated arguments); Smith and Ennis edited the volume Language and Concepts in Education (1961); and R.D. Archambault edited Philosophical Analysis and Education (1965), consisting of essays by a number of British writers who were becoming prominent—most notably R.S. Peters (whose status in Britain paralleled that of Scheffler in the USA), Paul Hirst, and John Wilson. Topics covered in the Archambault volume were typical of those that became the “bread and butter” of analytic philosophy of education throughout the English-speaking world—education as a process of initiation, liberal education, the nature of knowledge, types of teaching, and instruction versus indoctrination.

Among the most influential products of APE was the analysis developed by Hirst and Peters (1970), and Peters (1973), of the concept of education itself. Using as a touchstone “normal English usage”, it was concluded that a person who has been educated (rather than instructed or indoctrinated) has been (i) changed for the better; (ii) this change has involved the acquisition of knowledge and intellectual skills, and the development of understanding; and (iii) the person has come to care for, or be committed to, the domains of knowledge and skill into which he or she has been initiated. The method used by Hirst and Peters comes across clearly in their handling of the analogy with the concept of “reform”, one they sometimes drew upon for expository purposes. A criminal who has been reformed has changed for the better, and has developed a commitment to the new mode of life (if one or other of these conditions does not hold, a speaker of standard English would not say the criminal has been reformed). Clearly the analogy with reform breaks down with respect to the knowledge and understanding conditions. Elsewhere Peters developed the fruitful notion of “education as initiation”.

The concept of indoctrination was also of great interest to analytic philosophers of education, for—it was argued—getting clear about precisely what constitutes indoctrination also would serve to clarify the border that demarcates it from acceptable educational processes. Unfortunately, ordinary language analysis did not lead to unanimity of opinion about where this border was located, and rival analyses of the concept were put forward (Snook, 1972). Thus, whether or not an instructional episode was a case of indoctrination was determined by: the content that had been taught; or by the intention of the instructor; or by the methods of instruction that had been used; or by the outcomes of the instruction; or, of course, by some combination of these. Adherents of the different analyses used the same general type of argument to make their case, namely, appeal to normal and aberrant usage. Two examples will be sufficient to make the point: (i) The first criterion mentioned above—the nature of the content being imparted—was supported by an argument that ran roughly as follows: “If some students have learned, as factual, some material that is patently incorrect (like ‘The capital city of Canada is Washington D.C.’), then they must have been indoctrinated. This conclusion is reinforced by the consideration that we would never say students must have been indoctrinated if they believe an item that is correct!” However, both portions of this argument have been challenged. (ii) The method criterion—how the knowledge was imparted to the students—usually was supported by an argument that, while different, clearly paralleled the previous one in its logic. It ran roughly like this: “We never would say that students had been indoctrinated by their teacher if he or she had fostered open inquiry and discussion, encouraged exploration in the library and on the net, allowed students to work in collaborative groups, and so on. However, if the teacher did not allow independent inquiry, quashed classroom questions, suppressed dissenting opinions, relied heavily on rewards and punishments, used repetition and fostered rote memorization, and so on, then it is likely we would say the students were being indoctrinated”. (The deeper issue in this second example is that the first method of teaching allows room for the operation of the learners' rationality, while the second method does not. Siegel, 1988, stresses this in his discussion of indoctrination.)

After a period of dominance, for a number of important reasons the influence of APE went into decline. First, there were growing criticisms that the work of analytic philosophers of education had become focused upon minutiae and in the main was bereft of practical import; I can offer as illustration a presidential address at a US Philosophy of Education Society annual meeting that was an hour-long discourse on the various meanings of the expression “I have a toothache”. (It is worth noting that the 1966 article in Time , cited earlier, had put forward the same criticism of mainstream philosophy.) Second, in the early 1970's radical students in Britain accused the brand of linguistic analysis practiced by R.S. Peters of conservatism, and of tacitly giving support to “traditional values”—they raised the issue of whose English usage was being analyzed?

Third, criticisms of language analysis in mainstream philosophy had been mounting for some time, and finally after a lag of many years were reaching the attention of philosophers of education. There even had been a surprising degree of interest in this arcane topic on the part of the general reading public in the UK as early as 1959, when Gilbert Ryle, editor of the journal Mind , refused to commission a review of Ernest Gellner's Words and Things (1959)—a detailed and quite acerbic critique of Wittgenstein's philosophy and its espousal of ordinary language analysis. (Ryle argued that Gellner's book was too insulting, a view that drew Bertrand Russell into the fray on Gellner's side—in the daily press, no less; Russell produced examples of insulting remarks drawn from the work of great philosophers of the past. See Mehta, 1963)

Richard Peters had been given warning that all was not well with APE at a conference in Canada in 1966; after delivering a paper on “The aims of education: A conceptual inquiry” that was based on ordinary language analysis, a philosopher in the audience (William Dray) asked Peters “ whose concepts do we analyze?” Dray went on to suggest that different people, and different groups within society, have different concepts of education. Five years before the radical students raised the same issue, Dray pointed to the possibility that what Peters had presented under the guise of a “logical analysis” was nothing but the favored usage of a certain class of persons—a class that Peters happened to identify with. (See Peters, 1973, where to the editor's credit the interaction with Dray is reprinted.)

Fourth, during the decade of the seventies when these various critiques of analytic philosophy were in the process of eroding its luster, a spate of translations from the Continent stimulated some philosophers of education in Britain and North America to set out in new directions, and to adopt a new style of writing and argumentation. Key works by Gadamer, Foucault, and Derrida appeared in English, and these were followed in 1984 by Lyotard's foundational work on The Postmodern Condition . The classic works of Heidegger and Husserl also found new admirers; and feminist philosophers of education were finding their voices—Maxine Greene published a number of pieces in the 1970s; the influential book by Nel Noddings, Caring: A Feminine Approach to Ethics and Moral Education , appeared the same year as the work by Lyotard, followed a year later by Jane Roland Martin's Reclaiming a Conversation . APE was no longer the center of interest.

By the 1980s, the rather simple if not simplistic ordinary language analysis practiced in philosophy of education, was reeling under the attack from the combination of forces sketched above, but the analytic spirit lived on in the form of rigorous work done in other specialist areas of philosophy—work that trickled out and took philosophy of education in rich new directions. Technically-oriented epistemology, philosophy of science, and even metaphysics, flourished; as did the interrelated fields of social, political and moral philosophy. John Rawls published A Theory of Justice in 1971; a decade later MacIntyre's After Virtue appeared; and in another decade or so there was a flood of work on individualism, communitarianism, democratic citizenship, inclusion, exclusion, rights of children versus rights of parents, rights of groups (such as the Amish) versus rights of the larger polity. From the early 1990s philosophers of education have contributed significantly to the debates on these and related topics—indeed, this corpus of work illustrates that good philosophy of education flows seamlessly into work being done in mainstream areas of philosophy. Illustrative examples are Creating Citizens: Political Education and Liberal Democracy , Callan (1997); The Demands of Liberal Education , Levinson (1999); Social Justice and School Choice , Brighouse (2000); and Bridging Liberalism and Multiculturalism in American Education , Reich (2002). These works stand shoulder-to-shoulder with semi-classics on the same range of topics by Gutmann, Kymlicka, Macedo, and others. An excerpt from the book by Callan nicely illustrates that the analytic spirit lives on in this body of work; the broader topic being pursued is the status of the aims of education in a pluralistic society where there can be deep fundamental disagreements:

… the distinction must be underlined between the ends that properly inform political education and the extent to which we should tolerate deviations from those ends in a world where reasonable and unreasonable pluralism are entangled and the moral costs of coercion against the unreasonable variety are often prohibitive. Our theoretical as well as our commonsense discourse do not always respect the distinction…. If some of the teachings of the Roman Catholic Church conflict with our best theory of the ends of civic education, it does not follow that we have any reason to revise our theory; but neither does it mean we have any reason to impose these ends on Catholic schools and the families that they serve. (Callan, 1997, 44)

Callan and White (2003) have given an analysis of why the topics described above have become such a focus of attention. “What has been happening in philosophy of education in recent years”, they argue, mirrors “a wider self-examination in liberal societies themselves”. World events, from the fall of communism to the spread of ethnic conflicts “have all heightened consciousness of the contingency of liberal politics”. A body of work in philosophy, from the early Rawls on, has systematically examined (and critiqued) the foundations of liberalism, and philosophy of education has been drawn into the debates. Callan and White mention communitarianism as offering perhaps “the most influential challenge” to liberalism, and they write:

The debate between liberals and communitarians is far more than a theoretical diversion for philosophers and political scientists. At stake are rival understandings of what makes human lives and the societies in which they unfold both good and just, and derivatively, competing conceptions of the education needed for individual and social betterment. (Callan and White, 2003, 95-96)

It should be appended here that it is not only “external” world events that have stimulated this body of work; events internal to a number of democratic societies also have been significant. To cite one example that is prominent in the literature in North America at least, the US Supreme Court issued a ruling ( Wisconsin v. Yoder ) in which members of the Amish sect were allowed to withdraw their children from public schools before they had reached the age of sixteen—for, it had been argued, any deeper education would endanger the existence of the group and its culture. In assessing this decision—as of course philosophers have frequently done (see, for example, Kymlicka, 1995)—a balance has to be achieved between (i) the interest of civic society in having an informed, well-educated, participatory citizenry; (ii) the interest of the Amish as a group in preserving their own culture; and (iii) the interests of the Amish children, who have a right to develop into autonomous individuals who can make reflective decisions for themselves about the nature of the life they wish to lead. These are issues that fall squarely in the domain covered by the works mentioned above.

So much work is being produced on the complex and interrelated issues just outlined, that in a different context it seemed fair for me to remark (descriptively, and not judgmentally) that a veritable cottage industry had sprung up in post-Rawlsian philosophy of education. There are, of course, other areas of activity, where interesting contributions are being made, and the discusion will next turn to a sampling of these.

3. Other areas of contemporary activity

As was stressed at the outset, and illustrated with a cursory listing of examples, the field of education is huge and contains within it a virtually inexhaustible number of issues that are of philosophical interest. To attempt comprehensive coverage of how philosophers of education have been working within this thicket would be a quixotic task for a large single volume, and is out of the question for a solitary encyclopedia entry. Nevertheless, a valiant attempt to give an overview was made in the recent A Companion to the Philosophy of Education (Curren, 2003), which contained more than six-hundred pages divided into fourty-five chapters each of which surveyed a subfield of work. The following random selection of chapter topics gives a sense of the enormous scope of the field: Sex education, special education, science education, aesthetic education, theories of teaching and learning, religious education, knowledge and truth in learning, cultivating reason, the measurement of learning, multicultural education, education and the politics of identity, education and standards of living, motivation and classroom management, feminism, critical theory, postmodernism, romanticism, purposes of universities in a fluid age, affirmative action in higher education, and professional education.

There is no non-arbitrary way to select a small number of topics for further discussion, nor can the topics that are chosen be pursued in great depth. The choice of those below has been made with an eye to filling out—and deepening—the topographical account of the field that was presented in the preceding sections. The discussion will open with a topic that was not included in the Companion , despite it being one that is of great concern across the academic educational community, and despite it being one where adherents of some of the rival schools of philosophy (and philosophy of education) have had lively exchanges.

The educational research enterprise has been criticized for a century or more by politicians, policymakers, administrators, curriculum developers, teachers, philosophers of education, and by researchers themselves—but the criticisms have been contradictory. Charges of being “too ivory tower and theory-oriented” are found alongside “too focused on practice and too atheoretical”; but particularly since publication of the book by Stokes mentioned earlier, and also in light of the views of John Dewey and William James that the function of theory is to guide intelligent practice and problem-solving, it is becoming more fashionable to hold that the “theory v. practice” dichotomy is a false one.

A similar trend can be discerned with respect to the long warfare between two rival groups of research methods—on one hand quantitative/statistical approaches to research, and on the other hand the qualitative/ethnographic family. (The choice of labels here is its not entirely risk-free, for they have been contested; furthermore the first approach is quite often associated with “experimental” studies, and the latter with “case studies”, but this is an over-simplification.) For several decades these two rival methodological camps were treated by researchers and a few philosophers of education as being rival paradigms (Kuhn's ideas, albeit in a very loose form, have been influential in the field of educational research), and the dispute between them was commonly referred-to as “the paradigm wars”. In essence the issue at stake was epistemolgical: members of the quantitative/experimental camp believed that only their methods could lead to well-warranted knowledge claims, especially about the causal factors at play in educational phenomena, and on the whole they regarded qualitative methods as lacking in rigor; on the other hand the adherents of qualitative/ethnographic approaches held that the other camp was too “positivistic” and was operating with an inadequate view of causation in human affairs—one that ignored the role of motives and reasons, possession of relevant background knowledge, awareness of cultural norms, and the like. Few if any commentators in the “paradigm wars” suggested that there was anything prohibiting the use of both approaches in the one research program—provided that if both were used, they only were used sequentially or in parallel, for they were underwritten by different epistemologies and hence could not be blended together. But recently the trend has been towards rapprochement, towards the view that the two methodological families are, in fact, compatible and are not at all like paradigms in the Kuhnian sense(s) of the term; the melding of the two approaches is often called “mixed methods research”, and it is growing in popularity. (For more detailed discussion of these “wars” see Howe, 2003, and Phillips, 2008.)

