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An research proposal examples on mathematics is a prosaic composition of a small volume and free composition, expressing individual impressions and thoughts on a specific occasion or issue and obviously not claiming a definitive or exhaustive interpretation of the subject.

Some signs of mathematics research proposal:

  • the presence of a specific topic or question. A work devoted to the analysis of a wide range of problems in biology, by definition, cannot be performed in the genre of mathematics research proposal topic.
  • The research proposal expresses individual impressions and thoughts on a specific occasion or issue, in this case, on mathematics and does not knowingly pretend to a definitive or exhaustive interpretation of the subject.
  • As a rule, an essay suggests a new, subjectively colored word about something, such a work may have a philosophical, historical, biographical, journalistic, literary, critical, popular scientific or purely fiction character.
  • in the content of an research proposal samples on mathematics , first of all, the author’s personality is assessed - his worldview, thoughts and feelings.

The goal of an research proposal in mathematics is to develop such skills as independent creative thinking and writing out your own thoughts.

Writing an research proposal is extremely useful, because it allows the author to learn to clearly and correctly formulate thoughts, structure information, use basic concepts, highlight causal relationships, illustrate experience with relevant examples, and substantiate his conclusions.

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Students completing their PhD thesis proposal will enroll in one of the following courses, depending on whether they are in the MATH, APMA, or Operations Research program:

  • MATH 879 - PhD Thesis Proposal  (MATH and OR)
  • APMA 995 - PhD Oral Candidacy Exam

The thesis proposal should ideally be completed by the end of the sixth semester of enrollment in the PhD program . Students should discuss with their supervisor about when to enroll in this course.


1. At the beginning of the semester, students will enroll in one of the following courses, depending on whether they are in the MATH or APMA program:

  • MATH 879 - PhD Thesis Proposal

2. The student presents a written thesis proposal to their supervisory committee. The written version of the thesis proposal is generally due two weeks before the proposal presentation. This deadline should be confirmed by the committee at the time the proposal presentation is scheduled.

3. The student and senior supervisor arrange a date and time with the supervisory committee and the GPA is to be emailed ( [email protected] ) the following information  3 weeks prior to the thesis proposal:

  • Proposal Title
  • Date and Time
  • Room/video conference information.

4. The student delivers a seminar talk, (approximately 30 minutes in duration) attended by members of the supervisory committee and chaired by the senior supervisor.

  • If the committee approves the thesis proposal, the members sign a form stating that the student has passed the general examination.
  • If the committee is not satisfied, then the process must be repeated at a later date.

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  • How to Write a Research Proposal | Examples & Templates

How to Write a Research Proposal | Examples & Templates

Published on October 12, 2022 by Shona McCombes and Tegan George. Revised on November 21, 2023.

Structure of a research proposal

A research proposal describes what you will investigate, why it’s important, and how you will conduct your research.

The format of a research proposal varies between fields, but most proposals will contain at least these elements:


Literature review.

  • Research design

Reference list

While the sections may vary, the overall objective is always the same. A research proposal serves as a blueprint and guide for your research plan, helping you get organized and feel confident in the path forward you choose to take.

Table of contents

Research proposal purpose, research proposal examples, research design and methods, contribution to knowledge, research schedule, other interesting articles, frequently asked questions about research proposals.

Academics often have to write research proposals to get funding for their projects. As a student, you might have to write a research proposal as part of a grad school application , or prior to starting your thesis or dissertation .

In addition to helping you figure out what your research can look like, a proposal can also serve to demonstrate why your project is worth pursuing to a funder, educational institution, or supervisor.

Research proposal length

The length of a research proposal can vary quite a bit. A bachelor’s or master’s thesis proposal can be just a few pages, while proposals for PhD dissertations or research funding are usually much longer and more detailed. Your supervisor can help you determine the best length for your work.

One trick to get started is to think of your proposal’s structure as a shorter version of your thesis or dissertation , only without the results , conclusion and discussion sections.

Download our research proposal template

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Writing a research proposal can be quite challenging, but a good starting point could be to look at some examples. We’ve included a few for you below.

  • Example research proposal #1: “A Conceptual Framework for Scheduling Constraint Management”
  • Example research proposal #2: “Medical Students as Mediators of Change in Tobacco Use”

Like your dissertation or thesis, the proposal will usually have a title page that includes:

  • The proposed title of your project
  • Your supervisor’s name
  • Your institution and department

The first part of your proposal is the initial pitch for your project. Make sure it succinctly explains what you want to do and why.

Your introduction should:

  • Introduce your topic
  • Give necessary background and context
  • Outline your  problem statement  and research questions

To guide your introduction , include information about:

  • Who could have an interest in the topic (e.g., scientists, policymakers)
  • How much is already known about the topic
  • What is missing from this current knowledge
  • What new insights your research will contribute
  • Why you believe this research is worth doing

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As you get started, it’s important to demonstrate that you’re familiar with the most important research on your topic. A strong literature review  shows your reader that your project has a solid foundation in existing knowledge or theory. It also shows that you’re not simply repeating what other people have already done or said, but rather using existing research as a jumping-off point for your own.

In this section, share exactly how your project will contribute to ongoing conversations in the field by:

  • Comparing and contrasting the main theories, methods, and debates
  • Examining the strengths and weaknesses of different approaches
  • Explaining how will you build on, challenge, or synthesize prior scholarship

Following the literature review, restate your main  objectives . This brings the focus back to your own project. Next, your research design or methodology section will describe your overall approach, and the practical steps you will take to answer your research questions.

To finish your proposal on a strong note, explore the potential implications of your research for your field. Emphasize again what you aim to contribute and why it matters.

