visual representation 8 letters

VISUAL REPRESENTATION Crossword clue

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Visual representation - Crossword Clue

Below are possible answers for the crossword clue Visual representation .

5 letter answer(s) to visual representation

• (Jungian psychology) a personal facade that one presents to the world; "a public image is as fragile as Humpty Dumpty"
• (mathematics) the set of values of the dependent variable for which a function is defined; "the image of f(x) = x^2 is the set of all non-negative real numbers if the domain of the function is the set of all real numbers"
• a representation of a person (especially in the form of sculpture); "the coin bears an effigy of Lincoln"; "the emperor's tomb had his image carved in stone"
• a standard or typical example; "he is the prototype of good breeding"; "he provided America with an image of the good father"
• a visual representation (of an object or scene or person or abstraction) produced on a surface; "they showed us the pictures of their wedding"; "a movie is a series of images projected so rapidly that the eye integrates them"
• an iconic mental representation; "her imagination forced images upon her too awful to contemplate"

9 letter answer(s) to visual representation

• a representation by picture or portraiture
• a word picture of a person's appearance and character
• acting the part of a character on stage; dramatically representing the character by speech and action and gesture
• any likeness of a person, in any medium; "the photographer made excellent portraits"
• representation by drawing or painting etc

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Visual representation (9)

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(Other definitions for portrayal that I've seen before include "Artistic depiction" , "Depicting characters" , "Study" , "Representation" , "It depicts" .)

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Visual Representation

What is visual representation.

Visual Representation refers to the principles by which markings on a surface are made and interpreted. Designers use representations like typography and illustrations to communicate information, emotions and concepts. Color, imagery, typography and layout are crucial in this communication.

Alan Blackwell, cognition scientist and professor, gives a brief introduction to visual representation:

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We can see visual representation throughout human history, from cave drawings to data visualization :

Art uses visual representation to express emotions and abstract ideas.

Financial forecasting graphs condense data and research into a more straightforward format.

Icons on user interfaces (UI) represent different actions users can take.

The color of a notification indicates its nature and meaning.

Van Gogh's "The Starry Night" uses visuals to evoke deep emotions, representing an abstract, dreamy night sky. It exemplifies how art can communicate complex feelings and ideas.

© Public domain

Importance of Visual Representation in Design

Designers use visual representation for internal and external use throughout the design process . For example:

Storyboards are illustrations that outline users’ actions and where they perform them.

Sitemaps are diagrams that show the hierarchy and navigation structure of a website.

Wireframes are sketches that bring together elements of a user interface's structure.

Usability reports use graphs and charts to communicate data gathered from usability testing.

User interfaces visually represent information contained in applications and computerized devices.

This usability report is straightforward to understand. Yet, the data behind the visualizations could come from thousands of answered surveys.

© Interaction Design Foundation, CC BY-SA 4.0

Visual representation simplifies complex ideas and data and makes them easy to understand. Without these visual aids, designers would struggle to communicate their ideas, findings and products . For example, it would be easier to create a mockup of an e-commerce website interface than to describe it with words.

Visual representation simplifies the communication of designs. Without mockups, it would be difficult for developers to reproduce designs using words alone.

Types of Visual Representation

Below are some of the most common forms of visual representation designers use.

Text and Typography

Text represents language and ideas through written characters and symbols. Readers visually perceive and interpret these characters. Typography turns text into a visual form, influencing its perception and interpretation.

We have developed the conventions of typography over centuries , for example, in documents, newspapers and magazines. These conventions include:

Text arranged on a grid brings clarity and structure. Gridded text makes complex information easier to navigate and understand. Tables, columns and other formats help organize content logically and enhance readability.

Contrasting text sizes create a visual hierarchy and draw attention to critical areas. For example, headings use larger text while body copy uses smaller text. This contrast helps readers distinguish between primary and secondary information.

Adequate spacing and paragraphing improve the readability and appearance of the text. These conventions prevent the content from appearing cluttered. Spacing and paragraphing make it easier for the eye to follow and for the brain to process the information.

Balanced image-to-text ratios create engaging layouts. Images break the monotony of text, provide visual relief and illustrate or emphasize points made in the text. A well-planned ratio ensures neither text nor images overwhelm each other. Effective ratios make designs more effective and appealing.

