Introduction to using visual representations in math

Introduction to Using
Visual Representations in
Math


What is Using Visual
Representations?
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Using visual representations is a strategy to display and think
through mathematical information.

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Students draw upon visual representations when they are working
to understand a concept or problem.


Key Elements of Using Visual
Representations
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Students choose and use visual representations to help them solve
problems.
Possible displays of information include:
• Number lines
• Arrays
• Pictures of geometric
• Graphs

• features


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How Does Using Visual
Representations Help
Students?
Provides a concrete way to work with abstract mathematics without
a physical model.
Supports students in moving from informal to formal representations
of mathematical ideas.
Helps students remember and relate to the abstract symbols most
often used in mathematics.


Discussion Questions 1
1. When you introduce your students to visual
representations, what are the key elements
that are important to highlight?
2. How can you use visual representations to
support your students as they solve
problems?
3. How can you use visual representations to
support your students’ learning and
understanding of mathematical concepts?

How Can I Support Students'
Use of Visual Representations?


Use Evidence-Based
Instructional Practices
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Provide clear explanations

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Use varied examples, materials, and models

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Provide ongoing formative assessment


Differentiated Instruction
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Plan instruction that considers students' readiness, learning needs,
and interests.
Use a range of technology tools to:

– engage learners at varying levels
– engage learners in multiple ways.
– offer students options for demonstrating

understanding and mastery


Teacher-Dependent
Ways to Differentiate
• By Content
– Different levels of reading or resource materials, reading
buddies, small group instruction, curriculum compacting, multilevel computer programs and Web Quests, audio materials, etc.

• By Product

– Activity choice boards, tiered activities, multi-level learning
center tasks, similar readiness groups, choice in group work,
varied journal prompts, mixed readiness groups with targeted
roles for students, etc.

• By Process

– Tiered products, students choose mode of presentation to
demonstrate learning, independent study, varied rubrics,
mentorships, interest-based investigations


Student-Dependent
Ways to Differentiate
• By Readiness
– Options in content, topic, or theme, options in the
tools needed for production, options in methods for
engagement

• By Profile

– Consideration of gender, culture, learning styles,
strengths, and weaknesses

• By Process

– Identification of background knowledge/gaps in
learning, vary amount of direct instruction, and
practice, pace of instruction, complexity of activities,
and exploration of a topic


Discussion Questions 2
1. How does the use of visual representations support the CCSS
Mathematical Practices and the UDL principles?
2. How have you used technology to differentiate instruction to
construct and use visual representations?


Provide Clear Explanations
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Explain the connection between the problem and the
representation.
When students find a solution, be sure they connect the
representation to the solution in terms of the original problem.
Highlight for students, or have students tell you, what each

dimension represents when more than one dimension is used.


Use Varied Examples,
Materials, and Models
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Share alternative visual representations and discuss their
similarities and differences.
Offer students a variety of tools to create visual representations.
Vary representations’ shapes/orientations so students only focus on
the important features.


Provide Ongoing Formative
Assessment
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Have students identify a missing feature from a representation, such
as a graph or a table.
Ask questions that guide students’ thinking about the information
they can get from a visual representation.
Observe students to assess their ability to choose appropriate
representations and their understanding of representations.

Use Online and Offline Tools
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Manipulatives

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Interactive whiteboard

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Web-based applets

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Math drawing tools

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Calculators

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3D design software

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Graphing and charting software

Use Research-Based Strategies
and Tools
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To launch the lesson
During the learning task
As you bring closure to the lesson


Discussion Questions 3
1. What challenges have your students had
when using visual representations?
2. How do you help your students to determine
an appropriate visual representation for a
particular problem or situation?
3. How can you use visual representations as a
response to student difficulties or
misconceptions?


Disclaimer
Awarded through a cooperative agreement from the U.S. Department of
education, Office of Special Education Programs (OSEP), Grant
#H327G090004-10, PowerUp What Works was developed by a team
of experts in education, technology, differentiated instruction/UDL, and
special education at the Center for Technology Implementation,
operated by the American Institutes for Research (AIR) in collaboration
with the Education Development Center, Inc. (EDC) and the Center for

Applied Special Technology (CAST).

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