For example, your results might have implications for:

  • Improving best practices
  • Informing policymaking decisions
  • Strengthening a theory or model
  • Challenging popular or scientific beliefs
  • Creating a basis for future research

Last but not least, your research proposal must include correct citations for every source you have used, compiled in a reference list . To create citations quickly and easily, you can use our free APA citation generator .

Some institutions or funders require a detailed timeline of the project, asking you to forecast what you will do at each stage and how long it may take. While not always required, be sure to check the requirements of your project.

Here’s an example schedule to help you get started. You can also download a template at the button below.

Download our research schedule template

If you are applying for research funding, chances are you will have to include a detailed budget. This shows your estimates of how much each part of your project will cost.

Make sure to check what type of costs the funding body will agree to cover. For each item, include:

  • Cost : exactly how much money do you need?
  • Justification : why is this cost necessary to complete the research?
  • Source : how did you calculate the amount?

To determine your budget, think about:

  • Travel costs : do you need to go somewhere to collect your data? How will you get there, and how much time will you need? What will you do there (e.g., interviews, archival research)?
  • Materials : do you need access to any tools or technologies?
  • Help : do you need to hire any research assistants for the project? What will they do, and how much will you pay them?

If you want to know more about the research process , methodology , research bias , or statistics , make sure to check out some of our other articles with explanations and examples.


  • Sampling methods
  • Simple random sampling
  • Stratified sampling
  • Cluster sampling
  • Likert scales
  • Reproducibility


  • Null hypothesis
  • Statistical power
  • Probability distribution
  • Effect size
  • Poisson distribution

Research bias

  • Optimism bias
  • Cognitive bias
  • Implicit bias
  • Hawthorne effect
  • Anchoring bias
  • Explicit bias

Once you’ve decided on your research objectives , you need to explain them in your paper, at the end of your problem statement .

Keep your research objectives clear and concise, and use appropriate verbs to accurately convey the work that you will carry out for each one.

I will compare …

A research aim is a broad statement indicating the general purpose of your research project. It should appear in your introduction at the end of your problem statement , before your research objectives.

Research objectives are more specific than your research aim. They indicate the specific ways you’ll address the overarching aim.

A PhD, which is short for philosophiae doctor (doctor of philosophy in Latin), is the highest university degree that can be obtained. In a PhD, students spend 3–5 years writing a dissertation , which aims to make a significant, original contribution to current knowledge.

A PhD is intended to prepare students for a career as a researcher, whether that be in academia, the public sector, or the private sector.

A master’s is a 1- or 2-year graduate degree that can prepare you for a variety of careers.

All master’s involve graduate-level coursework. Some are research-intensive and intend to prepare students for further study in a PhD; these usually require their students to write a master’s thesis . Others focus on professional training for a specific career.

Critical thinking refers to the ability to evaluate information and to be aware of biases or assumptions, including your own.

Like information literacy , it involves evaluating arguments, identifying and solving problems in an objective and systematic way, and clearly communicating your ideas.

The best way to remember the difference between a research plan and a research proposal is that they have fundamentally different audiences. A research plan helps you, the researcher, organize your thoughts. On the other hand, a dissertation proposal or research proposal aims to convince others (e.g., a supervisor, a funding body, or a dissertation committee) that your research topic is relevant and worthy of being conducted.

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Research Proposal Example/Sample

Detailed Walkthrough + Free Proposal Template

If you’re getting started crafting your research proposal and are looking for a few examples of research proposals , you’ve come to the right place.

In this video, we walk you through two successful (approved) research proposals , one for a Master’s-level project, and one for a PhD-level dissertation. We also start off by unpacking our free research proposal template and discussing the four core sections of a research proposal, so that you have a clear understanding of the basics before diving into the actual proposals.

  • Research proposal example/sample – Master’s-level (PDF/Word)
  • Research proposal example/sample – PhD-level (PDF/Word)
  • Proposal template (Fully editable) 

If you’re working on a research proposal for a dissertation or thesis, you may also find the following useful:

  • Research Proposal Bootcamp : Learn how to write a research proposal as efficiently and effectively as possible
  • 1:1 Proposal Coaching : Get hands-on help with your research proposal

Free Webinar: How To Write A Research Proposal

FAQ: Research Proposal Example

Research proposal example: frequently asked questions, are the sample proposals real.

Yes. The proposals are real and were approved by the respective universities.

Can I copy one of these proposals for my own research?

As we discuss in the video, every research proposal will be slightly different, depending on the university’s unique requirements, as well as the nature of the research itself. Therefore, you’ll need to tailor your research proposal to suit your specific context.

You can learn more about the basics of writing a research proposal here .

How do I get the research proposal template?

You can access our free proposal template here .

Is the proposal template really free?

Yes. There is no cost for the proposal template and you are free to use it as a foundation for your research proposal.

Where can I learn more about proposal writing?

For self-directed learners, our Research Proposal Bootcamp is a great starting point.

For students that want hands-on guidance, our private coaching service is recommended.

Literature Review Course

Psst… there’s more!

This post is an extract from our bestselling Udemy Course, Research Proposal Bootcamp . If you want to work smart, you don't want to miss this .

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Mathematics Research Proposals Samples For Students

24 samples of this type

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Research Proposal On Whiteboard on Mathematics Classroom

Virtual architecture model, smashing research proposal about research questions, impacts of interactive boards in mathematics classrooms..

- What are the effects of white board technology on mathematics student’s performance and attention? - Do mathematics students engage better while using interactive white boards than without the white board?