The most lively contemporary debates about education research, however, were set in motion around the turn of the millenium when the US Federal Government moved in the direction of funding only rigorously scientific educational research—the kind that could establish causal factors which could then guide the development of practically effective policies. (It was held that such a causal knowledge base was available for medical decisionmaking.) The definition of “rigorously scientific”, however, was decided by politicans and not by the research community, and it was given in terms of the use of a specific research method—the net effect being that the only research projects to receive Federal funding were those that carried out randomized controlled experiments or field trials (RFTs). It has beome common over the last decade to refer to the RFT as the “gold standard” methodology.

The National Research Council (NRC)—an arm of the U.S. National Academies of Science—issued a report, influenced by postpostivistic philosophy of science (NRC, 2002), that argued this criterion was far too narrow. Numerous essays have appeared subsequently that point out how the “gold standard” account of scientific rigor distorts the history of science, how the complex nature of the relation between evidence and policy-making has been distorted and made to appear overly simple (for instance the role of value-judgments in linking empirical findings to policy directives is often overlooked), and qualitative researchers have insisted upon the scientific nature of their work.

Nevertheless, and possibly because it tried to be balanced and supported the use of RFTs in some research contexts, the NRC report has been the subject of symposia in four journals, where it has been supported by a few and attacked from a variety of philosophical fronts: Its authors were positivists, they erroneously believed that educational inquiry could be value-neutral and that it could ignore the ways in which exercise of power constrains the research process, they misunderstood the nature of educational phenomena, they were guilty of advocating “your father's paradigm”(clearly this was not intended as a compliment). One critic with postmodernist leanings asserted that educational research should move “toward a Nietzschean sort of ‘unnatural science’ that leads to greater health by fostering ways of knowing that escape normativity”—a suggestion that evokes the reaction discussed in Section 1.3 above, namely, one of incomprehension on the part of most researchers and those philosophers of education who work within a different tradition where a “way of knowing”, in order to be a “way”, must inevitably be normative.

The final complexity in the debates over the nature of educational research is that there are some respected members of the philosophy of education community who claim, along with Carr, that “the forms of human association characteristic of educational engagement are not really apt for scientific or empirical study at all” (Carr, 2003, 54-5). His reasoning is that educational processes cannot be studied empirically because they are processes of “normative initiation”—a position that as it stands begs the question by not making clear why such processes cannot be studied empirically.

The issue of what should be taught to students at all levels of education—the issue of curriculum content—obviously is a fundamental one, and it is an extraordinarily difficult one with which to grapple. In tackling it, care needs to be taken to distinguish between education and schooling—for although education can occur in schools, so can mis-education (as Dewey pointed out), and many other things can take place there that are educationally orthogonal (such as the provision of free or subsidized lunches, or the development of social networks); and it also must be recognized that education can occur in the home, in libraries and museums, in churches and clubs, in solitary interaction with the public media, and the like.

In developing a curriculum (whether in a specific subject area, or more broadly as the whole range of offerings in an educational institution or in a system), a number of difficult decisions need to be made. Issues such as the proper ordering or sequencing of topics in the chosen subject, the time to be allocated to each topic, the lab work or excursions or projects that are appropriate for particular topics, can all be regarded as technical issues best resolved either by educationists who have a depth of experience with the target age group or by experts in the psychology of learning and the like. But there are deeper issues, ones concerning the validity of the justifications that have been given for including particular subjects or topics in the offerings of formal educational institutions. (Why is evolution included, or excluded, as a topic within the standard high school subject Biology? Why is Driver Education part of the high school curriculum, and methods of birth control usually not—even though sex has an impact on the life of teenagers that at least is comparable to the impact of car-driving? Is the justification that is given for teaching Economics in some schools coherent and convincing? Does the justification for not including the Holocaust or the phenomenon of wartime atrocities in the curriculum in some countries stand up to critical scrutiny?)

The different justifications for particular items of curriculum content that have been put forward by philosophers and others since Plato's brilliant pioneering efforts all draw upon, explicitly or implicitly, the positions that the respective theorists hold about at least three sets of issues. First, what are the aims and/or functions of education (aims and functions are not necessarily the same), or alternatively, what constitutes the good life and human flourishing. These two formulations are related, for presumably our educational institutions should aim to equip individuals to pursue this good life. Thus, for example, if our view of human flourishing includes the capacity to act rationally and/or autonomously, then the case can be made that educational institutions—and their curricula—should aim to prepare, or help to prepare, autonomous individuals. How this is to be done, of course, is not immediately obvious, and much philosophical ink has been spilled on the matter. One influential line of argument was developed by Paul Hirst, who argued that knowledge is essential for developing a conception of the good life, and then for pursuing it; and because logical analysis shows—he argued—that there are seven basic forms of knowledge, the case can be made that the function of the curriculum is to introduce students to each of these forms. Luckily for Hirst, the typical British high school day was made up of seven instructional periods. (Hirst, 1965; for a critique see Phillips, 1987, ch.11.)

Second, is it justifiable to treat the curriculum of an educational institution as vehicle for furthering the socio-political interests and goals of a ruler or ruling class; and relatedly, is it justifiable to design the curriculum so that it serves as a medium of control or of social engineering? In the closing decades of the twentieth century there were numerous discussions of curriculum theory, particularly from Marxist and postmodern perspectives, that offered the sobering analysis that in many educational systems, including those in Western democracies, the curriculum did indeed reflect, and serve, the interests of the ruling class. Michael Apple is typical:

… the knowledge that now gets into schools is already a choice from a much larger universe of possible social knowledge and principles. It is a form of cultural capital that comes from somewhere, that often reflects the perspectives and beliefs of powerful segments of our social collectivity. In its very production and dissemination as a public and economic commodity—as books, films, materials, and so forth—it is repeatedly filtered through ideological and economic commitments. Social and economic values, hence, are already embedded in the design of the institutions we work in, in the ‘formal corpus of school knowledge’ we preserve in our curricula….(Apple, 1990, 8-9)

Third, should educational programs at the elementary and secondary levels be made up of a number of disparate offerings, so that individuals with different interests and abilities and affinities for learning can pursue curricula that are suitable? Or should every student pursue the same curriculum as far as each is able—a curriculum, it should be noted, that in past cases nearly always was based on the needs or interests of those students who were academically inclined or were destined for elite social roles. Mortimer Adler and others in the late twentieth century (who arguably were following Plato's lead in the Republic ), sometimes used the aphorism “the best education for the best is the best education for all”.

The thinking here can be explicated in terms of the analogy of an out-of-control virulent disease, for which there is only one type of medicine available; taking a large dose of this medicine is extremely beneficial, and the hope is that taking only a little—while less effective—is better than taking none at all! Medically, this probably is dubious, while the educational version—forcing students to work, until they exit the system, on topics that do not interest them and for which they have no facility or motivation—has even less merit. (For a critique of Adler and his Paideia Proposal , see Noddings, 2007.) It is interesting to compare the modern “one curriculum track for all” position with Plato's system outlined in the Republic , according to which all students—and importantly this included girls—set out on the same course of study. Over time, as they moved up the educational ladder it would become obvious that some had reached the limit imposed upon them by nature, and they would be directed off into appropriate social roles in which they would find fulfillment, for their abilities would match the demands of these roles. Those who continued on with their education would eventually be able to contemplate the metaphysical realm of the “forms”, thanks to their advanced training in mathematics and philosophy. Having seen the form of the Good, they would be eligible after a period of practical experience to become members of the ruling class of Guardians.

Plato's educational scheme was guided, presumably, by the understanding he thought he had achieved of the transcendental realm of fixed “forms”. John Dewey, ever a strong critic of positions that were not naturalistic, or that incorporated a priori premises, commented as follows:

Plato's starting point is that the organization of society depends ultimately upon knowledge of the end of existence. If we do not know its end, we shall be at the mercy of accident and caprice…. And only those who have rightly trained minds will be able to recognize the end, and ordering principle of things. (Dewey, 1916, 102-3)

Furthermore, as Dewey again put it, Plato “had no perception of the uniqueness of individuals…. they fall by nature into classes”, which masks the “infinite diversity of active tendencies” which individuals harbor (104). In addition, Plato tended to talk of learning using the passive language of seeing, which has shaped our discourse down to the present (witness “Now I see it!” when a difficult point has become clear).

In contrast, for Dewey each individual was an organism situated in a biological and social environment in which problems were constantly emerging, forcing the individual to reflect and act, and learn. Dewey, following William James, held that knowledge arises from reflection upon our actions; and the worth of a putative item of knowledge is directly correlated with the problem-solving success of the actions performed under its guidance. Thus Dewey, sharply disagreeing with Plato, regarded knowing as an active rather than a passive affair—a strong theme in his writings is his opposition to what is sometimes called “the spectator theory of knowledge”. All this is made clear enough in a passage containing only a thinly-veiled allusion to Plato's famous analogy of the prisoners in the cave whose eyes are turned to the light by education:

In schools, those under instruction are too customarily looked upon as acquiring knowledge as theoretical spectators, minds which appropriate knowledge by direct energy of intellect. The very word pupil has almost come to mean one who is engaged not in having fruitful experiences but in absorbing knowledge directly. Something which is called mind or consciousness is severed from the physical organs of activity. (164)

This passage also illuminates a passage that many have found puzzling: “philosophy is the theory of education” (387). For in the sentences above it is easy to see the tight link between Dewey's epistemology and his views on education—his anti-spectator epistemology morphs directly into advocacy for anti-spectator learning by students in school—students learn by being active inquirers. Over the past few decades this view of learning has inspired a major tradition of research by educational psychologists, and related theory-development (the “situated cognition” framework); and these bodies of work have in turn led to innovative efforts in curriculum development. (For a discussion of these, see Phillips, 2003.)

The final important difference with Plato is that, for Dewey, each student is an individual who blazes his or her unique trail of growth; the teacher has the task of guiding and facilitating this growth, without imposing a fixed end upon the process. Dewey sometimes uses the term “curriculum” to mean “the funded wisdom of the human race”, the point being that over the course of human history an enormous stock of knowledge and skills has accumulated and the teacher has the task of helping the student to make contact with this repertoire—but helping by facilitating rather than by imposing. (All this, of course, has been the subject of intense discussion among philosophers of education: Does growth imply a direction? Is growth always good—can't a plant end up misshapen, and can't a child develop to become bad? Is Dewey some type of perfectionist? Is his philosophy too vague to offer worthwhile educational guidance? Isn't it possible for a “Deweyan” student to end up without enough relevant knowledge and skills to be able to make a living in the modern world?)

Dewey's work was of central importance for the American progressive education movement in its formative years, although there was a fair degree of misunderstanding of his ideas as progressives interpreted his often extremely dense prose to be saying what they personally happened to believe. Nevertheless, Dewey became the “poster child” or the “house philosopher” of progressive education, and if he didn't make it onto many actual posters he certainly made it onto a postage stamp.

His popularity, however, sharply declined after the Soviets launched Sputnik, for Dewey and progressive education were blamed for the USA losing the race into space (illustrating the point about scapegoating made at the start of this essay). But he did not remain in disgrace for long; and for some time has been the focus of renewed interest—although it is still noticeable that commentators interpret Dewey to be holding views that mirror their own positions or interests. And interestingly, there now is slightly more interest in Dewey on the part of philosophers of education in the UK than there was in earlier years, and there is growing interest by philosophers from the Continent (see, for example, Biesta and Burbules, 2003).

To be a poster child for progressivism, however, is not to be the parent. Rather than to Dewey, that honor must go to Jean-Jacques Rousseau, and to his educational novel written in soaring prose, Emile (1762). Starting with the premise that “God makes all things good; man meddles with them and they become evil” (Rousseau, 1955, 5), Rousseau held that contemporary man has been misshapen by his education; the “crushing force” of social conventions has stifled the “Nature within him”. The remedy adopted in the novel is for the young Emile to be taken to his family estate in the country where, away from the corrupting influence of society, and under the watchful eye of his tutor, “everything should … be brought into harmony with these natural tendencies”. (This idea of education according to nature, it will be recalled, was the object of Hardie's analytic attention almost two centuries later.)

