Introduction to Using Visual
Representations in Math
What is Using Visual
Representations?
• Using visual representations is a strategy
to display and think through mathematical
information.
• Students draw upon visual representations
when they are working to understand a
concept or problem.
Key Elements of Using Visual
Representations
• Students choose and use visual representations to help them solve
problems.
• Possible displays of information include:
• Number lines
• Arrays
• Pictures of geometric
• features
• Graphs
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
• Provide clear explanations
• Use varied examples, materials, and
models
• Provide ongoing formative assessment
Differentiated Instruction
• 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
• 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
• 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
• 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
Interactive whiteboard
Web-based applets
Math drawing tools
Calculators
3D design software
Graphing and charting software
Use Research-Based Strategies
and Tools
• 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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