Designers use these conventions because people are familiar with them and better understand text presented in this manner.

This table of funerals from the plague in London in 1665 uses typographic conventions still used today. For example, the author arranged the information in a table and used contrasting text styling to highlight information in the header.

Illustrations and Drawings

Designers use illustrations and drawings independently or alongside text. An example of illustration used to communicate information is the assembly instructions created by furniture retailer IKEA. If IKEA used text instead of illustrations in their instructions, people would find it harder to assemble the furniture.

IKEA assembly instructions use illustrations to inform customers how to build their furniture. The only text used is numeric to denote step and part numbers. IKEA communicates this information visually to: 1. Enable simple communication, 2. Ensure their instructions are easy to follow, regardless of the customer’s language.

© IKEA, Fair use

Illustrations and drawings can often convey the core message of a visual representation more effectively than a photograph. They focus on the core message , while a photograph might distract a viewer with additional details (such as who this person is, where they are from, etc.)

For example, in IKEA’s case, photographing a person building a piece of furniture might be complicated. Further, photographs may not be easy to understand in a black-and-white print, leading to higher printing costs. To be useful, the pictures would also need to be larger and would occupy more space on a printed manual, further adding to the costs.

But imagine a girl winking—this is something we can easily photograph. 

Ivan Sutherland, creator of the first graphical user interface, used his computer program Sketchpad to draw a winking girl. While not realistic, Sutherland's representation effectively portrays a winking girl. The drawing's abstract, generic elements contrast with the distinct winking eye. The graphical conventions of lines and shapes represent the eyes and mouth. The simplicity of the drawing does not draw attention away from the winking.

A photo might distract from the focused message compared to Sutherland's representation. In the photo, the other aspects of the image (i.e., the particular person) distract the viewer from this message.

© Ivan Sutherland, CC BY-SA 3.0 and Amina Filkins, Pexels License

Information and Data Visualization

Designers and other stakeholders use data and information visualization across many industries.

Data visualization uses charts and graphs to show raw data in a graphic form. Information visualization goes further, including more context and complex data sets. Information visualization often uses interactive elements to share a deeper understanding.

For example, most computerized devices have a battery level indicator. This is a type of data visualization. IV takes this further by allowing you to click on the battery indicator for further insights. These insights may include the apps that use the most battery and the last time you charged your device.

macOS displays a battery icon in the menu bar that visualizes your device’s battery level. This is an example of data visualization. Meanwhile, macOS’s settings tell you battery level over time, screen-on-usage and when you last charged your device. These insights are actionable; users may notice their battery drains at a specific time. This is an example of information visualization.

© Low Battery by Jemis Mali, CC BY-NC-ND 4.0, and Apple, Fair use

Information visualization is not exclusive to numeric data. It encompasses representations like diagrams and maps. For example, Google Maps collates various types of data and information into one interface:

Data Representation: Google Maps transforms complex geographical data into an easily understandable and navigable visual map.

Interactivity: Users can interactively customize views that show traffic, satellite imagery and more in real-time.

Layered Information: Google Maps layers multiple data types (e.g., traffic, weather) over geographical maps for comprehensive visualization.

User-Centered Design : The interface is intuitive and user-friendly, with symbols and colors for straightforward data interpretation.

The volume of data contained in one screenshot of Google Maps is massive. However, this information is presented clearly to the user. Google Maps highlights different terrains with colors and local places and businesses with icons and colors. The panel on the left lists the selected location’s profile, which includes an image, rating and contact information.

© Google, Fair use

Symbolic Correspondence

Symbolic correspondence uses universally recognized symbols and signs to convey specific meanings . This method employs widely recognized visual cues for immediate understanding. Symbolic correspondence removes the need for textual explanation.

For instance, a magnifying glass icon in UI design signifies the search function. Similarly, in environmental design, symbols for restrooms, parking and amenities guide visitors effectively.

The Interaction Design Foundation (IxDF) website uses the universal magnifying glass symbol to signify the search function. Similarly, the play icon draws attention to a link to watch a video.

How Designers Create Visual Representations

Visual language.

Designers use elements like color , shape and texture to create a communicative visual experience. Designers use these 8 principles:

Size – Larger elements tend to capture users' attention readily.

Color – Users are typically drawn to bright colors over muted shades.

Contrast – Colors with stark contrasts catch the eye more effectively.