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Example Of Research Proposal On The Correlation Between Student Anxiety And Academic Performance In Low-Level College

This paper examines the correlative effects of stress levels on examination results, particularly in areas of academic study where students are already struggling. The research examines the test scores and stress levels of remedial and basic-level mathematics students in the undergraduate level, tracking their changes in stress level over time and the effects that changes in stress level has on a student’s academic performance in in-class mathematics examinations.


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Introduction Hippocrates made mathematical advancement during the Golden Age in which fundamental concepts of geometry began thriving in the social dynamics (Huffman, and Filolaos 197). Some of the two core mathematic techniques that occurred during this era include axiomatic techniques to geometry and introduction of paradoxes by the Zeno of Elea (Bell 138). Principally, the paradoxes were concerned with the determination of infinite and infinitesimal mathematic concepts (Klette, and Azriel 455).

Good Research Proposal About Project-Based Learning

This research proposal will employ a longitudinal experimental design to investigate student learning using Project-based learning for middle school literature classrooms within the same school. The results will be measured by IOWA testing every term over a 3 year time period and compared to the results of the students from traditional classroom setting. Assessment scores will be the dependent variables. The literature review of six peer-reviewed articles is included. The purpose of the study, hypotheses, methodology, participants, procedure, instruments and data analysis will be described.

Radiation Detector Failures Research Proposals Examples

Proper research proposal example about the impact of computers on individual learning, unknown cumulative distribution function research proposal, problem statement research proposal example.

Dropping Out or Pushed Out: The Impact of High School Dropout Rate Relative To High Stakes Testing Policy In The State Of Michigan

The Research Project Research Proposal Examples

Doctor candidate:.

Philosophy of Transformation: Differentiation or Subtraction Summary in Key Words Philosophy of transformation; Deleuze; Badiou; differentiation, subtraction, (re-, de-) territorialization; folding; plane of consistency; events (interventions); truth procedure; subject; the capitalism; the democratic materialism

Summary of the Theme and the Aim of the Project

Research questions: a sample research proposal for inspiration & mimicking, exemplar research proposal on winston educational foundation to write after, improvements in public education.

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Anaheim, California


Dear City Councilman Roberts:

Example of components of a computer research proposal.

Introduction The application of computers is widespread in the current generation. Computers form a fundamental part of our daily lives as well as activities. The application of computers ranges from simple mathematical computations in devices like calculators to complex mathematical computations in industries. Virtually everything depends on computers for operation and completion of various tasks and processes in equal measure. The use of computer presents a variety of advantages over other alternative methods of accomplishing tasks (Krishnamoorthy, et al, 2009).

Background Research

Good recidivism among paroled inmates: discussion research proposal example.


Returning to prison for paroled inmates: Introduction

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Dropping Out or Pushed Out: The Impact of High School Dropout Rate Relative to High Stakes Testing Policy in Wayne County, State of Michigan

Dissertation Prospectus Dropping Out or Pushed Out: The Impact of High School Dropout Rate Relative to High Stakes Testing Policy in Wayne County, State of Michigan <Insert Chair Name>

Dissertation Prospectus

Preparing design and technology students for the future research proposal, research proposal on nursing homes, statement of the problem.

Old age is associated with several mental illnesses, which culminate into other psychosocial issues. For example, dementia and other related conditions such as the Creutzfeudz Jacob’s disease – as caused by advanced senility – have become common in the modern world. Usually, these diseases affect old people, which become more and more problematic as the age advances. The role of caring for the old people has therefore become very vital, usually requiring increased care and special treatment to these people.

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17 Research Proposal Examples

research proposal example sections definition and purpose, explained below

A research proposal systematically and transparently outlines a proposed research project.

The purpose of a research proposal is to demonstrate a project’s viability and the researcher’s preparedness to conduct an academic study. It serves as a roadmap for the researcher.

The process holds value both externally (for accountability purposes and often as a requirement for a grant application) and intrinsic value (for helping the researcher to clarify the mechanics, purpose, and potential signficance of the study).

Key sections of a research proposal include: the title, abstract, introduction, literature review, research design and methods, timeline, budget, outcomes and implications, references, and appendix. Each is briefly explained below.

Research Proposal Sample Structure

Title: The title should present a concise and descriptive statement that clearly conveys the core idea of the research projects. Make it as specific as possible. The reader should immediately be able to grasp the core idea of the intended research project. Often, the title is left too vague and does not help give an understanding of what exactly the study looks at.

Abstract: Abstracts are usually around 250-300 words and provide an overview of what is to follow – including the research problem , objectives, methods, expected outcomes, and significance of the study. Use it as a roadmap and ensure that, if the abstract is the only thing someone reads, they’ll get a good fly-by of what will be discussed in the peice.

Introduction: Introductions are all about contextualization. They often set the background information with a statement of the problem. At the end of the introduction, the reader should understand what the rationale for the study truly is. I like to see the research questions or hypotheses included in the introduction and I like to get a good understanding of what the significance of the research will be. It’s often easiest to write the introduction last

Literature Review: The literature review dives deep into the existing literature on the topic, demosntrating your thorough understanding of the existing literature including themes, strengths, weaknesses, and gaps in the literature. It serves both to demonstrate your knowledge of the field and, to demonstrate how the proposed study will fit alongside the literature on the topic. A good literature review concludes by clearly demonstrating how your research will contribute something new and innovative to the conversation in the literature.