Out in the countryside, rather than having a set curriculum that he is forced to follow, Emile learns when some natural stimulus or innate interest motivates him—and under these conditions learning comes easily. He is allowed to suffer the natural consequences of his actions (if he breaks a window, he gets cold; if he takes the gardener's property, the gardener will no longer do him favors), and experiences such as these lead to the development of his moral system. Although Rousseau never intended these educational details to be taken literally as a blueprint (he saw himself as developing and illustrating the basic principles), over the ages there have been attempts to implement them, one being the famous British “free school”, A.S. Neill's Summerhill. (It is worth noting that Neill claimed not to have read Rousseau; but he was working in a milieu in which Rousseau's ideas were well-known—intellectual influence can follow a less than direct path.) Furthermore, over the ages these principles also have proven to be fertile soil for philosophers of education to till.

Even more fertile ground for comment, in recent years, has been Rousseau's proposal for the education of girls, developed in a section of the novel (Book V) that bears the name of the young woman who is destined to be Emile's soul-mate, Sophy. The puzzle has been why Rousseau—who had been so far-sighted in his discussion of Emile's education—was so hide-bound if not retrograde in his thinking about her education. One short quotation is sufficient to illustrate the problem: “If woman is made to please and to be in subjection to man, she ought to make herself pleasing in his eyes and not provoke him …her strength is in her charms” (324).

The educational principles developed by Rousseau and Dewey, and numerous educational theorists and philosophers in the interregnum, are alive and well in the twenty-first century. Of particular contemporary interest is the evolution that has occurred of the progressive idea that each student is an active learner who is pursuing his or her own individual educational path. By incorporating elements of the classical empiricist epistemology of John Locke, this progressive principle has become transformed into the extremely popular position known as constructivism, according to which each student in a classroom constructs his or her own individual body of understandings even when all in the group are given what appears to be the same stimulus or educational experience. (A consequence of this is that a classroom of thirty students will have thirty individually-constructed, and possibly different, bodies of “knowledge”, in addition to that of the teacher!) There is also a solipsistic element here, for constructivists also believe that none of us—teachers included—can directly access the bodies of understandings of anyone else; each of us is imprisoned in a world of our own making. It is an understatement to say that this poses great difficulties for the teacher. The education journals of the past two decades contain many thousands of references to discussions of this position, which elsewhere I claimed has become a type of educational “secular religion”; for reasons that are hard to discern it is particularly influential in mathematics and science education. (For a discussion of the underlying philosophical ideas in constructivism, and for an account of some of its varieties, see the essays in Phillips, ed., 2000.)

As stressed earlier, it is impossible to do justice the whole field of philosophy of education in a single encyclopedia entry. Different countries around the world—France, Germany, the Netherlands, Japan, to mention only a few—have their own intellectual traditions, and their own ways of institutionalizing philosophy of education into the academic universe, and no discussion of any of this appears in the present essay. But even in the Anglo-American world, there is such a diversity of approaches to the discipline that any author attempting to produce a synoptic account will quickly run into the borders of his or her areas of competence. Clearly this has happened in the present case.

Fortunately, in the last twenty years or so resources have become available that significantly alleviate these problems. There has been a flood of encyclopedia entries, commenting on the field as a whole or on many specific topics not well-covered in the present essay (see, as a sample, Burbules, 1994; Chambliss, 1996; Phillips, 1985; Siegel, 2007; Smeyers, 1994); two large volumes—a “Guide” (Blake, Smeyers, Smith and Standish, 2003) and a “Companion” (Curren, 2003)—have been produced by Blackwell in their well-known philosophy series; and the same publisher recently released an anthology, with 60 papers considered to be important in the field, and which also are representative of the range of work that is being done (Curren, 2007). Several encyclopedias of philosophy of education have been published or are in the works (for example, Chambliss, 1996; Siegel, 2008); there is a dictionary of key concepts in the field (Winch and Gingell, 1999), and a good textbook or two (see Noddings, 2007); in addition there are numerous volumes both of reprinted selections and of specially commissioned essays on specific topics, some of which were given short shrift in the present work (for another sampling see A. Rorty, 1998; Smeyers and Marshall, 1995; Stone, 1994); and several international journals appear to be flourishing— Educational Philosophy and Theory , Educational Theory , Journal of Philosophy of Education , Studies in Philosophy and Education , Theory and Research in Education . Thus there is enough material available to keep the interested reader busy, and to provide alternative assessments to the ones presented in this present essay.

• Apple, M., 1990, Ideology and Curriculum , New York: Routledge, 2 nd . Editon.
• Archambault, R., (ed.), 1965, Philosophical Analysis and Education , London: Routledge.
• Biesta, G., and Burbules, N., 2003, Pragmatism and Educational Research , Lanham, MD: Rowman & Littlefield.
• Blake, N., Smeyers, P., Smith, R., and Standish, P., (eds.), 2003, The Blackwell Guide to the Philosophy of Education , Oxford: Blackwell.
• Brighouse, H., 2000, Social Justice and School Choice , Oxford: Oxford University Press.
• Burbules, N., 1994, “Marxism and Educational Thought”, in The International Encyclopedia of Education , (Volume 6), T. Husen and N. Postlethwaite (eds.), Oxford: Pergamon, 2 nd . Edition, pp. 3617-22.
• Callan, E., 1997, Creating Citizens: Political Education and Liberal Democracy , Oxford: Clarendon Press, Oxford.
• Callan, E., and White, J., 2003, “Liberalism and Communitarianism”, in The Blackwell Guide to the Philosophy of Education , N. Blake, P. Smeyers, R. Smith and P. Standish (eds.), Oxford: Blackwell, pp.95-109.
• Carr, D., 2003, Making Sense of Education: An Introduction to the Philosophy and Theory of Education and Teaching , London: RoutledgeFalmer.
• Chambliss, J., 1996, “History of Philosophy of Education”, in Philosophy of Education: An Encyclopedia , J. Chambliss (ed.), New York: Garland, pp.461-72.
• Cleverley, J., and Phillips, D.C., 1986, Visions of Childhood , New York: Teachers College Press.
• Curren, R., (ed.), 2003, A Companion to the Philosophy of Education , Oxford: Blackwell.
• Curren, R., (ed.), 2007, Philosophy of Education: An Anthology , Oxford: Blackwell.
• Dewey, J., 1916, Democracy and Education: An Introduction to the Philosophy of Education , New York: Macmillan.
• Gellner, E., 1959, Words and Things , London: Gollancz.
• Hardie, C., 1962, Truth and Fallacy in Educational Theory , New York: Teachers College Bureau of Publications.
• Hirst, P., 1965, “Liberal Education and the Nature of Knowledge”, in Philosophical Analysis and Education , R. Archambault, (ed.), London: Routledge, pp. 113-138.
• Hirst, P., and Peters, R., 1970, The Logic of Education , London: Routledge.
• Howe, K., 2003, Closing Methodological Divides: Toward Democratic Educational Research . Dordrecht: Kluwer.
• Kaminsky, J., 1996, “Philosophy of Education: Professional Organizations In”, in Philosophy of Education: An Encyclopedia , J. Chambliss, (ed.), New York: Garland, pp. 475-79.
• Kohli, W., (ed.), 1995, Critical Conversations in Philosophy of Education , New York: Routledge.
• Kymlicka, W., 1995, Multicultural Citizenship , Oxford: Clarendon Press, Oxford.
• Levinson, M., 1999, The Demands of Liberal Education , Oxford: Oxford University Press.
• Lucas, C., (ed.), 1969, What is Philosophy of Education? London: Macmillan.
• Martin, J., 1985, Reclaiming a Conversation , New Haven, Conn.: Yale University Press.
• Mehta, V., 1963, Fly and the Fly-Bottle : London: Weidenfeld and Nicolson.
• Murphy, M., (ed.), 2006, The History and Philosophy of Education: Voices of Educational Pioneers , New Jersey: Pearson.
• Noddings, N., 1984, Caring: A Feminine Approach to Ethics and Moral Education , Berkeley: University of California Press.
• –––, 2007, Philosophy of Education , Boulder, CO: Westview, 2 nd . Edition.
• National Research Council (NRC), 2002, Scientific Research in Education , Washington, DC: National Academies Press.
• O'Connor, D., 1957, An Introduction to Philosophy of Education , London: Routledge.
• Peters, R., (ed.), 1973, The Philosophy of Education , Oxford: Oxford University Press.
• Phillips, D.C., 1985, “Philosophy of Education”, in International Encyclopedia of Education, T. Husen and N. Postletwaite, (eds.), pp.3859-3877.
• –––, 1987, Philosophy, Science, and Social Inquiry , Oxford: Pergamon.
• –––, (ed.), 2000, Constructivism in Education: Opinions and Second Opinions on Controversial Issues , (Series: 99 th . Yearbook of the National Society for the Study of Education), Chicago: University of Chicago Press.
• –––, 2003, “Theories of Teaching and Learning”, in A Companion to the Philosophy of Education , R. Curren, (ed.), Oxford: Blackwell, pp. 232-245.
• –––, 2008, “Empirical Educational Research: Charting Philosophical Disagreements in an Undisciplined Field”, in The Oxford Handbook of Philosophy of Education , H. Siegel (ed.), Oxford: Oxford University Press, in press.
• Reich, R., 2002, Bridging Liberalism and Multiculturalism in American Education , Chicago: University of Chicago Press.
• Rorty, A., (ed.), 1998, Philosophers on Education: New Historical Perspectives , New York: Routledge.
• Rousseau, J-J., 1955, Emile , B. Foxley, (tr.), London: Dent/Everyman.
• Scheffler, I., 1960, The Language of Education , Illinois: Thomas.
• Siegel, H., 1988, Educating Reason: rationality, Critical Thinking, and Education , New York: Routledge.
• –––, 2007, “Philosophy of Education”, in Britannica Online Encyclopedia , [ Available online ].
• –––, (ed.), 2008, The Oxford Handbook of Philosophy of Education , Oxford: Oxford University Press, in press.
• Smeyers, P., 1994, “Philosophy of Education: Western European Perspectives”, in The International Encyclopedia of Education , (Volume 8), T. Husen and N. Postlethwaite, (eds.), Oxford: Pergamon, 2 nd . Edition, pp. 4456-61.
• Smeyers, P., and Marshall, J., (eds.), 1995, Philosophy and Education: Accepting Wittgenstein's Challenge , Dordrecht: Kluwer.
• Smith, B., and Ennis, R., (eds.), 1961, Language and Concepts in Education , Chicago: Rand McNally.
• Snook, I., 1972, Indoctrination and Education , London: Routledge.
• Stokes, D., 1997, Pasteur's Quadrant: Basic Science and Technological Innovation , Washington, DC: Brookings.
• Stone, L., (ed.), 1994, The Education Feminism Reader , New York: Routledge.
• Ulich, R., 1954, Three Thousand Years of Educational Wisdom , Cambridge, MA: Harvard University Press, Revised Ed.
• Winch, C., and Gingell, J., 1999, Key Concepts in the Philosophy of Education , London: Routledge.
• PES (Philosophy of Education Society, North America)
• PESA (Philosophy of Education Society of Australasia)
• PESGB (Philosophy of Education Society of Great Britain)
• INPE (International Network of Philosophers of Education)
• UNESCO/International Bureau of Education: Thinkers on Education

autonomy: personal | -->Dewey, John --> | feminist (interventions): ethics | feminist (interventions): liberal feminism | feminist (interventions): political philosophy | -->feminist (topics): perspectives on autonomy --> | feminist (topics): perspectives on disability | Foucault, Michel | Gadamer, Hans-Georg | liberalism | Locke, John | -->Lyotard, Jean François --> | -->ordinary language --> | Plato | postmodernism | Rawls, John | rights: of children | -->Rousseau, Jean Jacques -->

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Theories of Teaching in Language Teaching

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Tomas Yambi

Before the late nineteenth century, second-language instruction was served by the so-called Classical Method of teaching Latin and Greek. Lessons were based on mental-aerobics exercises—repetition drills and out-of-context vocabulary drills as well as lots of reading and translations of ancient texts (Richards & Rodgers 1986). For them, languages were not being taught primarily to learn oral/aural communication, but to learn for the sake of reading proficiency. Theories of second-language acquisition didn’t start to pop up until the instructional objective became oral competence. Since the 1940s, with the advent of oral competence, the definitive solution to successful ESL instruction has been discovered and rediscovered. Some second-language theories and methodologies seemed to have its high position and then others emerged challenging the previous (Richards & Rodgers 1986). The language teacher usually depends on the research done by linguists, educationalists, psycho-linguists and socio-linguists. These theories, which eventually lead to methods, help the teacher to create techniques to teach a foreign language in the classroom effectively. Thus language theories guide a teacher to select and follow an approach to the teaching of any new language. It will therefore be argued that there are links between learning theories and the various existing methodologies. To accomplish this end, the paper is structured into four main parts: the first part presents a brief history of Language teaching; in the second part four key terms namely: theory, method, procedure and technique are contrasted; in the third part a Critical review of the three most influential learning theories is displayed; and in the last part eight teaching methods are presented and related to one of the three theories foremost mentioned.

dafina begaj

I t is to be noted that language learning/teaching as a Methodological problem knew a considerable amounts of research and theorizing to reach most influential methods and approach of teaching a foreign language, and in my paper I will try to deal with one of those methods, which is the Audio-lingual Method or the "Army Method". One purpose of this paper is to provide information and simultaneously to examine the effectiveness of the "Army Method" in the Moroccan schools, where the opportunity of speak and practise English are limited in the classroom. It is worthy mentioning that we will learn about this method by entering a beginning level classroom (1st year of high school), where it is being practised. In order to give an overview about the Audio-lingual Method I will divide this monograph into two major parts. To achieve this purpose the first part will be about the theoretical view of the method, and it will be consisted the history of language teaching methodologies and I will give a brief definition of the Audiolingualism and its origin. To sum this part up, I am going to shed light on the patterns of classroom interaction or relationship that concern the teacher and student as well. Part two will be concerned with the observation I will take from the classroom. Then I shall try to deal with applying the principles on the experience. After I have identified the principles I will analyse the methods techniques as well as I will attempt to evaluate the applicability of Audio-lingual Method in Moroccan schools from what I observed so far. In short, this humble work will divide into two major parts the theoretical and practical part. This later is important since it is needed for considering some raising questions, such as what should be the goal of language instruction? Is this method effective in reaching it? What is the best means of evaluation to see if it has been reaching it? And what is the goal of teacher who uses the method?