Alignment – Unaligned elements are more noticeable than those aligned ones.

Repetition – Similar styles repeated imply a relationship in content.

Proximity – Elements placed near each other appear to be connected.

Whitespace – Elements surrounded by ample space attract the eye.

Texture and Style – Users often notice richer textures before flat designs.

The 8 visual design principles.

In web design , visual hierarchy uses color and repetition to direct the user's attention. Color choice is crucial as it creates contrast between different elements. Repetition helps to organize the design—it uses recurring elements to establish consistency and familiarity.

In this video, Alan Dix, Professor and Expert in Human-Computer Interaction, explains how visual alignment affects how we read and absorb information:

Correspondence Techniques

Designers use correspondence techniques to align visual elements with their conceptual meanings. These techniques include color coding, spatial arrangement and specific imagery. In information visualization, different colors can represent various data sets. This correspondence aids users in quickly identifying trends and relationships .

Color coding enables the stakeholder to see the relationship and trend between the two pie charts easily.

In user interface design, correspondence techniques link elements with meaning. An example is color-coding notifications to state their nature. For instance, red for warnings and green for confirmation. These techniques are informative and intuitive and enhance the user experience.

The IxDF website uses blue for call-to-actions (CTAs) and red for warnings. These colors inform the user of the nature of the action of buttons and other interactive elements.

Perception and Interpretation

If visual language is how designers create representations, then visual perception and interpretation are how users receive those representations. Consider a painting—the viewer’s eyes take in colors, shapes and lines, and the brain perceives these visual elements as a painting.

In this video, Alan Dix explains how the interplay of sensation, perception and culture is crucial to understanding visual experiences in design:

Copyright holder: Michael Murphy _ Appearance time: 07:19 - 07:37 _ Link: https://www.youtube.com/watch?v=C67JuZnBBDc

Visual perception principles are essential for creating compelling, engaging visual representations. For example, Gestalt principles explain how we perceive visual information. These rules describe how we group similar items, spot patterns and simplify complex images. Designers apply Gestalt principles to arrange content on websites and other interfaces. This application creates visually appealing and easily understood designs.

In this video, design expert and teacher Mia Cinelli discusses the significance of Gestalt principles in visual design . She introduces fundamental principles, like figure/ground relationships, similarity and proximity.

Interpretation

Everyone's experiences, culture and physical abilities dictate how they interpret visual representations. For this reason, designers carefully consider how users interpret their visual representations. They employ user research and testing to ensure their designs are attractive and functional.

Leonardo da Vinci's "Mona Lisa", is one of the most famous paintings in the world. The piece is renowned for its subject's enigmatic expression. Some interpret her smile as content and serene, while others see it as sad or mischievous. Not everyone interprets this visual representation in the same way.

Color is an excellent example of how one person, compared to another, may interpret a visual element. Take the color red:

In Chinese culture, red symbolizes luck, while in some parts of Africa, it can mean death or illness.

A personal experience may mean a user has a negative or positive connotation with red.

People with protanopia and deuteranopia color blindness cannot distinguish between red and green.

In this video, Joann and Arielle Eckstut, leading color consultants and authors, explain how many factors influence how we perceive and interpret color:

Learn More about Visual Representation

Read Alan Blackwell’s chapter on visual representation from The Encyclopedia of Human-Computer Interaction.

Learn about the F-Shaped Pattern For Reading Web Content from Jakob Nielsen.

Read Smashing Magazine’s article, Visual Design Language: The Building Blocks Of Design .

Take the IxDF’s course, Perception and Memory in HCI and UX .

Questions related to Visual Representation

Some highly cited research on visual representation and related topics includes:

Roland, P. E., & Gulyás, B. (1994). Visual imagery and visual representation. Trends in Neurosciences, 17(7), 281-287. Roland and Gulyás' study explores how the brain creates visual imagination. They look at whether imagining things like objects and scenes uses the same parts of the brain as seeing them does. Their research shows the brain uses certain areas specifically for imagination. These areas are different from the areas used for seeing. This research is essential for understanding how our brain works with vision.

Lurie, N. H., & Mason, C. H. (2007). Visual Representation: Implications for Decision Making. Journal of Marketing, 71(1), 160-177.