Research Design and Methods: This section needs to clearly demonstrate how the data will be gathered and analyzed in a systematic and academically sound manner. Here, you need to demonstrate that the conclusions of your research will be both valid and reliable. Common points discussed in the research design and methods section include highlighting the research paradigm, methodologies, intended population or sample to be studied, data collection techniques, and data analysis procedures . Toward the end of this section, you are encouraged to also address ethical considerations and limitations of the research process , but also to explain why you chose your research design and how you are mitigating the identified risks and limitations.

Timeline: Provide an outline of the anticipated timeline for the study. Break it down into its various stages (including data collection, data analysis, and report writing). The goal of this section is firstly to establish a reasonable breakdown of steps for you to follow and secondly to demonstrate to the assessors that your project is practicable and feasible.

Budget: Estimate the costs associated with the research project and include evidence for your estimations. Typical costs include staffing costs, equipment, travel, and data collection tools. When applying for a scholarship, the budget should demonstrate that you are being responsible with your expensive and that your funding application is reasonable.

Expected Outcomes and Implications: A discussion of the anticipated findings or results of the research, as well as the potential contributions to the existing knowledge, theory, or practice in the field. This section should also address the potential impact of the research on relevant stakeholders and any broader implications for policy or practice.

References: A complete list of all the sources cited in the research proposal, formatted according to the required citation style. This demonstrates the researcher’s familiarity with the relevant literature and ensures proper attribution of ideas and information.

Appendices (if applicable): Any additional materials, such as questionnaires, interview guides, or consent forms, that provide further information or support for the research proposal. These materials should be included as appendices at the end of the document.

Research Proposal Examples

Research proposals often extend anywhere between 2,000 and 15,000 words in length. The following snippets are samples designed to briefly demonstrate what might be discussed in each section.

1. Education Studies Research Proposals

See some real sample pieces:

  • Assessment of the perceptions of teachers towards a new grading system
  • Does ICT use in secondary classrooms help or hinder student learning?
  • Digital technologies in focus project
  • Urban Middle School Teachers’ Experiences of the Implementation of
  • Restorative Justice Practices
  • Experiences of students of color in service learning

Consider this hypothetical education research proposal:

The Impact of Game-Based Learning on Student Engagement and Academic Performance in Middle School Mathematics

Abstract: The proposed study will explore multiplayer game-based learning techniques in middle school mathematics curricula and their effects on student engagement. The study aims to contribute to the current literature on game-based learning by examining the effects of multiplayer gaming in learning.

Introduction: Digital game-based learning has long been shunned within mathematics education for fears that it may distract students or lower the academic integrity of the classrooms. However, there is emerging evidence that digital games in math have emerging benefits not only for engagement but also academic skill development. Contributing to this discourse, this study seeks to explore the potential benefits of multiplayer digital game-based learning by examining its impact on middle school students’ engagement and academic performance in a mathematics class.

Literature Review: The literature review has identified gaps in the current knowledge, namely, while game-based learning has been extensively explored, the role of multiplayer games in supporting learning has not been studied.

Research Design and Methods: This study will employ a mixed-methods research design based upon action research in the classroom. A quasi-experimental pre-test/post-test control group design will first be used to compare the academic performance and engagement of middle school students exposed to game-based learning techniques with those in a control group receiving instruction without the aid of technology. Students will also be observed and interviewed in regard to the effect of communication and collaboration during gameplay on their learning.

Timeline: The study will take place across the second term of the school year with a pre-test taking place on the first day of the term and the post-test taking place on Wednesday in Week 10.

Budget: The key budgetary requirements will be the technologies required, including the subscription cost for the identified games and computers.

Expected Outcomes and Implications: It is expected that the findings will contribute to the current literature on game-based learning and inform educational practices, providing educators and policymakers with insights into how to better support student achievement in mathematics.

2. Psychology Research Proposals

See some real examples:

  • A situational analysis of shared leadership in a self-managing team
  • The effect of musical preference on running performance
  • Relationship between self-esteem and disordered eating amongst adolescent females

Consider this hypothetical psychology research proposal:

The Effects of Mindfulness-Based Interventions on Stress Reduction in College Students

Abstract: This research proposal examines the impact of mindfulness-based interventions on stress reduction among college students, using a pre-test/post-test experimental design with both quantitative and qualitative data collection methods .

Introduction: College students face heightened stress levels during exam weeks. This can affect both mental health and test performance. This study explores the potential benefits of mindfulness-based interventions such as meditation as a way to mediate stress levels in the weeks leading up to exam time.

Literature Review: Existing research on mindfulness-based meditation has shown the ability for mindfulness to increase metacognition, decrease anxiety levels, and decrease stress. Existing literature has looked at workplace, high school and general college-level applications. This study will contribute to the corpus of literature by exploring the effects of mindfulness directly in the context of exam weeks.

Research Design and Methods: Participants ( n= 234 ) will be randomly assigned to either an experimental group, receiving 5 days per week of 10-minute mindfulness-based interventions, or a control group, receiving no intervention. Data will be collected through self-report questionnaires, measuring stress levels, semi-structured interviews exploring participants’ experiences, and students’ test scores.

Timeline: The study will begin three weeks before the students’ exam week and conclude after each student’s final exam. Data collection will occur at the beginning (pre-test of self-reported stress levels) and end (post-test) of the three weeks.

Expected Outcomes and Implications: The study aims to provide evidence supporting the effectiveness of mindfulness-based interventions in reducing stress among college students in the lead up to exams, with potential implications for mental health support and stress management programs on college campuses.

3. Sociology Research Proposals

  • Understanding emerging social movements: A case study of ‘Jersey in Transition’
  • The interaction of health, education and employment in Western China
  • Can we preserve lower-income affordable neighbourhoods in the face of rising costs?