Marian Fica

Sahana Giri

Puya Navidi

Foreign Language Annals

Carol Hosenfeld

ALSAYED MAHMOUD

ibn eljazwi

To teach grammar or not. To focus on form, meaning or combine them together. To immerse learners in the environment of the target language in order to acquire it, or they should learn first and then communicate to acquire other language components. And so on.According to (DeKeyser 1997, Ellis 1997, MacWinning 2004, Rutherford and Sharwood 1988), there is a non-stop research and arguments amongst scholars of(FL) on a variety of differences between language acquisition and learning, knowledge should be presented explicitly or implicitly, focus on form or meaning and the function of skills and knowledge. All these and many others are controversial issues in the field of language teaching and learning that have been under research for decades and perhaps some for centuries. These issues have undergone and still under research by large number of pedagogical experts.Those scholars have been trailing and searching these issues for such a long time in order to support methodologists and teachers with ideal theoretical background beyond different methods of teaching. They have also been trying to find models and approaches that are effective for the teaching of (FL). To find such practical effective approaches of teaching, theoreticians; in addition to the psychological and linguistic features, need to account for personal, contextual and environmental factors affecting the learning of FL. With regard to what has been mentioned previously about the factors, that need to be considered when choosing or inventing a suitable teaching approach, specifically the environmental and internal ones, this essay focuses on some of the concepts of the cognitive linguistics (Johnson, 2008:98). The essay discusses whether teaching should be form-orientated, meaning-orientated or both of them combined with reference to an article by Montgomery and Eisnestien (1985) discussed in Johnson (2008:107). The discussion is heldwith regard to the cognitive linguistics by (Skehan, 1998, Johnson, 1996, and McLaughlin, 1987). Johnson (2008:98) suggests that cognitive linguistics sees language and its learning linked to psychological or cognitive operations. The approaches of form-orientated and focus-orientated can be discussed under the concepts of declarative and procedural knowledge. They are also affected by other concepts like automaisation, and the negligence of any of these concepts could lead to fossilisation. All these concepts are discussed later in some detail with linkage to different teaching methods andthen their teaching implications will be illustrated at some point at the end of the paper.

Sarah Wulandari

Anas Raheel

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Freudian’s Concept of Education Essay

Introduction, reference list.

Freud’s assertion that psychology is an impossible profession is contradictory and needs to be analyzed. Freud clearly points to the repressive function of educational mechanisms, and thus argues that the child cannot be taught, it can only be forced. Obviously, education means social constraint that the child must impose on himself in order to better maneuver within society (Freud, 1991). Thus, the role of the teacher is actually not to give new knowledge, but to prohibit or eradicate the more uncontrolled activity of the child (Freud, 1969). However, the connection of psychoanalysis and the learning process is still potentially possible, at least through the inclusion of Freudian theories in the preparation of educational events.

One might assume that the child is not capable of taking in Freud’s theories and somehow translating them into reality. This does not change the fact that such a psychoanalytic mechanism should be tried on by the teacher in such a way that they understand the possible psychological implications of their own activities (Hook & Watts, 2009). The psychoanalysis of an educational specialist can be a very important step towards a balanced educational process in which there will be no place, for example, for repressed aspirations or desires that are forced out on children by a teacher.

Post-Freudian educational theorists point out that psychoanalysis, like the process of education, must potentially serve the same purpose, that is, to establish control of the ego over the id. Bettelheim (1969) notes the paradoxical echoes of Freud’s teachings with theories of education, but at the same time he notes that in practice the unification of these two theories is almost impossible. The unconscious currents prevailing in the non-adult personality must gradually become aware of the clarity of the intrinsic ego and obey it. Therefore, the problem of teachers using psychoanalytic theories often lies in the lack of understanding that the manifestations of the unconscious in a child are not a sign of adequate education. It is not uncommon for educators to believe that outbursts of energy and out-of-control behavior are tantamount to self-discovery through self-expression. However, in essence, such energy impulses are not synchronous with the idea of a psychoanalytic process of self-knowledge. The child does not learn in this way to understand his internal movements, but rather loses the ability to control them.

Another example of a negative understanding of Freud’s theories on education is the problem of student motivation. For example, there are cases when teachers misunderstood what makes children interested in the process of acquiring knowledge. It was not uncommon for teachers to become frustrated with their students and their teaching activities because they were unable to keep students motivated on a long-term basis. The pedagogical problem of such disappointment lies in the lack of familiarity with Freud’s theories, in particular with the pleasure principle in the rational world. It should be understood that in the modern world overflowing with all sorts of choices, pleasures and attractions, the problem of forming a motivated personality is quite strong. For example, a child may be inclined to make the simplest decisions guided by superficial and momentary desires. This is due to the fact that the motivation for the ego no longer seems significant enough to the child, which is why children are not able to force themselves to learn lessons in the long term.

In the past, when religion played a more fundamental role in Western society, people’s motivation to act was a sacred reward in the long run. This allowed people to work selflessly and ascetically restrain themselves in pleasures and needs, comforting themselves with the hope of happiness and bliss in the afterlife. Their second motivation was the fear of punishment in hell, which triggered the processes of the superego, which also gave motivation for action and work. In the modern world, such motivation cannot be long-term, and the promise of a reward for learning, which is guaranteed to be but in the extremely long term, no longer seems to be satisfactory for children. Therefore, the problem of the modern teacher lies in the impossibility of starting in the child the process of realizing the real inner need for the knowledge received, which is followed by disappointment.

Education cannot be obtained by a child who is strictly guided by the principle of pleasure, that is, who is engaged in lessons to the extent that he is interested in it. A teacher may certainly take pride in drawing attention to the subject he is expounding to the student, but this spark of interest is not enough to trigger the psychological drive for education (Bojesen, 2019). In this impossibility of the natural generation of motivation, Freud obviously observed the problem of this profession. The educational process is also difficult to combine with the problem of internal and external social development of the child. Psychoanalysis as a discipline tends to destroy the internal barriers within a person, to identify and neutralize his subconscious passions and control mechanisms repressed in the superego (Mayes, 2020). At the same time, it is practically impossible to force this control mechanism out of the child, because there is a risk that only pure manifestations of the unconscious will remain in its place.

The process of education in the official tradition implies familiarity with external rules and restrictions imposed by society. Psychoanalysis, on the other hand, is largely aimed at revealing their artificiality, making a person stop attaching such great importance to them in order to develop a fixed internal neurosis (Felman, 1982). In essence, education enslaves creativity and makes natural children more obedient and controllable. Psychoanalysis, on the other hand, is rather the next stage in the development of a person, when the imposed restrictions that produce a enslaving impression are removed as internally imposed.

Modern psychologists often emphasize the task of education as something similar to the essence of psychoanalysis. Britzman (2009) is perceiving the work of a teacher as a remedy for individuality, and the process of combining knowledge with desire. Education can be likened to the process of knowing oneself, since it also includes a feeling of inferiority, work with an excessive complex of informational variables (Britzman, 2021). Thus, the connection of psychoanalysis to the educational process could remove the fear of knowing the world, forcing the student to look at his ego from the outside.

The theory of education in connection with psychology can also acquire forms that differ from Freud’s theoretical prism. A prime example of child educational psychology in practice is the theory of Jean Piaget, who spent decades striving to find the key to the educational process for children. He paid attention not to individual differences between children, but to similar logical patterns in their thinking, which he called patterns (Furth, 1971). Gradually, the psychology of the child is built in this way as the realization that around them are objects that exist separately from themselves. These structures form the intellect, which exists as a complex network of regularities in behavior.

At the same time, Piaget observes the difference between training and education, arguing that education is not capable of forming experiential knowledge in a child. Thus, in this there is a certain confirmation of Freud’s idea that it is impossible to teach a child, since only the child learns and develops by himself through contact with objects. However, the teaching of moral principles, which Freud spoke more about in connection with education, works somewhat differently. The child tends to repeat the world of adults and therefore does not understand the relativity of actions depending on the context. Therefore, bad deeds are perceived by the child from the point of view of deviation from the norm, regardless of motivation (Furth, 1971). This emphasizes the need for communication and cooperation in the process of understanding the world, otherwise the system will be perceived solely as a limiter and not as a rationally operating moral mechanism.

Despite the fact that the process of education is an act of oppression of the child and oppression of their potential, its role for society is rather important and necessary than vice versa. Freud did not believe that the manifestation of libido in a child should be freely encouraged, but at the same time he was aware that its suppression did not solve the problem. Thus, the impossibility of this process with all reality does not require the rejection of this task. On the contrary, modern researchers are in constant search for hybrid models of education and psychoanalysis, which would take into account the shortcomings of both disciplinary and society. Pedagogy should be non-reactive but penetrating and focused on continuous improvement, so experimental combinations of education and psychoanalysis seem not only possible but potentially useful.

Bettelheim, B. (1969)’Psychoanalysis and education,’ The School Review , 77(2).

Bojesen, E. (2019) Forms of education: rethinking educational experience against and outside the humanist legacy. London: Routledge.

Britzman, D. (2009) The very thought of education: psychoanalysis and the impossible professions. Albany: State University Press.

Britzman, D. (2021). Anticipating education: concepts for imagining pedagogy with psychoanalysis. Gorham: Myers Education Press.

Felman, S. (1982) ‘Psychoanalysis and education: Teaching terminable and interminable’, Yale French Studies 63, pp. 21-44.

Freud, S. (1991) Introductory lectures on psychoanalysis. Harmondsworth: Penguin Books.

Freud, S. (1969) An outline of psycho-analysis. London: Hogarth Press

Furth, H. G. (1971) Piaget for teachers. Englewood Cliffs, New Jersey: Prentice Hall

Mayes, C. (2020). Archetype, culture, and the individual in education: the three pedagogical narratives. London: Routledge.

Watts, J., Cockcroft, K. & Duncan, N. (2009) Developmental psychology. Lansdowne: UCT Press.

• Jung’s and Freud’s Approaches to Psychoanalysis
• Presenting Freudian Concepts: Mr. and Mrs. Smith
• Freud's Psychoanalytic Theory of Personality
• Donald Schon's Reflective Thinking Model
• The Brain-Based Teaching and Learning
• Skinner's, Pavlov's, and Bandura's Experiments
• Elements of an Evaluation Plan Based on Kirkpatrick's Model
• Idealism in the Australian Education System
• Chicago (A-D)
• Chicago (N-B)

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A Theory of Teaching

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Whether one can claim to have a theory of teaching depends on what one takes to constitute teaching and what one means by theory. This chapter characterizes both. Given those characterizations, I claim that we already have a theory of teaching, which specifies that teachers’ in-the-moment classroom decisions can be modeled by attending to three major factors: the resources at the teachers’ disposal (both their knowledge and material resources), their orientations (beliefs, preferences, values, etc.), and their goals (which exist at multiple levels and change dynamically according to evolving events). Beyond that, the Teaching for Robust Understanding (TRU) framework indicates that the following five dimensions of learning environments are consequential and comprehensive – the degree to which the environment: (1) offers affordances for rich engagement with content; (2) operates within the students’ zone of proximal development; (3) supports all students in engaging with core content; (4) provides opportunities for students to contribute to classroom discourse and develop a sense of agency and disciplinary identity; and, (5) reveals and responds to student thinking. Combining these two theoretical frames yields a theoretical specification of what has been called “ambitious teaching.” There is much more to be concerned with, however. In general, the field’s understanding of relevant knowledge and resources for ambitious teaching is weak, a problem exacerbated by the widespread adoption of virtual instruction due to the presence of Covid-19. Moreover, little is understood regarding teachers’ developmental trajectories. Such knowledge will be necessary to establish effective long-term professional development efforts.