This article looks at how visualization tools help in understanding complicated marketing data. It discusses how these tools affect decision-making in marketing. The article gives a detailed method to assess the impact of visuals on the study and combination of vast quantities of marketing data. It explores the benefits and possible biases visuals can bring to marketing choices. These factors make the article an essential resource for researchers and marketing experts. The article suggests using visual tools and detailed analysis together for the best results.

Lohse, G. L., Biolsi, K., Walker, N., & Rueter, H. H. (1994, December). A classification of visual representations. Communications of the ACM, 37(12), 36+.

This publication looks at how visuals help communicate and make information easier to understand. It divides these visuals into six types: graphs, tables, maps, diagrams, networks and icons. The article also looks at different ways these visuals share information effectively.

​​If you’d like to cite content from the IxDF website , click the ‘cite this article’ button near the top of your screen.

Some recommended books on visual representation and related topics include:

Chaplin, E. (1994). Sociology and Visual Representation (1st ed.) . Routledge.

Chaplin's book describes how visual art analysis has changed from ancient times to today. It shows how photography, post-modernism and feminism have changed how we see art. The book combines words and images in its analysis and looks into real-life social sciences studies.

Mitchell, W. J. T. (1994). Picture Theory. The University of Chicago Press.

Mitchell's book explores the important role and meaning of pictures in the late twentieth century. It discusses the change from focusing on language to focusing on images in cultural studies. The book deeply examines the interaction between images and text in different cultural forms like literature, art and media. This detailed study of how we see and read visual representations has become an essential reference for scholars and professionals.

Koffka, K. (1935). Principles of Gestalt Psychology. Harcourt, Brace & World.

"Principles of Gestalt Psychology" by Koffka, released in 1935, is a critical book in its field. It's known as a foundational work in Gestalt psychology, laying out the basic ideas of the theory and how they apply to how we see and think. Koffka's thorough study of Gestalt psychology's principles has profoundly influenced how we understand human perception. This book has been a significant reference in later research and writings.

A visual representation, like an infographic or chart, uses visual elements to show information or data. These types of visuals make complicated information easier to understand and more user-friendly.

Designers harness visual representations in design and communication. Infographics and charts, for instance, distill data for easier audience comprehension and retention.

For an introduction to designing basic information visualizations, take our course, Information Visualization .

Text is a crucial design and communication element, transforming language visually. Designers use font style, size, color and layout to convey emotions and messages effectively.

Designers utilize text for both literal communication and aesthetic enhancement. Their typography choices significantly impact design aesthetics, user experience and readability.

Designers should always consider text's visual impact in their designs. This consideration includes font choice, placement, color and interaction with other design elements.

In this video, design expert and teacher Mia Cinelli teaches how Gestalt principles apply to typography:

Designers use visual elements in projects to convey information, ideas, and messages. Designers use images, colors, shapes and typography for impactful designs.

In UI/UX design, visual representation is vital. Icons, buttons and colors provide contrast for intuitive, user-friendly website and app interfaces.

Graphic design leverages visual representation to create attention-grabbing marketing materials. Careful color, imagery and layout choices create an emotional connection.

Product design relies on visual representation for prototyping and idea presentation. Designers and stakeholders use visual representations to envision functional, aesthetically pleasing products.

Our brains process visuals 60,000 times faster than text. This fact highlights the crucial role of visual representation in design.

Our course, Visual Design: The Ultimate Guide , teaches you how to use visual design elements and principles in your work effectively.

Visual representation, crucial in UX, facilitates interaction, comprehension and emotion. It combines elements like images and typography for better interfaces.

Effective visuals guide users, highlight features and improve navigation. Icons and color schemes communicate functions and set interaction tones.

UX design research shows visual elements significantly impact emotions. 90% of brain-transmitted information is visual.

To create functional, accessible visuals, designers use color contrast and consistent iconography. These elements improve readability and inclusivity.

An excellent example of visual representation in UX is Apple's iOS interface. iOS combines a clean, minimalist design with intuitive navigation. As a result, the operating system is both visually appealing and user-friendly.

Michal Malewicz, Creative Director and CEO at Hype4, explains why visual skills are important in design:

Learn more about UI design from Michal in our Master Class, Beyond Interfaces: The UI Design Skills You Need to Know .

The fundamental principles of effective visual representation are:

Clarity : Designers convey messages clearly, avoiding clutter.