Consider this hypothetical sociology research proposal:

The Impact of Social Media Usage on Interpersonal Relationships among Young Adults

Abstract: This research proposal investigates the effects of social media usage on interpersonal relationships among young adults, using a longitudinal mixed-methods approach with ongoing semi-structured interviews to collect qualitative data.

Introduction: Social media platforms have become a key medium for the development of interpersonal relationships, particularly for young adults. This study examines the potential positive and negative effects of social media usage on young adults’ relationships and development over time.

Literature Review: A preliminary review of relevant literature has demonstrated that social media usage is central to development of a personal identity and relationships with others with similar subcultural interests. However, it has also been accompanied by data on mental health deline and deteriorating off-screen relationships. The literature is to-date lacking important longitudinal data on these topics.

Research Design and Methods: Participants ( n = 454 ) will be young adults aged 18-24. Ongoing self-report surveys will assess participants’ social media usage, relationship satisfaction, and communication patterns. A subset of participants will be selected for longitudinal in-depth interviews starting at age 18 and continuing for 5 years.

Timeline: The study will be conducted over a period of five years, including recruitment, data collection, analysis, and report writing.

Expected Outcomes and Implications: This study aims to provide insights into the complex relationship between social media usage and interpersonal relationships among young adults, potentially informing social policies and mental health support related to social media use.

4. Nursing Research Proposals

  • Does Orthopaedic Pre-assessment clinic prepare the patient for admission to hospital?
  • Nurses’ perceptions and experiences of providing psychological care to burns patients
  • Registered psychiatric nurse’s practice with mentally ill parents and their children

Consider this hypothetical nursing research proposal:

The Influence of Nurse-Patient Communication on Patient Satisfaction and Health Outcomes following Emergency Cesarians

Abstract: This research will examines the impact of effective nurse-patient communication on patient satisfaction and health outcomes for women following c-sections, utilizing a mixed-methods approach with patient surveys and semi-structured interviews.

Introduction: It has long been known that effective communication between nurses and patients is crucial for quality care. However, additional complications arise following emergency c-sections due to the interaction between new mother’s changing roles and recovery from surgery.

Literature Review: A review of the literature demonstrates the importance of nurse-patient communication, its impact on patient satisfaction, and potential links to health outcomes. However, communication between nurses and new mothers is less examined, and the specific experiences of those who have given birth via emergency c-section are to date unexamined.

Research Design and Methods: Participants will be patients in a hospital setting who have recently had an emergency c-section. A self-report survey will assess their satisfaction with nurse-patient communication and perceived health outcomes. A subset of participants will be selected for in-depth interviews to explore their experiences and perceptions of the communication with their nurses.

Timeline: The study will be conducted over a period of six months, including rolling recruitment, data collection, analysis, and report writing within the hospital.

Expected Outcomes and Implications: This study aims to provide evidence for the significance of nurse-patient communication in supporting new mothers who have had an emergency c-section. Recommendations will be presented for supporting nurses and midwives in improving outcomes for new mothers who had complications during birth.

5. Social Work Research Proposals

  • Experiences of negotiating employment and caring responsibilities of fathers post-divorce
  • Exploring kinship care in the north region of British Columbia

Consider this hypothetical social work research proposal:

The Role of a Family-Centered Intervention in Preventing Homelessness Among At-Risk Youthin a working-class town in Northern England

Abstract: This research proposal investigates the effectiveness of a family-centered intervention provided by a local council area in preventing homelessness among at-risk youth. This case study will use a mixed-methods approach with program evaluation data and semi-structured interviews to collect quantitative and qualitative data .

Introduction: Homelessness among youth remains a significant social issue. This study aims to assess the effectiveness of family-centered interventions in addressing this problem and identify factors that contribute to successful prevention strategies.

Literature Review: A review of the literature has demonstrated several key factors contributing to youth homelessness including lack of parental support, lack of social support, and low levels of family involvement. It also demonstrates the important role of family-centered interventions in addressing this issue. Drawing on current evidence, this study explores the effectiveness of one such intervention in preventing homelessness among at-risk youth in a working-class town in Northern England.

Research Design and Methods: The study will evaluate a new family-centered intervention program targeting at-risk youth and their families. Quantitative data on program outcomes, including housing stability and family functioning, will be collected through program records and evaluation reports. Semi-structured interviews with program staff, participants, and relevant stakeholders will provide qualitative insights into the factors contributing to program success or failure.

Timeline: The study will be conducted over a period of six months, including recruitment, data collection, analysis, and report writing.

Budget: Expenses include access to program evaluation data, interview materials, data analysis software, and any related travel costs for in-person interviews.

Expected Outcomes and Implications: This study aims to provide evidence for the effectiveness of family-centered interventions in preventing youth homelessness, potentially informing the expansion of or necessary changes to social work practices in Northern England.

Research Proposal Template

This is a template for a 2500-word research proposal. You may find it difficult to squeeze everything into this wordcount, but it’s a common wordcount for Honors and MA-level dissertations.

Your research proposal is where you really get going with your study. I’d strongly recommend working closely with your teacher in developing a research proposal that’s consistent with the requirements and culture of your institution, as in my experience it varies considerably. The above template is from my own courses that walk students through research proposals in a British School of Education.


Chris Drew (PhD)

Dr. Chris Drew is the founder of the Helpful Professor. He holds a PhD in education and has published over 20 articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education. [Image Descriptor: Photo of Chris]

  • Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 41 Important Classroom Expectations (for This School Year)
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8 thoughts on “17 Research Proposal Examples”

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Very excellent research proposals

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Dear Sir, I need some help to write an educational research proposal. Thank you.