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Processes of Building Theories of Learning: Three Contrasting Cases

Taking Teaching Philosophies Seriously: Pedagogical Identity, Philosophy of Education, and New Opportunities for Publication

Connecting Theory to Concept Building: Designing Instruction for Learning

• Ambitious instruction
• Models of teaching
• Teaching for robust understanding
• Teachers’ decision making
• Theories of teaching

1 Introduction and Overview

This essay grapples with the framing questions offered by the book’s editors:

What is a theory (of teaching)?

What should it contain and why?

Can such a theory accommodate differences across subject matters and student populations taught? If so, how? If not, why?

Do we already have a theory/theories on teaching? If so, which are they?

In the future, in what ways might it be possible, if at all, to create a (more comprehensive) theory of teaching?

In a concluding discussion I also address some of the larger issues of context raised in Hill and Lampert’s foreword

For the purposes of this paper I will use the standard dictionary definition of what it means to teach. The Merriam-Webster dictionary ( 2020 ) defines “teach” as follows: “to cause to know something… to guide the studies of… to impart the knowledge of (e.g., teach algebra) to instruct by precept, example, or experience… to conduct instruction regularly in teach school” ( https://www.merriam-webster.com/dictionary/teach ). It goes without saying that there is more to the totality of teaching than this – for example, planning, creating materials, and meeting with students outside of class, to name but a few. But the common-sense definition of teaching is “the act of instructing students in the classroom.” That definition frames most of what follows.

To put my theoretical cards on the table: There does exist a theory of human in-the-moment decision making in complex social contexts (Schoenfeld, 2011 ). This empirically validated theory includes as a subset the decision making by teachers during the act of instruction– that is, “teaching” in the sense characterized above. As elaborated in Sect. 2 , the theory says that it suffices to understand teachers’ resources, orientations, and goals in order to model teachers’ choices during instruction. Hence, we already have a theory of teaching. I suspect, however, that such a value-neutral question was not the sole intention of the editors. The question most people are interested in is, do we have a theory of “good teaching” (or, as characterized below, “teaching for robust understanding”)?

A theory of teaching as framed above does not address the question of what the appropriate goals for instruction should be, or how to achieve them. By analogy, consider the fact that there has been a theory of internal combustion engines for almost two centuries: Samuel Brown obtained a patent for an internal combustion engine suitable for industrial use in 1823, and Gottlieb Daimler and Karl Benz patented gasoline engines in the late 1870s. Thus in a sense, there was a “theory of cars” a century and a half ago. Nonetheless, the contexts in which automobiles operate and the goals for automotive performance have evolved continuously over the decades. The relevant question for automobiles is, what are current or emerging performance goals (including safety, etc.) and how can they be achieved?

With regard to teaching then, the question is what goals are appropriate for learning environments – in the sense that if learning environments attain those goals, students will emerge from them being knowledgeable and agentive thinkers and problem solvers. Notice the fundamental shift in frame. The key question is not “what should a teacher do,” which is teacher-focused, but “what properties should the learning environment have?”, which focuses on the experiences of students. It goes without saying that the teacher is the key agent in establishing and maintaining the learning environment – but the goals for the teacher are then focused on how students experience it.

Here too, there exists a theoretical framing that addresses the issue in principle. The Teaching for Robust Understanding (TRU) Framework (Schoenfeld, 2014 ; Teaching for Robust Understanding Project, 2018 ) identifies key dimensions of productive learning environments. As such it serves to establish appropriate teaching goals. See Sect. 3 .

Such a theoretical framing, however, leaves much work to be done. There are questions of how to frame materials and learning experiences for teachers, so they can develop the resources to attain the goals specified in Sect. 3 . And there are questions about next steps in an R&D agenda that pursues these issues. See Sect. 4 .

2 A Theory of In-The-Moment Decision Making

I begin with a characterization of “theory.” The web definition provides a good start: “a supposition or a system of ideas intended to explain something, especially one based on general principles independent of the thing to be explained.” Footnote 1 The implied generality in this definition is important, in that a theory applies to a class of objects, actions, and relations: “under certain circumstances, specific objects interact in specific ways.” The National Academy of Sciences ( 1999 , p. 2) elaborates, “Theory: In science, a well-substantiated explanation of some aspect of the natural world that can incorporate facts, laws, inferences, and tested hypotheses.” Popper ( 1963 ) goes further, arguing that theories should be falsifiable. The idea is that ( pace Schrödinger) most theories should enable predictions in a wide range of cases. With each confirmation, if it comes, there is more reason to believe in the robustness of the theory.

With these characterizations in mind I discuss the idea of a theory of teaching – more generally, a theory of knowledge-based decision making in complex social contexts. The general question is as follows. Suppose you are trying to explain/predict the decisions made by an individual while they are engaged in a “well practiced” endeavor – something they’re been doing for a while, so they have a body of knowledge and routines at their disposal. In general, what would you have to know about that person, and the context, in order to explain/predict that person’s decision making? Specifically in the case of teaching, what would you have to know about a teacher in order to explain or predict what a teacher does when confronted by various circumstances as instructional activities unfold?

The key idea is that human decision-making is goal oriented and can be modeled as such . In-the-moment decision making in any context can be modeled as a function of three categories of things:

The decision maker’s goals in that context at that time.

The decision maker’s orientations (beliefs, preferences, values, tastes, biases, etc.), which shape the choice and prioritizing of goals and

The resources (mostly knowledge, but also material resources) available in the context where the decision making is taking place.

The fundamental mechanism governing decision makers’ choices is outlined in Fig. 6.1 .

How people make decisions, in outline Reprinted with permission from Schoenfeld ( 2011 , p. 18)

A comprehensive case for this theoretical framing is provided in Schoenfeld ( 2011 ), which offers a series of models of teachers’ decision making. A few examples will convey the ways in which goals, orientations and resources operate.

First, goals operate at multiple levels and multiple goals may be activated at the same time. A teacher may want to cover the curriculum, teach for understanding, prepare students for an upcoming test, create a welcoming environment, help students become reflective learners, and more (see, e.g., Lampert, 2001 ). Second, prior to entering the classroom, the teacher may have a plan that establishes top-level goals and subgoals: “I want to introduce this material today. I’ll review the homework, spend the bulk of time on the new material, and close by assigning homework.”

The selection of goals and their prioritization is shaped by the teacher’s orientations (primarily belief systems, which evolve over time), as is the set of resources the teacher will bring to bear in any context. For example, one teacher taught a particular class in a very procedural manner: “Step 1, do this. Step 2, do this…” Asked if he would consider asking the students an open question, his response was “Not these students, it would confuse them. I do that with my honors students.” That is, his beliefs about appropriate pedagogies for students with different “abilities” resulted in his choosing different pedagogies for teaching them (Schoenfeld, 1988 ). Footnote 2 Equity-oriented goals may result in the prioritization of particular classroom routines, as will goals of “teaching for understanding” rather than being “mastery oriented.” At a more fine-grained level, seeing a typically quiet student volunteer may lead the teacher to call on that student and frame the interaction with the student in ways that support the student differently than the teacher would approach an interaction with a student who is more voluble. Thus, goals are very much context-dependent, grounded in history and immediate constraints. (And, I note, they are grounded in the teacher’s perceptions of what is possible given their understanding of the environment. That’s the issue of beliefs, discussed immediately below.) Nonetheless, the evidence is clear that the set of highly activated goals at any particular time is the fundamental shaper of which resources will be selected and employed.

Belief systems and orientations develop slowly over time, and they are developed (often unconsciously) as a result of experience (see, e.g., Cooney, 1985 ; Kuhn, 1996 ; Patterson & Norwood, 2004 ; Philipp, 2007 ; Richardson, 1996 ; Thompson, 1985 , 1992 ; Usó-Doménech & Nescolarde-Selva, 2016 ). Likewise, the establishment of a rich body of knowledge for teaching develops slowly over time. The very notion of pedagogical content knowledge (Shulman, 1986 , 1987 ) is testimony to the evolution of a special teaching-specific kind of learning: beginning teachers who are at first surprised by a student writing “(a + b) 2  = a 2  + b 2 ” will, after a few years of teaching experience, have a repertoire of responses to choose from.

Moreover, as elaborated below, belief systems and pedagogical resources are interwoven in development. A classic example of this is “Mrs. Oublier” (Cohen, 1990 ), a teacher who aspired to implement “reform” ideas but some of whose pedagogical practices were so grounded in established networks of beliefs that her ongoing teaching did not yet reflect those aspirations. For all of these reasons, change is hard – a topic to which we will return toward the end of this chapter. For the moment, however, the key point is that a goal-oriented architecture, as described in Schoenfeld ( 2011 ), provides the foundation of a theory of teaching. The next question is, what is a relevant set of goals, orientations, and resources that produces desirable teaching outcomes ?

Before proceeding, however, it is essential to note that this question, as important as it is, is different from a theory of teaching. A theory of teaching describes the mechanisms by which teaching takes place. As such, the theory is value-neutral: it should enable one to characterize teaching that one finds laudable but also teaching that one finds problematic. Once one asks about “ambitious” or “effective” teaching – whatever one’s definition of those terms may be – one is asking a different type of question. Footnote 3 One way to frame the question of ambitious or effective teaching is, “what kinds of actions on the part of teachers result in powerful learning? As will be seen below, I believe it is much more profitable to address that question in stages.

One can first ask, what are the properties of learning environments from which students emerge as knowledgeable and agentive learners? This is a theoretical question, which can result in a theory of learning environments. Then, one can reframe ambitious teaching as the decisions make while creating and maintaining productive learning environments. With that framing, one can revisit the theory of decision making described above and ask, what sets of goals, resources and orientations result in the creation of powerful learning environments – environments from which learners emerge as knowledgeable and agentive thinkers and problem solvers? That is the approach taken here.

3 Establishing Goals for “Ambitious Teaching” (Key Dimensions of Productive Learning Environments) and Thinking About the Development of Orientations and Resources

We begin with a discussion of the goals for teaching. Historically the focus of instruction has been on disciplinary content. That is a desired aspect of learning, of course, but this framing is far too narrow. For one thing, goals for mathematics instruction have expanded from “mastering” content to becoming proficient at both the content and the practices that typify rich mathematical understanding (Common Core State Standards Initiative, 2010 ; National Council of Teachers of Mathematics, 1989 , 2000 ). But this is just a start: it is in our classrooms that students develop their beliefs about the nature of mathematics and their relationship to it; where they come to see themselves as agentive (or not) in mathematics; where they develop their sense of mathematical identity; where they are positioned by others; and much more. When thinking about learning as a whole, it is best to think about the opportunities the learning environment provides for growth along all these dimensions. The teacher is responsible for orchestrating all of this. Hence a more encompassing definition of “ambitious” teaching or “teaching for robust understanding” is: Teaching for robust understanding is the shaping of learning environments and interactions in them, in ways aimed at enhancing student learning.

The key question for powerful learning – for teaching for robust understanding – then becomes:

What are the attributes of powerful learning environments – learning environments from which students emerge as agentive, knowledgeable and resourceful thinkers and problem solvers?

An answer to this question provides the goals for a theory of productive teaching (a theory of teaching aimed at desirable teaching outcomes, as suggested in Sect. 2 ).

To cut to the chase, the Teaching for Robust Understanding (TRU) Framework (Schoenfeld, 2013 , 2014 ; Teaching for Robust Understanding Project, 2018 ) provides the answer to the key question above. Here as in Sect. 2 the discussion will be telegraphic, with references to sources that provide the analytic and empirical justifications of the claims made.

Schoenfeld ( 2013 , 2014 ) documents the process by which the extensive literature on “what counts” in ambitious teaching was distilled into five essential dimensions of classroom practice and subjected to empirical testing. The result of that work, the Teaching for Robust Understanding (TRU) Framework, provides evidence that students will emerge from learning environments as powerful, agentive, and empowered thinkers and learners to the degree that the five dimensions highlighted in Fig. 6.2 are consistently reflected in instructional practice.

Five dimensions of powerful mathematics classrooms. (Reproduced with permission from the TRU Observation Guide, p. 1)

Before incorporating the substance of Fig. 6.2 (and Fig. 6.3 to come) into a theory of powerful teaching, I briefly summarize some of the properties of the framework. For extensive detail, see the TRU Framework web site ( https://truframework.org/ ).

For purposes of specificity and because of its historical origins, Fig. 6.2 describes powerful learning environments in mathematics. In fact, the framework is general: replace “mathematics” by “X” and the TRU framework provides a characterization of learning environments from which participants emerge aspowerful and agentive learners and practitioners of X.

All five dimensions are necessary, and learning outcomes will be significantly weakened if the learning environment does not do well along any of those dimensions. That is: If the mathematics is not rich; if activities are not crafted in ways that support all students in engageing productive struggle; if some students are not engaged with core content; if some students do not have opportunities co contribute to discussions and the mutual refinement of ideas; or if the environment does not adapt in meaningful ways to what students reveal of their thinking, then at least some students will be significantly shortchanged.