Simplicity : Embrace simple designs for ease and recall.

Emphasis : Designers highlight key elements distinctively.

Balance : Balance ensures design stability and structure.

Alignment : Designers enhance coherence through alignment.

Contrast : Use contrast for dynamic, distinct designs.

Repetition : Repeating elements unify and guide designs.

Designers practice these principles in their projects. They also analyze successful designs and seek feedback to improve their skills.

Read our topic description of Gestalt principles to learn more about creating effective visual designs. The Gestalt principles explain how humans group elements, recognize patterns and simplify object perception.

Color theory is vital in design, helping designers craft visually appealing and compelling works. Designers understand color interactions, psychological impacts and symbolism. These elements help designers enhance communication and guide attention.

Designers use complementary , analogous and triadic colors for contrast, harmony and balance. Understanding color temperature also plays a crucial role in design perception.

Color symbolism is crucial, as different colors can represent specific emotions and messages. For instance, blue can symbolize trust and calmness, while red can indicate energy and urgency.

Cultural variations significantly influence color perception and symbolism. Designers consider these differences to ensure their designs resonate with diverse audiences.

For actionable insights, designers should:

Experiment with color schemes for effective messaging. 

Assess colors' psychological impact on the audience. 

Use color contrast to highlight critical elements. 

Ensure color choices are accessible to all.

In this video, Joann and Arielle Eckstut, leading color consultants and authors, give their six tips for choosing color:

Learn more about color from Joann and Arielle in our Master Class, How To Use Color Theory To Enhance Your Designs .

Typography and font choice are crucial in design, impacting readability and mood. Designers utilize them for effective communication and expression.

Designers' perception of information varies with font type. Serif fonts can imply formality, while sans-serifs can give a more modern look.

Typography choices by designers influence readability and user experience. Well-spaced, distinct fonts enhance readability, whereas decorative fonts may hinder it.

Designers use typography to evoke emotions and set a design's tone. Choices in font size, style and color affect the emotional impact and message clarity.

Designers use typography to direct attention, create hierarchy and establish rhythm. These benefits help with brand recognition and consistency across mediums.

Read our article to learn how web fonts are critical to the online user experience .

Designers create a balance between simplicity and complexity in their work. They focus on the main messages and highlight important parts. Designers use the principles of visual hierarchy, like size, color and spacing. They also use empty space to make their designs clear and understandable.

The Gestalt law of Prägnanz suggests people naturally simplify complex images. This principle aids in making even intricate information accessible and engaging.

Through iteration and feedback, designers refine visuals. They remove extraneous elements and highlight vital information. Testing with the target audience ensures the design resonates and is comprehensible.

Michal Malewicz explains how to master hierarchy in UI design using the Gestalt rule of proximity:

Literature on Visual Representation

Here’s the entire UX literature on Visual Representation by the Interaction Design Foundation, collated in one place:

Learn more about Visual Representation

Take a deep dive into Visual Representation with our course Perception and Memory in HCI and UX .

How does all of this fit with interaction design and user experience? The simple answer is that most of our understanding of human experience comes from our own experiences and just being ourselves. That might extend to people like us, but it gives us no real grasp of the whole range of human experience and abilities. By considering more closely how humans perceive and interact with our world, we can gain real insights into what designs will work for a broader audience: those younger or older than us, more or less capable, more or less skilled and so on.

“You can design for all the people some of the time, and some of the people all the time, but you cannot design for all the people all the time.“ – William Hudson (with apologies to Abraham Lincoln)

While “design for all of the people all of the time” is an impossible goal, understanding how the human machine operates is essential to getting ever closer. And of course, building solutions for people with a wide range of abilities, including those with accessibility issues, involves knowing how and why some human faculties fail. As our course tutor, Professor Alan Dix, points out, this is not only a moral duty but, in most countries, also a legal obligation.

Portfolio Project

In the “ Build Your Portfolio: Perception and Memory Project ”, you’ll find a series of practical exercises that will give you first-hand experience in applying what we’ll cover. If you want to complete these optional exercises, you’ll create a series of case studies for your portfolio which you can show your future employer or freelance customers.

This in-depth, video-based course is created with the amazing Alan Dix , the co-author of the internationally best-selling textbook  Human-Computer Interaction and a superstar in the field of Human-Computer Interaction . Alan is currently a professor and Director of the Computational Foundry at Swansea University.

