Introduction to using visual representations in math

• Using visual representations is a strategy to display and think through mathematical information.. Key Elements of Using Visual Representations • Students choose and use visual represe

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

• Graphs

• features

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, multi-level 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

• 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?

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#H327G090004-10, PowerUp What Works was developed by a team

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Applied Special Technology (CAST)