The five dimensions are sufficient for the desired outcomes, a fact that comes from the derivation of the framework (Schoenfeld, 2013 , 2014 ; Schoenfeld et al., 2018 ) and from empirical testing (Prediger & Neugebauer, 2021 ; Schoenfeld, 2016 , 2018 ).

There is no claim that the five dimensions reflect a unique distillation of the literature. They are best thought of as analogous to “basis vectors,” spanning the space of powerful (or if you prefer, “ambitious”) teaching. Other decompositions are possible, and they might highlight different aspects of teaching. One feature of this choice of five dimensions, however, is that they have been chosen in ways that they can each be the focus of meaningful professional development.

The description of each dimension with a short phrase that is given in Fig. 6.2 provides merely the briefest characterization of the explicit and implied contents of the dimension. For instance, “students feeling safe to venture ideas” is a necessary condition for Dimension 4, opportunities for the development of agency, ownership over content, and the development of positive disciplinary identities. Likewise, much more can be said about the richness of disciplinary content (e.g., the role of mathematical representations, mathematics as a language, what it means to understand content deeply, etc.) or any of the other dimensions.

The framework is not prescriptive. That is, it does not imply that one must teach in any particular way in order to achieve positive outcomes. (We have all observed wonderful teachers whose styles and classroom routines are very different.) Rather, the five dimensions of TRU can be seen as representing five key principles underlying ambitious, powerful, or robust instruction. There are as many ways to live up to those principles as there are superb teachers.

Again, it is essential to note that the TRU framework focuses on the attributes of the learning environment and the affordances it offers students for their learning and development. Figure 6.3 is useful in reminding us of the goals of instruction, when seen from the student’s perspective.

Framing lesson goals, from the student perspective. (Reproduced with permission from the TRU Observation Guide, p. 2)

With this as background, it is now possible to begin to flesh out some of the goal structure for a theory of ambitious (mathematics) teaching. Footnote 4 In what follows I will focus on decisions during the act of teaching – but as elaborated in Sect. 4 , these goals are relevant both in planning instruction and in reviewing instructional events afterward. Once again, this discussion will be somewhat terse; more detail can be found in Schoenfeld ( 2020b ).

3.1.1 Mathematics-Related Goals

First, let us consider goals for the student’s engagement with mathematics. High priority goals include that the student will experience/learn about, and come to internalize:

Mathematics as a sense-making discipline, not one of memorizing facts and procedures

Big mathematical ideas – that students see “what counts” and don’t get lost in minutia

Reasoning and problem solving

Ties between concepts and procedures

Multiple representations

Productive patterns of mathematical thinking (Schoenfeld, 2017 )

Moreover, these goals operate at multiple levels: the student should experience these at the micro-level when engaging in any day’s lesson, and experience them at aggregate (topic and unit) levels. Ultimately, students should come to see (and experience) mathematics as a sense making enterprise.

Once again, I stress that these are the very top-level versions of the goals. In any particular context (say a particular day’s instruction), they would be elaborated with regard to that day’s instruction – e.g., “what are the opportunities for sense making with regard to today’s content, and how can students be positioned to experience them?; how can the lesson support students in engaging with and understanding the big ideas?”, etc.

These are just the beginnings of questions. In Sect. 4 we will introduce the TRU Conversation Guide (Louie et al., 2016 ) and the TRU Observation guide (Schoenfeld and the Teaching for Robust Understanding Project, 2016 ), which elaborate on the bullet points immediately above. Each of those can be used to generate a more refined set of goals regarding the students’ mathematical experience.

3.1.2 Cognitive Demand-Related Goals

The top-level goal for cognitive demand (see Fig. 6.2 ) is that students should be in a position to engage productively with the central mathematical ideas of the lesson – with the level of challenge being such that the students are stretched, and that they grow from their sense making experience. The key idea is to sustain “productive struggle.” Some subgoals can be inferred from Fig. 6.3 : giving students time to engage with the challenges, providing scaffolding in ways that keep tasks within reach but don’t turn them into rote exercises; asking for explanations rather than simply for answers.

The challenge is to maintain cognitive demand in the moment, as students are working together. This can implicate task design, in planning – for example, a task that has multiple entry points or employs multiple representations can be approachable in different ways, and these different handholds can allow students to find places to engage meaningfully with the mathematics. Likewise, different classroom activity structures can offer different affordances for meaningful engagement. Of course, most of these goals are emergent – it’s when one sees a student bored or struggling in what seems to be an unproductive way that the goals for cognitive demand get activated.

3.1.3 Equitable Access-Related Goals

One key point with regard to dimension 3 is that the equity-related goal is not simply to keep students engaged; it is for all students to be engaged with the core content of the lesson. A classroom is not equitable if, by virtue of the activities they engage with, the “rich get richer and the poor get poorer.” So, the goal in that regard is to find and implement activities that engage every student meaningfully with the big ideas. A second key point, of course, is that there are various ways to participate in classroom activities: responding to questions, participating in discussions, volunteering ideas, and more. As implied by Fig. 6.2 , all students should have opportunities for significant amounts of “air time” – a top-level goal not just for whole class discussions but for small group activities as well. And as implied by Fig. 6.3 , another major goal is for all students (even those who are initially reluctant) to be supported in engaging meaningfully.

As in the case of all of the TRU dimensions, some of the more fine-grained questions elaborating the top-level goals can be found in the TRU Conversation guide (Louie et al., 2016 ). For example, the first few reflection questions related to agency, ownership and identity,

What is the range of ways that students can and do participate in the mathematical work of the class (talking, writing, leaning in, listening hard; manipulating symbols, making diagrams, interpreting text, using manipulatives, connecting different ideas, etc.)?

Which students participate in which ways?

Which students are most active, and when?

In what ways can particular students’ strengths or preferences be used to engage them in the mathematical activity of the class? (TRU Conversation guide, page 8)

give rise to opportunities for lesson planning and for modifying the lesson as a lesson unfolds.

3.1.4 Agency, Ownership, and Identity-Related Goals

There is a large literature documenting the negative impacts of mathematics instruction – the very existence of “math anxiety” as a phenomenon (see https://en.wikipedia.org/wiki/Mathematical_anxiety ) gives testimony to the often negative impact that mathematics instruction has on students. Goals related to Dimension 4 move in precisely opposite directions:

One goal is for students to feel mathematical agentive: “I can do mathematics, and I’m willing to jump in and give it my best.”

Another is for them to take possession of knowledge by making it their own – “I figured this out; it makes sense; it’s not simply what ‘they’ told me is true.”

A third is for their mathematical Identities to flower: “I like math and look forward to doing it – it makes sense and I can figure things out.”

It goes without saying that the development of positive agency/ownership/identity hinges on having had some degree of success in facing and working on mathematical challenges – not necessarily solving all of them, but having frequent opportunities to venture ideas, critique and build on others’ ideas, and have one’s own ideas both critiqued and built upon. Thus, highly dialogic classrooms are essential (see, e.g., Mercer et al., 2019 ); top-level goals are to create and sustain classroom practices that provide all (cf. dimension 3) students opportunities to generate, expand on, and explain their own ideas, responding in kind to the ideas of others. Additional goals (again, see the TRU Conversation Guide) include developing students’ capacity to do so, by opening up the kinds of ideas students have opportunities to generate and share (concerning, for example, strategies, connections, partial understandings, prior knowledge, and representations), placing responsibilities of evaluation and response more in students’ hands, and increasing the depth of expected explanations.

3.1.5 Formative Assessment-Related Goals

For an extended discussion of formative assessment see Burkhardt & Schoenfeld ( 2019 ). The first major goal related to formative assessment is to elicit student thinking and have it become public. This provides a clear example of how goals and subgoals cascade: students who fear being embarrassed by incorrect answers are not going to venture away from safe territory, so top-level goals for formative assessment activate a series of subgoals regarding classroom climate. Finding ways to reveal what students think is also a major component of dimension 2: it’s hard to know what level of cognitive demand to aim for if you have little idea of what students are thinking! A second major goal is for those student thoughts to be pursued in ways that advance individuals’, groups’, and the whole class’s mathematical agenda. Some of this is suggested by the last row of Fig. 6.3 . But there is more. One misconception regarding formative assessment is that once student misunderstandings are revealed, it is the teacher’s responsibility to set everything straight. (One teacher with whom we worked complained that, now that she was aware of student misconceptions, she felt like she was playing whack-a-mole: as soon as she addressed one student’s misconception, another cropped up!) This framing neglects the fact that the students themselves can serve as tremendous resources for each other. They can often “hear” each other’s misunderstandings in ways that the teacher, who is trying to attend to all of the students in the class, may not hear them, and they can respond in student language and often at each other’s level. Regarding formative assessment, student goals from the TRU Observation Guide include:

Taking ownership of the learning process in planning, monitoring, and reflecting on individual and/or collective work

Asking questions and making suggestions that support analyzing, evaluating, applying and synthesizing ideas

Building on the contributions of others and helping others see or make connections

Holding classmates and themselves accountable for justifying their positions, through the use of evidence and/or elaborating on their reasoning. (TRU Observation Guide, p. 4)

Thus, another major goal for formative assessment is for the teacher to create an environment in which students become skilled in working toward the goals above.

3.2 Orientations

The task of identifying high priority goals – the focus of Sect. 3.1 – is relatively easy. It should be noted, however, that the goals highlighted in Sect. 3.1 reflect a particular set of values, those embodied by the TRU framework. The premises that:

mathematics learning should result in deep and connected understandings, above and beyond a set of well honed skills

the learning environment should be tailored to support all students as opposed to letting “natural ability” separate those who should pursue mathematics from those who should not

all students should have opportunities to engage meaningfully with mathematics, at all levels

a major goal of mathematics instruction should be the development of productive mathematical identities

teachers are responsible for ongoing monitoring of student understanding and adjusting their instruction so that students have maximal opportunities for sense making, as opposed to being responsible for presenting the mathematics clearly (with the responsibility for making sense of the mathematics, once presented, falling on the shoulders of the students)

are consistent with the idea of “ambitious” or “powerful” instruction and are consonant with much of the “reform” movement in the U.S., but they are not universally shared. Footnote 5 That said, suppose we stipulate the kinds of goals discussed in Sect. 3.1 . That is still the easy part: the challenge is the development of orientations and resources that enable the implementation of activities to attain those goals.

As explained in Schoenfeld ( 2011 ), there are multiple interactions between goals, orientations, and resources. For purposes of exposition, I have chosen to begin with goals. Part of what makes things challenging, however, is the fact that (cf. Fig. 6.1 ) the goals one establishes in the moment are a function of one’s beliefs and orientations, which are a function of one’s history – and beliefs are formed over time, often unconsciously. Recall the teacher who taught his regular students in a very step-by-step manner, because anything less rigid would “confuse” them. That’s a matter of beliefs. Moreover, beliefs operate as parts of belief systems , but specific beliefs may be triggered by specific events and override other beliefs.

For example, Cohen ( 1990 ) tells the story of “Mrs. Oublier,” who espouses the rhetoric of reform but doesn’t live up to it. The point I wish to make is that this kind of situation is not only natural, but to be expected. The decisions that teachers make are a complex combination of their goals, their belief systems and orientations, and the mental and material resources at their disposal.

Consider a teacher in transition, akin to Mrs. Oublier. This teacher wants to do less “telling” and open up her classroom to contributions from students, as suggested by the literature and the professional development she has experienced. She has students discuss their work in groups and has students come to the board to present their work. So far, so good. But then, what a student writes on the board is incorrect – say a typical error such as “(a + b) 2 = a 2 + b 2 ”. Now what does the teacher do?

This teacher may have a previously established set of beliefs and orientations that get triggered by this error, and a set of goals and actions that correspond to them. For example, the teacher may have a cluster of beliefs related to the idea that “it’s bad to have incorrect mathematics written on the board, especially because students may copy it into their notebooks.” As a result, the teacher may move almost automatically to have the student erase the incorrect statement from the board. This action, so natural for the pre-transition teacher, well may undermine the teacher’s currently espoused goal of having students engage in mathematical sense making.

When things function smoothly in decision making, it’s because nested clusters of goals and subgoals are largely consistent with comparably nested clusters of beliefs and orientations, and the teacher’s repertoire of techniques (resources) includes a collection of actions consonant with those orientations and goals. That’s the baseline for “well practiced” behavior as captured in Fig. 6.1 .

It goes without saying that building a (mostly) coherent repertoire of linked resources, goals, and orientations is a long and slow process. That, in part, is what lies behind the notion of “pedagogical content knowledge” (Shulman, 1986 , 1987 ), the idea that “mere” content knowledge is far from enough for effective teaching. Shulman’s key idea was that the wisdom of practice is represented by the accumulation, over time, of ways to respond to student understandings. The first time a teacher sees a student make a particular error, the teacher may be floored, and make up something on the spot. Over time, the teacher builds a repertoire of responses, and chooses from them when the need arises.