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Hi Levi, use the site search bar to ask a question and I’ll likely have a guide already written for your specific question. Thanks for reading!

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very good research proposal

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Thank you so much sir! ❤️

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Research sampler 5: examples in learning mathematics, by annie and john selden.

Successful Math Majors Generate Their Own Examples Being Asked For Examples Can Be Disconcerting Generating Counterexamples That Are Explanatory "If I Don't Know What It Says, How Can I Find an Example of It?" Coda

Examining examples and non-examples can help students understand definitions. While a square may be defined as a quadrilateral with four equal sides and one right angle, seeing concrete examples of squares of various sizes, as well as considering rectangular non-examples, can help children clarify the notion of square. When we teach linear algebra and introduce the concept of subspace, we often provide examples and non-examples for students. We may point out that the polynomials of degree less than or equal to two form a subspace of the space of all polynomials, whereas the polynomials of degree two do not. Is the provision of such examples always desirable? Would it perhaps be better to ask undergraduate students to provide their own examples and non-examples? Would they be able to? Given a false conjecture, would students be able to come up with counterexamples? Several studies shed light on these questions.

Successful Math Majors Generate Their Own Examples

In upper-division courses like abstract algebra and real analysis, students often encounter a host of formal definitions, many new to them. After presenting a few examples and non-examples along with a few proofs of theorems, we hope they will use these definitions to tackle problems, examine conjectures, and construct their own proofs. Is this the best way to proceed? How do such students deal with new definitions?

To answer this question, Randall P. Dahlberg and David L. Housman of Allegheny College conducted an in-depth study of eleven undergraduate students - ten seniors and one junior. All but one, who was in computer science, were math majors. The students had successfully completed introductory real analysis and algebra, as well as courses in linear algebra and foundations and a seminar covering set theory and the foundations of analysis. In individually conducted audio-taped interviews, the authors presented the students with a written definition of a "fine function," which they had made up to see how the students would deal with a formally defined concept. A function was called fine if it had a root (zero) at each integer. When interviewed, students were first asked to study this definition for five to ten minutes, saying or writing as much as possible of what they were thinking, after which they were asked to generate examples and non-examples of "fine functions." Subsequently, they were given functions, such as

and asked to determine whether these were examples and, if so, why. Next, they were asked to determine the truth of four conjectures, such as "No polynomial is a fine function." Finally they were asked about their perceptions of the interview.

Four basic learning strategies were used by the students on being presented with this new definition - example generation, reformulation, decomposition and synthesis, and memorization. Examples generated included the constant zero function and a sinusoidal graph with integer x -intercepts. Reformulations included

Decomposition and synthesis included underlining parts of the definition and asking about the meaning of "root." Two students simply read the definition - they could not provide examples without interviewer help and were the ones who most often misinterpreted the definition. They found the interview quite different from their usual mathematics classes, where examples and explanations were provided.

Of these four strategies, example generation (together with reflection) elicited the most powerful "learning events," i.e., instances where the authors thought students made real progress in understanding the newly introduced concept. Students who initially employed example generation as their learning strategy came up with a variety of discontinuous, periodic continuous, and non-periodic continuous examples and were able to use these in their explanations. Those who employed memorization or decomposition and synthesis as their learning strategies often misinterpreted the definition, e.g., interpreting the phrase "root at each integer" to mean a fine function must vanish at each integer in its domain, but that need not include all integers. Students who employed reformulation as their learning strategy developed algorithms to decide whether functions given them were fine, but had difficulty providing counterexamples to false conjectures. [Cf. "Facilitating Learning Events Through Example Generation," Educ. Studies in Math. 33, 283-299, 1997.]

Finally, Dahlberg and Housman note the relative ineffectualness of their attempted interventions. One student agreed, after a question and answer period with the interviewer, that the zero function was indeed a fine function, but immediately switched her attention to other ideas, not returning until much later when, through self-discovery, she actually realized the zero function was a fine function. Dahlberg and Housman suggest it might be beneficial to introduce students to new concepts by having them generate their own examples or having them decide whether teacher-provided candidates are examples or non-examples, before providing students examples and explanations. However, some of their students were reluctant to engage in either example generation or usage -- a not uncommon phenomenon in such circumstances.

Being Asked For Examples Can Be Disconcerting

Coming up with examples requires different cognitive skills from carrying out algorithms - one needs to look at mathematical objects in terms of their properties. To be asked for an example, whether of a "fine function" or something else, can be disconcerting. Students have no prelearned algorithms to show the "correct way." This is what Orit Hazzan and Rina Zazkis, of the Technion - Israel Institute of Technology, found when they asked three groups of preservice elementary teachers to provide examples of (1) a 6-digit number divisible first by 9, then by 17, (2) a function whose value at x = 3 is -2, and (3) a sample space and an event that has probability 2/7 in that space. In addition, they asked the students to explain how they generated their examples and to provide five additional examples.

The students used a variety of approaches to generate examples, beginning with trial and error, e.g., some simply picked a number at random and checked whether it was divisible by 9. Others picked a number N , and upon dividing by 17 and getting a remainder of 2, would use N -2 for their next trial. Students often found constructing examples and making the necessary choices difficult, e.g., they inquired of the interviewers whether the elements of the sample space were to be numbers, letters, or other objects. Some students designed their own algorithms for generating functions, e.g., one focused on y = ax + b , plugged in (3, -2) to get -2 = a *3 + b , chose a = 2 and solved for b = -8, finally declaring her function to be y = 2 x - 8.