Gain an Industry-Recognized UX Course Certificate

Use your industry-recognized Course Certificate on your resume , CV , LinkedIn profile or your website.

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Crossword Solver > Clues > Crossword-Clue: a visual representation of an object or scene or person produced on a surface

A VISUAL REPRESENTATION OF AN OBJECT OR SCENE OR PERSON PRODUCED ON A SURFACE Crossword Clue

• A visual presentation of an object or scene (81.15%)
• a visual representation of something (53.55%)
• a representation of a person (52.15%)
• Person on the scene (47.02%)
• Produce producers (42.38%)
• Produce producer (42.38%)
• an electronically recorded visual representation of speech (42.04%)
• PRODUCE dull surface (41.31%)
• Person on the scene: Abbr. (40.59%)
• HEAD and shoulder representation of person (39.59%)

Know another solution for crossword clues containing a visual representation of an object or scene or person produced on a surface ? Add your answer to the crossword database now.

Visual representation of this puzzle’s trick (go to 38-Down) NYT Crossword

Visual representation of this puzzles trick go to 38 Down New York Times Crossword Clue The NYTimes Crossword is a classic crossword puzzle. Both the main and the mini crosswords are published daily and published all the solutions of those puzzles for you. Two or more clue answers mean that the clue has appeared multiple times throughout the years.

VISUAL REPRESENTATION OF THIS PUZZLES TRICK GO TO 38 DOWN New York Times Clue Answer

  This clue was last seen on NYTimes October 19, 2023 Puzzle . If you are done solving this clue take a look at the other clues found on today's puzzle in case you may need help with another. Before each clue, you have its number and orientation on the puzzle for easier navigation.

Initial Thoughts

Perspectives & resources, what is high-quality mathematics instruction and why is it important.

• Page 1: The Importance of High-Quality Mathematics Instruction
• Page 2: A Standards-Based Mathematics Curriculum
• Page 3: Evidence-Based Mathematics Practices

What evidence-based mathematics practices can teachers employ?

• Page 4: Explicit, Systematic Instruction

Page 5: Visual Representations

• Page 6: Schema Instruction
• Page 7: Metacognitive Strategies
• Page 8: Effective Classroom Practices
• Page 9: References & Additional Resources
• Page 10: Credits

Research Shows

• Students who use accurate visual representations are six times more likely to correctly solve mathematics problems than are students who do not use them. However, students who use inaccurate visual representations are less likely to correctly solve mathematics problems than those who do not use visual representations at all. (Boonen, van Wesel, Jolles, & van der Schoot, 2014)
• Students with a learning disability (LD) often do not create accurate visual representations or use them strategically to solve problems. Teaching students to systematically use a visual representation to solve word problems has led to substantial improvements in math achievement for students with learning disabilities. (van Garderen, Scheuermann, & Jackson, 2012; van Garderen, Scheuermann, & Poch, 2014)
• Students who use visual representations to solve word problems are more likely to solve the problems accurately. This was equally true for students who had LD, were low-achieving, or were average-achieving. (Krawec, 2014)

Visual representations are flexible; they can be used across grade levels and types of math problems. They can be used by teachers to teach mathematics facts and by students to learn mathematics content. Visual representations can take a number of forms. Click on the links below to view some of the visual representations most commonly used by teachers and students.

How does this practice align?

High-leverage practice (hlp).

• HLP15 : Provide scaffolded supports

CCSSM: Standards for Mathematical Practice

• MP1 : Make sense of problems and persevere in solving them.

Number Lines

Definition : A straight line that shows the order of and the relation between numbers.

Common Uses : addition, subtraction, counting

Strip Diagrams

Definition : A bar divided into rectangles that accurately represent quantities noted in the problem.

Common Uses : addition, fractions, proportions, ratios

Definition : Simple drawings of concrete or real items (e.g., marbles, trucks).

Common Uses : counting, addition, subtraction, multiplication, division

Graphs/Charts

Definition : Drawings that depict information using lines, shapes, and colors.

Common Uses : comparing numbers, statistics, ratios, algebra

Graphic Organizers

Definition : Visual that assists students in remembering and organizing information, as well as depicting the relationships between ideas (e.g., word webs, tables, Venn diagrams).