What goes beyond Shulman’s notion, however, is that the different responses serve different goals and orientations. The teacher who is invested and well practiced in “mastery” may well provide a reminder of the formula, possibly with a justification for it, and give students some practice so that they are more likely to remember the formula. The teacher who is invested and well practiced in “teaching for understanding” may ask the student to check the formula and then work through something like an area model to build or strengthen the linkage between the distributive law and underlying representations of it. That is, different resources are not value-neutral: the decision to call upon them is tied to clusters of orientations and goals. For the well practiced teacher in a familiar content arena, these clusters cohere and the chain of decisions described in Fig. 6.1 proceeds smoothly. For the novice teacher, sparse resources can lead to challenges (Schoenfeld, 2011 ). For the teacher in transition, the challenge is not only to construct the relevant resource-orientation-goal clusters, but to supplant some of the clusters that are already well engrained.

That said, we can return to the question of orientations and resources relevant for teaching for robust understanding. In the remainder of this section I point to challenges in characterizing them. In the following section I discuss some tools that hold promise for progress.

A key issue about beliefs and orientations is that they are formed slowly over time. They may be held unconsciously, and thus challenging to address – it can be hard to alter an orientation you are not aware of! (Schoenfeld, 1985 ). Thus, either consistent experience for an extended period of time or an eye-opening experience that casts some currently held beliefs into doubt are the catalysts for change.

As a thought experiment, consider the set of goals identified in Sect. 3.1 . At the very top level, teaching for robust understanding requires a fundamental shift in perspective, from thinking about the central question of teaching being “what activities do I prepare for my students?” to “how are my students experiencing the classroom activities and environment? This is a major shift, which entails changes in beliefs and orientations in all five dimensions of TRU. To mention just one example regarding Dimension 1, consider beliefs regarding the nature of problem solving and the kinds of experiences that would enable students to make progress on problems that they have not been shown how to solve. Understanding that this is a major curricular goal and that it requires a different kind of student experience is not only challenging at the top level, but (as discussed above) requires families of context- and content-specific beliefs and orientations consistent with that perspective. (For example, what is the appropriate kind of response when students run into difficulty?) Employing formative assessment (Dimension 5) in order to adjust the level of cognitive demand (Dimension 2) requires some faith in students’ abilities to figure things out by themselves (recall the teacher who said that he would give his honors students room to explore, but not his regular students – “it would just confuse them”) and the belief that students can serve as meaningful resources for each other (Black & Wiliam, 1998 ; Burkhardt & Schoenfeld, 2019 ; Swan, 2006 ). Likewise, there are huge numbers of beliefs about race, tracking, differentiation, deficit perspectives, and more that impede the consideration and implementation of activities that could enhance equitable access to core content for all students. Constructing an environment that is conducive to the development of agency, ownership, and identity means believing that students are capable of making progress on complex issues, that they can be supported in making conjectures, building on each other’s ideas, etc. Believing that there is value in handing over some of the responsibility for learning to the students, and that – appropriately supported – they can interact in ways that lead not only to understanding rich mathematical content but becoming agentive and “owning” the content they generate, can require a significant leap of faith. In short, identifying and then supporting the development of beliefs and orientations that support teaching for robust understanding is a decidedly significant challenge. Developing them is that much more of a challenge.

3.3 Resources

Some key points with regard to resources are as follows. It should be noted that although some teaching routines (obviously central resources) are general, for example asking students “Can you tell me what you’re thinking,” the vast majority of resources are content- and context-specific. I touched on content-specificity with regard to the algebra error “(a + b) 2  = a 2  + b 2 ”. That error springs from a particular small grain-size piece of content. There are thousands of such, as, to give but one example, Brown & Burton’s ( 1978 ) pioneering error analyses in elementary subtraction indicate. Context and history matter, in that what was said yesterday may shape how one interprets what students say today.

In Schoenfeld ( 2019 ) I considered the issue of resources raised by the TRU Framework, highlighting issues that could profit from investigation. What follows are some of the main ideas.

3.3.1 Mathematics-Related Resources

At least two major issues regarding the practice of mathematics need to be addressed. First, although more that 30 years have passed since the NCTM ( 1989 ) Standards called for an increased emphasis on mathematical processes such as problem solving and reasoning, there is not nearly as much attention given to supporting students as reasoners and problem solvers – and in engaging more generally in powerful patterns of mathematical thinking (PPMT) such as problem solving, habits of mind, representation and modeling, abstracting, reasoning and proof as there should be (Schoenfeld, 2017 ). Far less attention is given to mathematical processes and practices than should be the case (Schoenfeld, 2020a ). Teachers need both material resources (curricular support) and rich experiences in problem solving, conjecturing and proving, and abstracting and generalizing in order to develop those mathematical habits of mind and the wherewithal to teach them.

Second, mathematics instruction, abetted by standards and testing, tends to emphasize a rather fine-grained level of curriculum and instruction – “this list (e.g., the Common Core State Standards for Instruction, 2010 ) identifies the skills we will teach and hold students accountable for.” This has long been a problem, as evidenced by what has been called the “summer slump,” the fact that students forget so much of what they learned the previous year over the few summer months they are away from school. The details don’t necessarily matter; the ideas behind them do.

For example, there are classical “work problems” such as this:

Pipe A can fill a swimming pool in 6 h. Pipe B can fill it in 8 h. How long does it take to fill the pool if both pipes are open simultaneously? If you don’t remember the formula, think about the problem.

Many years ago my research group included a graduate student who had recently been a high school teacher and an established mathematician visiting on sabbatical. The graduate student said “You use the following formula for problems like this” as found the answer in no time. The mathematician said, “I haven’t worked problems like this in 40 years. There’s a formula, but I don’t have a clue what it is.” Then he thought about what he could combine. Not hours, not pools, but… rates do combine. In 1 h, Pipe A fills 1/6 of the pool; in 1 h, pipe B fills 1/8 of the pool; hence the two together fill (1/6 + 1/8) = 7/24 of the pool. So, it takes 24/7 h to fill the pool.

The key point to observe is that the mathematician’s knowledge was generative . Unlike “summer slump” students who are at a loss when something falls out of memory, the mathematician remembered central ideas and principles that enabled him to regenerate the formula when he needed it.

A quick look through the curriculum yields myriad examples where the memory load placed on students is immense, and an understanding of key underlying ideas could ease that burden substantially. For example, many students memorize a range of formulas for determining the equation of a line in the plane: the two-point formula, the point-slope formula, the general formula, etc. It’s much more useful to understand that any two non-redundant pieces of information determine a line, and that one can find any of the formulas from any of the others.

It’s an open question as to what the most robust understandings of any body of content could or should be based on, and how to put these at the center of mathematics instruction.

3.3.2 Cognitive Demand-Related Resources

The goal for the cognitive demand dimension is “productive struggle,” based on the idea that if students are working productively within their zone of proximal development (Vygotsky, 1962 , 1978 ), they will build the kinds of knowledge that extends what they know in meaningful ways.

The challenge, then, is to arrange the environment so that each student has opportunities to make reasonable and reasoned progress. The word environment is stressed for multiple reasons. It includes both the tasks and the ways the students are set up to engage with them. For example, tasks that are simple exercises provide little opportunity for growth. The same is the case for tasks that are not within reach. However, a lot of this challenge can be mitigated both by task design and by classroom activity structures. If a task can only be solved in one way, then the solution is either within reach or not. But if a problem can be approached in multiple ways, or can be illuminated by employing multiple representations, then there are a range of ways in which students can engage with it profitably. Yet this is only the beginning, because the framing thus far invokes the image of an individual students working on the task in isolation. Things get much richer when students work on problems in collaborative groups. For one thing – and this can’t be stressed enough – students can serve as resources for each other. An individual teacher can only devote limited time to any student, but that student’s classmates are much more available. There is much to be learned from asking questions of or explaining to one’s classmates, and even more when one is collaborating with them. If a group of students is probing or building on each other’s ideas, the students are much more likely to be working within their zones of proximal development. In addition, comparing and contrasting the approaches they have taken to problems that support multiple approaches enhances the mathematical richness of the conversations. Thus crafting and using tasks that support rich conversations and implementing classroom activity structures that engage students productively with their fellow students are some of the cognitive demand-related resources teachers need to develop. (Cohen & Lotan, 2014 ; Cohen et al., 1999 ; Mercer et al., 2019 ).

3.3.3 Equitable Access-Related Resources

The key idea is that every student must have ample opportunity to engage meaningfully with the central mathematical content that is the focus of the lesson or unit. That means much more than some, perhaps peripheral, engagement with the topic. For example, the Wikipedia definition of “differentiated instruction” Footnote 6 says:

Differentiated classrooms have also been described as ones that respond to student variety in readiness levels, interests, and learning profiles. It is a classroom that includes and allows all students to be successful. To do this, a teacher sets different expectations for task completion for students, specifically based upon their individual needs.

The difficulty here lies in the phrase “a teacher sets different expectations for task completion for students.” If some students in a classroom are practicing factoring whole numbers while others are factoring quadratic polynomials, or some do just the first step of a procedure while others are expected to complete it, the students may all be engaged, but not in ways that does justice to each and everyone. The challenge is that there are many hidden biases, as revealed for example in the classic AAUW volume How schools shortchange girls (American Association of University Women,  1992 ). Data from that volume indicate that girls were called on less frequently than boys and asked lower-level questions. Bias and discrimination can be subtle or overt and occur across all ethnic and racial, gender and gender orientation, linguistic proficiency, and untold numbers of other categories. There are a wide range of equity-oriented tools and practices, including Complex Instruction (Cohen & Lotan, 2014 ; Cohen et al., 1999 ), Equity Pedagogy (Banks & Banks, 1995 ) and Equity Analytics (Reinholz & Shah, 2018 ). A first challenge is to become aware of such resources, a second to build classroom cultures that make productive use of them. This is highly context-sensitive. And it’s just the beginning, given the close links between Dimensions 3 and 4.

3.3.4 Agency, Ownership, and Identity-Related Resources

As noted in Sect. 3.1 , ambitious instruction aims for students to be agentive; for them to learn the mathematics in ways that gives them ownership over it; and for them to develop positive mathematical identities. The path to AOI lies in successful mathematical experiences, so the relevant resources consist of ways of crafting the learning environment in ways that are likely to improve them. Some of those resources include those mentioned for Dimension 2 – rich mathematical tasks with multiple entry points and classroom activity structures that support students in venturing and building on ideas are relevant. Likewise, the activity structures mentioned in Dimension 3, which focus on making sure that all students are engaged in significant ways, set the stage for AOI. Ultimately, however, supporting students’ development of AOI depend on a large set of resources deployed in the moment. Consider the questions given in Fig. 6.4 , drawn from the TRU conversation guide (Louie et al., 2016 ). Many can be planned for in advance, but many require real-time decision making based on what the teacher sees in classroom interactions. That brings us to Dimension 5.

Things to think about, re AOI. (Reprinted with permission from the TRU Conversation Guide, p. 10)

3.3.5 Formative Assessment-Related Resources

As indicated by Fig. 6.5 , Formative Assessment can be thought of as the glue that holds everything together in classrooms from which students emerge as mathematically powerful thinkers and learners.

The key roles of Formative Assessment. (Reprinted with permission from Burkhardt & Schoenfeld, 2019 , p. 43)

Learning mathematics means not only understanding content, but equally important, becoming proficient at mathematical processes and practices (conjecturing, reasoning and proving, problem solving, etc.). Supporting students to become effective mathematical thinkers (TRU Dimension 1) requires making their thinking available to others and interacting with it in the moment – the very definition of formative assessment. Similarly, cognitive demand (Dimension 2) is impossible to adjust unless student thinking is made public; providing equitable access (Dimension 3) requires constant attention; and as discussed immediately above, equitable access is only the gateway to the kinds of opportunities for sense making that support students in developing agency, ownership over content, and positive mathematical identities (Dimension 4).

As with the other dimensions, there are both material and pedagogical resources to be marshalled in the service of formative assessment. One set of material resources is the Formative Assessment Lessons (FALs) produced by the Mathematics Assessment project. These lessons, also known as classroom challenges, are available at no cost from https://www.map.mathshell.org/ . Independent evaluations of the FALs indicated that including 10–12 days worth of FAL-based instruction in the mathematics curriculum resulted, on average, in 4.6 months of learning gains (Herman et al., 2014 , Research for Action, 2015 ) – a gain likely attributable to the inference that teachers’ pedagogy during their regular lessons changed as a result of their being supported in different pedagogical practices while teaching using the FALs. But one should not give the impression that building the knowledge and pedagogical habits to employ formative assessment is straightforward. The FALs had the impact they did as the result of a quarter century of research and development, including content-specifics regarding typical student misconceptions and productive ways to structure classroom interactions to counter them. Developing such pedagogical content knowledge on one’s own is a long, slow process, as is developing the habits of mind that orient one to such knowledge (Black & Wiliam, 1998 ; Burkhardt & Schoenfeld, 2019 ).

