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 When you introduce your students to visual representations, what are the key elements that are important to highlight? How can you use visual representations to support your students as they solve problems? 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 How does the use of visual representations support the CCSS Mathematical Practices and the UDL principles? 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 What challenges have your students had when using visual representations? How you help your students to determine an appropriate visual representation for a particular problem or situation? How can you use visual representations as a response to student difficulties or misconceptions? 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