Common Uses : algebra, geometry

Before they can solve problems, however, students must first know what type of visual representation to create and use for a given mathematics problem. Some students—specifically, high-achieving students, gifted students—do this automatically, whereas others need to be explicitly taught how. This is especially the case for students who struggle with mathematics and those with mathematics learning disabilities. Without explicit, systematic instruction on how to create and use visual representations, these students often create visual representations that are disorganized or contain incorrect or partial information. Consider the examples below.

Elementary Example

Mrs. Aldridge ask her first-grade students to add 2 + 4 by drawing dots.

Notice that Talia gets the correct answer. However, because Colby draws his dots in haphazard fashion, he fails to count all of them and consequently arrives at the wrong solution.

High School Example

Mr. Huang asks his students to solve the following word problem:

The flagpole needs to be replaced. The school would like to replace it with the same size pole. When Juan stands 11 feet from the base of the pole, the angle of elevation from Juan’s feet to the top of the pole is 70 degrees. How tall is the pole?

Compare the drawings below created by Brody and Zoe to represent this problem. Notice that Brody drew an accurate representation and applied the correct strategy. In contrast, Zoe drew a picture with partially correct information. The 11 is in the correct place, but the 70° is not. As a result of her inaccurate representation, Zoe is unable to move forward and solve the problem. However, given an accurate representation developed by someone else, Zoe is more likely to solve the problem correctly.

Manipulatives

Some students will not be able to grasp mathematics skills and concepts using only the types of visual representations noted in the table above. Very young children and students who struggle with mathematics often require different types of visual representations known as manipulatives. These concrete, hands-on materials and objects—for example, an abacus or coins—help students to represent the mathematical idea they are trying to learn or the problem they are attempting to solve. Manipulatives can help students develop a conceptual understanding of mathematical topics. (For the purpose of this module, the term concrete objects refers to manipulatives and the term visual representations refers to schematic diagrams.)

It is important that the teacher make explicit the connection between the concrete object and the abstract concept being taught. The goal is for the student to eventually understand the concepts and procedures without the use of manipulatives. For secondary students who struggle with mathematics, teachers should show the abstract along with the concrete or visual representation and explicitly make the connection between them.

A move from concrete objects or visual representations to using abstract equations can be difficult for some students. One strategy teachers can use to help students systematically transition among concrete objects, visual representations, and abstract equations is the Concrete-Representational-Abstract (CRA) framework.

If you would like to learn more about this framework, click here.

Concrete-Representational-Abstract Framework

• Concrete —Students interact and manipulate three-dimensional objects, for example algebra tiles or other algebra manipulatives with representations of variables and units.
• Representational — Students use two-dimensional drawings to represent problems. These pictures may be presented to them by the teacher, or through the curriculum used in the class, or students may draw their own representation of the problem.
• Abstract — Students solve problems with numbers, symbols, and words without any concrete or representational assistance.

CRA is effective across all age levels and can assist students in learning concepts, procedures, and applications. When implementing each component, teachers should use explicit, systematic instruction and continually monitor student work to assess their understanding, asking them questions about their thinking and providing clarification as needed. Concrete and representational activities must reflect the actual process of solving the problem so that students are able to generalize the process to solve an abstract equation. The illustration below highlights each of these components.

For Your Information

One promising practice for moving secondary students with mathematics difficulties or disabilities from the use of manipulatives and visual representations to the abstract equation quickly is the CRA-I strategy . In this modified version of CRA, the teacher simultaneously presents the content using concrete objects, visual representations of the concrete objects, and the abstract equation. Studies have shown that this framework is effective for teaching algebra to this population of students (Strickland & Maccini, 2012; Strickland & Maccini, 2013; Strickland, 2017).

Kim Paulsen discusses the benefits of manipulatives and a number of things to keep in mind when using them (time: 2:35).