4 Summary and Next Steps

This concluding discussion summarizes the main theoretical points in this chapter. I revisit the issues raised by the editors, pointing also to some resources and next steps in a research and development agenda.

4.1 What Is a Theory (of Teaching)?

I hope to have addressed that question thoroughly – well, as thoroughly as one can in a few pages – in Sect. 2 . My book How We Think (Schoenfeld, 2011 ) offers a comprehensive theory of knowledge intensive and socially intensive in-the-moment decision making. That theory is a theory in the scientific sense. It specifies objects and the relations between them, specifying a mechanism by which in-the-moment decisions are made. The theory described in Sect. 2 is general, and it supports the creation of models that test the theory.

4.2 What Should It Contain and Why? Do We Already Have a Theory/Theories on Teaching? If So, Which Are They?

As noted in Sect. 2 , an individual’s in-the-moment decision making can be characterized and modelled by focusing on that individual’s resources, orientations, and goals, using a decision mechanism akin to (but obviously more detailed and fine-grained than) Fig. 6.1 . In that sense there does exist a robust and empirically verified theory of teaching. As discussed in Schoenfeld ( 2011 ), this theory is general; it generates models of particular teachers that apply in a wide range of situations.

As noted, however, I suspect that the editors really intended for the authors of this volume to address the issue of “ambitious” or “powerful” teaching – instruction from which students emerge as knowledgeable, resourceful, and agentive thinkers and problem solvers. This is a very different question, because what one takes as important depends on one’s goals and values; it is no longer simply a question of theory. To invoke the automotive metaphor once again: one can have a theory of internal combustion engines (and theories of aerodynamics, etc.) but one will build very different cars if one’s goal is (a) to win the Indy 500, where cost is no object, or (b) to build a comfortable and profitable family sedan.

That said, there is an empirically validated theory of “teaching for robust understanding” and a framework that identifies what matters in ambitious instruction. As described in Sect. 3 , the TRU framework (Teaching for robust understanding project, 2018 ) indicates that a learning environment will be successful in producing powerful thinkers and learners to the degree that (1) the content and practices with which students engage is disciplinarily rich; (2) students engage in sense making within their zones of proximal development; (3) all students engage with core content and practices; (4) students have opportunities to contribute to discussions and progress in ways that support the development of agency, ownership over content, and the development of disciplinary identity; and (5) student thinking is made public and the learning environment adjusts accordingly.

It should be clear that there is no one “right” way to teach; teachers with very different styles and routines may be successful along all five dimensions of the TRU framework, just as somewhat different automobiles can vie for “best in class.”

Nonetheless, the combination of the theory of decision making in Sect. 2 and the TRU framework as discussed in Sect. 3 provides the mechanism for constructing a theory of ambitious teaching, a.k.a. Teaching for Robust Understanding. The question is, what are combinations (note the plural) of resources, orientations, and goals that would support teachers in constructing learning environments that do well in the five TRU dimensions? This was the issue pursued in at least some depth in Sect. 3 . That discussion just scratches the surface. It will be pursued in Sect. 4.4 , which identifies directions for further work.

4.3 Can Such a Theory Accommodate Differences Across Subject Matters and Student Populations Taught? If So, How? If Not, Why?

In a word, yes. The theory of decision making elaborated in Sect. 2 applies to well-practiced decision making in all knowledge-intensive domains. Schoenfeld ( 2011 ) provided detailed models of beginning and experienced teachers at the elementary and secondary levels, an indication that neither level of expertise nor grade level is a theoretical obstacle. The TRU framework was developed in mathematics, but it is domain general – it is a theory of powerful learning environments, independent of content domain and age level. That is not so say that content specifics or student population don’t matter. To create a powerful learning environment in physics, chemistry, or English Language Arts, one needs to have a rich sense of the content and practices in those domains. To be an effective teacher of any group of students, one needs to know those particular students and have a sense of what supports their learning. But those are details – the details of the resources, orientations, and goals relevant for any particular model one wishes to build in detail. That is a huge empirical challenge, but it is not a theoretical challenge.

4.4 (From the Editors:) In the Future, In What Ways Might It Be Possible, If at All, to Create a (More Comprehensive) Theory of Teaching?

As indicated above, the issues facing us as a field are not theoretical: the theory of in-the-moment decision making during teaching and the TRU framework, together, provide a comprehensive theoretical framework regarding teaching for robust understanding. The issue before us is: what would be useful to know in order to flesh out the details of that theoretical framework and provide mechanisms to help teachers move in productive directions? Thus, I would reframe question 4.4as:

4.5 (Reframed:) In the Future, In What Ways Might It Be Possible, If at All, to Elaborate and Support the Mechanisms of Teaching for Robust Understanding, and to Understand the Impact of the Contexts Within Which Teaching Takes Place?

In the balance of this section I briefly identify four arenas essential for progress.

4.5.1 Research and Development on Resources for Teaching for Robust Understanding

Section 3.3 characterized some of the cognitive resources that can support teachers in teaching for robust understanding. The list in that section is just a “starter set” – as noted above, pedagogical content knowledge comes with experience, and is tied very specifically to the content that one teaches. A major question is how to catalyze the development of such resources.

That question is intimately tied to the issues of material resources and professional development. As an example of the former, consider the Formative Assessment Lessons (FALs) available at https://www.map.mathshell.org/ . Each these 100 lessons provides direct curricular support for teaching key content using formative assessment. The lessons are aimed at unearthing student thinking related to the content and building on it. The support materials included as part of the lessons (which take 2 to 3 days each to implement) include diagnostic tasks that reveal student misunderstandings to teachers, tables of “common student issues” and ways to lead students to address them, and very detailed lesson plans. The lessons themselves bolster content and process understandings for teachers. By virtue of orienting teachers to common student misunderstandings and providing mechanisms for addressing them, the lessons scaffold the development of teachers’ pedagogical knowledge. In fact, each of the FALs embodies pedagogical content knowledge with regard to the content and practices at hand. (See Swan, 2006 , 2017 ; Swan & Burkhardt, 2012 , 2014 ). A major issue is scaling up: the FALs, which required a highly skilled design team, were based on decades of research and cost upwards of $6 M USD to produce, only address a subset of the central topics in the high school curriculum.

But there is more to be said about the FALs. The lessons were designed to help teachers learn key aspects of formative assessment, in the expectation that some of the productive pedagogical habits learned by teaching the FALs would become parts of the teachers’ general repertoire. Although the evidence to date is still thin, it appears that that is the case. Kim ( 2017 ) documents the changes over the course of a year as a teacher taught five of the FALs. After the first FAL, there was little or no change in the teacher’s pedagogy: the lesson she taught the next day very closely resembled in style the lessons she had taught before teaching the FAL. However, there were some slight changes after the teacher taught the second FAL, and by the end of the year the teacher was doing significantly less “telling” and providing students with a great deal more time to raise questions and discuss them among themselves. This experience was hardly an unalloyed success; the loss of the previously rigid structure the teacher had employed resulted in challenges in classroom management, for example. But the fact that the pedagogical strategies implemented in the FALs influenced the teacher’s regular lessons indicates that it is possible for such materials to have an impact on teachers’ pedagogical practices. Indeed, such “travel” is the most likely explanation for the findings in Herman et al. ( 2014 ), that Kentucky teachers who taught 10–12 days of FALs saw their students gain an additional 4.6 months in terms of mathematics learning. The students only experienced 10–12 days of FAL content, but they most likely experienced a significant amount of FAL-related (and TRU-consistent) pedagogy.

Note that these are largely conjectures at this point, and a great deal more needs to be studied.

Along similar lines but not on nearly as large a scale, the Teaching for Robust Understanding project has created a number of tools for teachers’ professional development: see https://truframework.org/ . Figures 6.2 and 6.3 were drawn from the TRU Observation Guide (Schoenfeld & the Teaching for Robust Understanding Project, 2016 ), and Fig. 6.4 from TRU conversation Guide (Louie et al., 2016 ). These tools have been used in a wide range of professional development projects (See Schoenfeld et al., 2020 , ; see also Schoenfeld et al., 2019 for a description of Teaching for Robust Understanding with Lesson Study.) These projects, in general, are aimed at helping teachers develop richer pedagogical resources and orientations consistent with the TRU Framework. Two new books (Schoenfeld et al., 2023a , b ) provide additional tools and support for professional learning communities.

Over time, it will be valuable to flesh out the knowledge and orientation base that supports teaching for robust understanding. This is both a theoretical and engineering exercise. For example, there is much to be learned about how belief systems are formed and operate (e.g., how orientations prioritize resources) and how to unpack and support student thinking (the what and how of content-specific formative assessment). For a more detailed view of desirable R&D, see Schoenfeld ( 2020b ) and Burkhardt & Schoenfeld ( 2019 ).

4.5.2 Issues of Developmental Trajectories

The field lacks good data on how teachers grow with regard to the key dimensions of TRU, especially in environments meant to foster their growth. There is a literature on teacher growth. In broad brush strokes, that literature (see, for example, Fuller, 1969 ; Hord et al., 1987 ; Ryan, 1986 ; Smith, 2000 ) suggests that teachers tend to spend the first few years of their careers mastering issues of classroom management, after which they increasingly get involved in using and sometimes developing engaging mathematical activities. Along the way they develop pedagogical content knowledge (in the arenas they teach, consistent with their orientations and practices) and some small percentage of teachers become adept at focusing on student thinking.

Such trajectories are hardly inevitable, however. Management is an issue if students are not engaged. Thus, an early focus on rich and engaging materials and activities may both lessen challenges of classroom management and hasten the growth of pedagogical content knowledge. Moreover, having your teacher focus on your thinking and ideas is very engaging for students – so teachers whose classrooms feature formative assessment early on may display (currently) non-normative developmental trajectories. Studies of how teachers’ understandings and practices develop, under what conditions, could help to optimize professional development.

4.5.3 Theoretical and Pragmatic Challenges in an Increasingly Virtual Instructional World

The coronavirus pandemic has thrown teachers around the world headlong into virtual instruction, whether they were ready for it or not – and few were. We thus face the massive challenge of reconceiving teaching within a radically different social, technological, and instructional context. The key point I wish to make here is that two things remain the same as we consider these changes. The first is that the mechanisms of decision making during instruction remain the same. What teachers will do in the moment is a function of their goals, the resources available, and their orientations. Without doubt, the material and social resources available in virtual environments differ substantially from those in in-person instruction. But what a teacher chooses to do will be a function of that teacher’s resources, orientations, and goals. Second and perhaps more important in this context, the teaching for Robust Understanding Framework applies to all learning environments, including virtual learning environments. What that means is that TRU can be used to problematize virtual learning. The key questions to confront are:

How can whatever mode of instruction teachers are employing – whether it is in-person, virtual, or blended – be configured so that …

students engage in deep ways with disciplinary content and practices

cognitive demand is adjusted so that students engage in productive struggle

all students are meaningfully engaged with core content

all students have opportunities to contribute to exchanges in ways that support the development of agency, ownership over content, and the growth of positive disciplinary identities and identities as learners

student thinking is made public and instruction responds in ways that supports the first four bullets above?

This is a huge challenge in in-person instruction and will be that much more of a challenge as we take on the new challenges of virtual instruction. But the framing given above highlights what is important and points us to the research and development that will help us to address the challenge.

4.5.4 Broader Issues of Context

The focus of this chapter has been on elaborating a theory of what the teacher does, inside the walls of the classroom. It goes without saying that everything that takes place inside schools is shaped by myriad societal forces. Issues susch as the “savage inequalities” of school funding (Kozol, 1992 ) and pervasive racism, to name just two, are critically important. For a preliminary discussion of the impact of such issues and how to link them to the issues discussed in this chapter, see Schoenfeld ( 2022 ).

See Google “define theory”.

Please not that I am not endorsing this perspective, just reporting it.

Such questions are value-laden, depending on what one considers to be important student learning outcomes. My stance is made clear in the next paragraph.

Analogous characterizations can be developed for every discipline.

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Acknowledgments

The ideas discussed here have evolved over many years and profited immensely from refinement by the Functions Group, the Mathematics Assessment Project, and the Teaching for Robust Understanding Project, among others. This paper was produced with support from the U.S. National Science Foundation Grant 1503454, “TRUmath and Lesson Study: Supporting Fundamental and Sustainable Improvement in High School Mathematics Teaching,” a partnership between the Oakland Unified School District, Mills College, the SERP Institute, and the University of California at Berkeley.

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Schoenfeld, A.H. (2023). A Theory of Teaching. In: Praetorius, AK., Charalambous, C.Y. (eds) Theorizing Teaching. Springer, Cham. https://doi.org/10.1007/978-3-031-25613-4_6

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