Interestingly, very few students produced "trivial examples," such as 170,000 for a 6-digit number divisible by 17 or y = -2 as their function. Hazzan and Zazkis conjecture that these examples might not be seen as prototypical - a function is expected to involve x and a 6-digit number is seen as having a wider variety of digits. There was also a strong tendency to (directly) check the correctness of examples, e.g., some students who had created a number divisible by 17 by choosing a multiplier and performing the multiplication, verified the correctness of their example by division. Quite a number of students had difficulty dealing with "degrees of freedom," e.g., in order to find a number divisible by 9, one student who knew the sum of the digits needed to be divisible by 9, first chose 18, noted that 8 and 2 make 10, then broke 8 into the sum of 4, 3, and 1, and declared that 82431 should be divisible by 9. When asked for another strategy, she suggested something very similar -- making the initial sum 27, instead of 18.

Constructing examples proved to be more difficult for these students than checking the divisibility of a number, calculating the value of a function, or finding the probability of an event. They were often uncertain how to proceed and were especially troubled by having to make choices in mathematics. The authors suggest that teachers at all levels assign more "give an example" problems. [Cf. "Constructing Knowledge by Constructing Examples for Mathematical Concepts," Proceedings of the 21st Conference of the International Group for the Psychology of Mathematics Education , Vol. 4, 299-306, 1997]

Furthermore, when students are allowed to discuss mathematical ideas and propose conjectures in class, teachers need to be able to evaluate student-generated examples, as well as to be able to propose counterexamples for their students' consideration. Students quite often fail to see a single counterexample as disproving a conjecture. This can happen when a counterexample is perceived as "the only" one that exists, rather than being seen as generic, e.g., sometimes the square root of 2 is considered the only irrational or | x | is perceived as the only continuous, nondifferentiable function.

Generating Counterexamples That Are Explanatory

Perhaps not surprisingly, experienced secondary mathematics teachers are better at generating explanatory counterexamples than preservice teachers. Irit Peled, University of Haifa, and Orit Zaslavsky, the Technion, asked some of each to generate at least one counterexample for each of the two following unfamiliar, false geometry statements supposedly given by a secondary student. (1) Two rectangles, having congruent diagonals, are congruent. (2) Two parallelograms, having one congruent side and one congruent diagonal, are congruent. They were also asked to explain how they came up with their counterexamples. None generated more than one counterexample for each task.

Two groups participated in the study -- 38 inservice teachers, most of whom had more than five years of teaching experience and a B.Sc. in mathematics and 45 third year student-teachers who had completed several advanced undergraduate mathematics courses. For the first conjecture (Task 1), 97% of the inservice teachers gave adequate counterexamples, i.e., ones that refuted the claim, but only 53% of the student-teachers did so. For the second conjecture (Task 2), 76% of the teachers and 42% of the student-teachers gave adequate counterexamples.

The counterexamples were analyzed for their explanatory power as specific, semi-general, and general. A specific counterexample is one which contradicts the claim, but gives no indication as to how one might construct similar or related counterexamples. For example, for Task 1 one subject carefully drew two rectangles of different dimensions, but with congruent diagonals. A counterexample was called semi-general if it provided some idea how one might generate similar or related counterexamples, but did not tell "the whole story" or did not cover "the whole space" of counterexamples. For instance, on Task 1, one subject drew two rectangles with congruent diagonals, but the angle between the two diagonals of second rectangle was indicated as twice that of the first rectangle. (Here it should be noted that, while some conjectures might not lend themselves to the generation of numerous counterexamples, i.e., they might be correct except for a small number of special "pathological" cases, these two conjectures were chosen to be far from "almost correct.") A general counterexample provides insight as to why a conjecture is false and suggests a way to generate an entire counterexample space. In response to Task 1, one subject specified that the angle between the diagonals could be arbitrary, rather than merely double that of the first rectangle.

Both teachers and student-teachers produced counterexamples of all the above types, but the former produced more semi-general and general counterexamples (92% vs. 38% on Task 1, and 61% vs. 33% on Task 2). Both of these types were labeled explanatory by the authors. The difficulty in suggesting only a specific counterexample lies in its potential for misleading students, whereas the pedagogical value of explanatory counterexamples lies in their ability to provide insight into why a conjecture fails. The authors suggest that both prospective and in-service mathematics teachers could benefit from an analysis and discussion of the pedagogical aspects of counterexamples. [Cf. "Counter-Examples That (Only) Prove and Counter-Examples That (Also) Explain," Focus on Learning Problems in Mathematics 19 (3), 49-61, 1997.]

"If I Don't Know What It Says, How Can I Find an Example of It?"

This hypothetical quote, illustrates the chicken-and-egg quandary some students might typically face when encountering a formal definition, whether of "fine function" or quotient group. A definition asserts the existence of something having certain properties. However, the student has often never seen or considered such a thing. To give an example or non-example, he/she would need at least some understanding of the concept. But how can he/she obtain such understanding? A good, and possibly the best, way seems to be through an examination of examples. Thus, the student is faced with an epistemological dilemma: Mathematical definitions, by themselves, supply few (psychological) meanings. Meanings derive from properties. Properties, in turn, depend on definitions. [This is a paraphrase from Richard Noss' plenary address to the September 1996 Research in Collegiate Mathematics Education Conference, as reported in Focus 17(1), 1&3, February 1997.] For mathematicians, this does not seem to be a dilemma. We suspect they view definitions differently than students - this allows them to search for examples in order to gain understandings of formal definitions.