Kim Paulsen, EdD Associate Professor, Special Education Vanderbilt University

View Transcript

Transcript: Kim Paulsen, EdD

Manipulatives are a great way of helping kids understand conceptually. The use of manipulatives really helps students see that conceptually, and it clicks a little more with them. Some of the things, though, that we need to remember when we’re using manipulatives is that it is important to give students a little bit of free time when you’re using a new manipulative so that they can just explore with them. We need to have specific rules for how to use manipulatives, that they aren’t toys, that they really are learning materials, and how students pick them up, how they put them away, the right time to use them, and making sure that they’re not distracters while we’re actually doing the presentation part of the lesson. One of the important things is that we don’t want students to memorize the algorithm or the procedures while they’re using the manipulatives. It really is just to help them understand conceptually. That doesn’t mean that kids are automatically going to understand conceptually or be able to make that bridge between using the concrete manipulatives into them being able to solve the problems. For some kids, it is difficult to use the manipulatives. That’s not how they learn, and so we don’t want to force kids to have to use manipulatives if it’s not something that is helpful for them. So we have to remember that manipulatives are one way to think about teaching math.

I think part of the reason that some teachers don’t use them is because it takes a lot of time, it takes a lot of organization, and they also feel that students get too reliant on using manipulatives. One way to think about using manipulatives is that you do it a couple of lessons when you’re teaching a new concept, and then take those away so that students are able to do just the computation part of it. It is true we can’t walk around life with manipulatives in our hands. And I think one of the other reasons that a lot of schools or teachers don’t use manipulatives is because they’re very expensive. And so it’s very helpful if all of the teachers in the school can pool resources and have a manipulative room where teachers can go check out manipulatives so that it’s not so expensive. Teachers have to know how to use them, and that takes a lot of practice.

Selective visual representation of letters and words in the left ventral occipito-temporal cortex with intracerebral recordings

Affiliations.

• 1 Psychological Sciences Research Institute, UCLouvain, B-1348 Louvain-La-Neuve, Belgium.
• 2 Institute of Neuroscience, UCLouvain, B-1348 Louvain-La-Neuve, Belgium.
• 3 Cognitive Science and Assessment Institute, Education, Culture, Cognition, and Society Research Unit, Université du Luxembourg, L-4366 Esch-sur-Alzette, Luxembourg.
• 4 Center for Developmental Psychiatry, Department of Neuroscience, KU Leuven, B-3000 Leuven, Belgium.
• 5 Université de Lorraine, CNRS, CRAN, F-54000 Nancy, France.
• 6 Université de Lorraine, CHRU-Nancy, Service de Neurologie, F-54000 Nancy, France.
• 7 Université de Lorraine, CHRU-Nancy, Service de Neurochirurgie, F-54000 Nancy, France.
• 8 Psychological Sciences Research Institute, UCLouvain, B-1348 Louvain-La-Neuve, Belgium; [email protected].
• PMID: 30038000
• PMCID: PMC6094145
• DOI: 10.1073/pnas.1718987115

We report a comprehensive cartography of selective responses to visual letters and words in the human ventral occipito-temporal cortex (VOTC) with direct neural recordings, clarifying key aspects of the neural basis of reading. Intracerebral recordings were performed in a large group of patients ( n = 37) presented with visual words inserted periodically in rapid sequences of pseudofonts, nonwords, or pseudowords, enabling classification of responses at three levels of word processing: letter, prelexical, and lexical. While letter-selective responses are found in much of the VOTC, with a higher proportion in left posterior regions, prelexical/lexical responses are confined to the middle and anterior sections of the left fusiform gyrus. This region overlaps with and extends more anteriorly than the visual word form area typically identified with functional magnetic resonance imaging. In this region, prelexical responses provide evidence for populations of neurons sensitive to the statistical regularity of letter combinations independently of lexical responses to familiar words. Despite extensive sampling in anterior ventral temporal regions, there is no hierarchical organization between prelexical and lexical responses in the left fusiform gyrus. Overall, distinct word processing levels depend on neural populations that are spatially intermingled rather than organized according to a strict postero-anterior hierarchy in the left VOTC.

Keywords: SEEG; fusiform gyrus; intracerebral recordings; lexical representation; word reading.

Publication types

• Research Support, Non-U.S. Gov't
• Video-Audio Media
• Brain Mapping / instrumentation
• Brain Mapping / methods*
• Drug Resistant Epilepsy / diagnosis
• Electrocorticography / instrumentation
• Electrocorticography / methods*
• Epilepsies, Partial / diagnosis
• Occipital Lobe / physiology*
• Pattern Recognition, Visual / physiology*
• Temporal Lobe / physiology*

Associated data

• Dryad/10.5061/dryad.6s39h64