Not only does such circularity play a role in students' failure to construct examples, so does their limited knowledge of concepts involved in a formal definition. When Zaslavsky and Peled asked 67 preservice and 36 inservice secondary teachers to provide examples of binary operations which were commutative and nonassociative, their subjects had great difficulty. Only 33% of the experienced teachers and 4% of the third-year undergraduate students came up with complete, correct, and well-justified examples. Just 56% of the experienced teachers and 31% of the student teachers were able to provide any kind of example (correct or incorrect). Upon investigating why this might be so, the authors found their subjects' underlying mathematical knowledge was deficient. For example, one subject defined a * b = | a + b | and claimed this was nonassociative because | a + b | + | c | does not equal | a | + | b + c |. Another proposed the operation of subtraction claiming it was commutative because -2 - 3 = -3 - 2, rather than 3 - (-2). Yet another proposed the unary operation

and tried to check commutativity using

The authors suggest their subjects tended to conflate commutativity and associativity due to the way the "issue of order" is treated in schools. For example, when a child is asked to calculate 6 + 7 + 4, he/she is usually encourage to do it more efficiently as (6 + 4 ) + 7 and told "order doesn't matter." [Cf. "Inhibiting Factors in Generating Examples by Mathematics Teachers and Student Teachers: The Case of Binary Operations," JRME 27(1), 67-78, 1996.]

Dahlberg and Housman also noted that their undergraduate subjects had trouble with the underlying concepts, e.g., function and root, making it hard to generate examples and non-examples of "fine functions." One student identified "root" with "continuity," three others initially thought the graph of the zero function was a point, and one did not believe the zero function was periodic. In addition, most students' initially thought in terms of functions which were nonconstant polynomials or continuous.

Since success in mathematics, especially at the advanced undergraduate and graduate levels appears to be associated with the ability to generate examples and counterexamples, what is the best way to develop this ability? One suggestion, given above, is to ask students at all levels to "give me an example of . . . ". Granted the inherent epistemological difficulties of finding examples for oneself, are we, in a well-intentioned attempt to help students understand newly defined concepts, ultimately hobbling them, by providing them with predigested examples of our own? Are we inadvertently denying students the opportunity to learn to generate examples for themselves? Difficulties with the strikingly simple idea of "fine function" suggest some students may be excessively dependent upon explicit instruction. Another in-between suggestion, given above, is to provide students with a list of potential examples (or counterexamples) and ask them to decide whether they are indeed examples (or counterexamples) and why. Are there other ways we might help students become example generators? Finally, a tendency to generate examples is not the same as an ability to do so -- it would be interesting to know how each of these relates to understanding and doing mathematics.


research proposal sample mathematics

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    Action research is a methodology that has been found to be valuable as a problem-solving tool. It can provide opportunities for reflection, improvement, and transformation of teaching. The purpose of this study is to better understand these claims about the benefits of action research. Several research questions stand out: How is action

  15. How to Make Research Proposal for Mathematics PhD Project

    (Potential) solutions. Costs (both in human efforts and budgetary ones). Possible benefits. Of course, the action research proposal in mathematics content will change according to the specific mathematics research topics and corresponding college guidelines.

  16. How to write a postdoc research proposal in mathematics?

    So you have to make a few points in your proposal: [ WHY] that the problem you're studying is interesting and worthwhile. [ HOW] that your line of attack (briefly sketched) is plausible. [ WHO] and that you have the right skills to execute this plan. and all of this in 2 pages !

  17. PDF Sample Research Proposal for PhD in Mathematics

    RESEARCH PROPOSAL FOR PHD IN MATHEMATICS SAMPLE STUDYING MATHEMATICS THROUGH ART USING EDUCATIONAL GAMES Introduction The advancements in the field of digital technology are now currently making huge changes in our world. This gives birth to various digital technologies which are observed to be progressive.

  18. Mathematics Research Proposals Samples For Students

    Mathematics Research Proposals Samples For Students 24 samples of this type Regardless of how high you rate your writing abilities, it's always an appropriate idea to check out an expertly written Research Proposal example, especially when you're dealing with a sophisticated Mathematics topic.

  19. M.sc and Ph.d. Research Proposal in Mathematical Sciences Structure of

    Request PDF | M.SC AND PH.D. RESEARCH PROPOSAL IN MATHEMATICAL SCIENCES STRUCTURE OF THE PROPOSAL 1. TITLE | This is a research proposal guideline for postgraduate students doing M.Sc or...

  20. 17 Research Proposal Examples (2024)

    By Chris Drew (PhD) / September 21, 2023 A research proposal systematically and transparently outlines a proposed research project. The purpose of a research proposal is to demonstrate a project's viability and the researcher's preparedness to conduct an academic study. It serves as a roadmap for the researcher.

  21. Research Sampler 5: Examples in Learning Mathematics

    Some students designed their own algorithms for generating functions, e.g., one focused on y = ax + b, plugged in (3, -2) to get -2 = a *3 + b, chose a = 2 and solved for b = -8, finally declaring her function to be y = 2 x - 8. Interestingly, very few students produced "trivial examples," such as 170,000 for a 6-digit number divisible by 17 or ...

  22. Applied Mathematics (research proposal form) PhD Projects ...

    We have 39 Applied Mathematics (research proposal form) PhD Projects, Programmes & Scholarships A PhD in Applied Mathematics involves trying to simplify complex real-world problems to simple mathematical equations and working on finding possible solutions.

  23. Action Research Proposal: Mathematics Problem-Solving Skill ...

    Jul 24, 2022 8:09 PM EDT Unsplash, via Moren Hsu It cannot be denied that problem-solving is an important part of mathematics education. Mathematics, in general, is an important subject because of its practical role to a person and society as a whole.