Ms. Richardson’s Grade 6 class is working on a geometry unit. They have reviewed how to classify different quadrilaterals and triangles, and most students have become proficient at using mathematical terms. They have also been learning how to use...
Teach with Tech
Choosing the “right” visual representation often depends on content and context. In some contexts, there are multiple ways to represent the same idea. Your students need to view a variety of visual representations (see UDL Checkpoint 2.5: Illustrate through multiple media) in order to learn when and why they should choose each one. As you plan how to provide differentiated support and practice, consider ways technology tools can support the development of this critical practice.
Steps:
Step 1: Provide Clear Explanations

Check students’ understanding of a visual representation to determine a starting point. Ask them about features, including labels and scales when appropriate. Review any features they are unsure of and encourage them to ask questions.

As students use a variety of online tools to create visual representations (see UDL Checkpoint 5.2: Use multiple tools for construction and composition), ask questions about the format of the representation to ensure that students understand all the features.
Technology tools for visual representations Spreadsheets to provide structure for tables
 Graphing calculators or computerbased applications (such as GeoGebra) to quickly create accurate graphs
 Virtual tools (such as GeoGebra) to create geometric figures

Some representations, such as graphs, use more than one dimension. Highlight for students—or have students tell you—what each dimension represents (see UDL Checkpoint 3.2: Highlight patterns, critical features, big ideas, and relationships). When your students first learn how to use a representation, you may need to do this each time they use it. As students become familiar with the representation, you can check in with them to make sure they can interpret the dimensions.
IES Recommendations
Instruction during the intervention should be explicit and systematic. This includes providing models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review.
Interventions should include instruction on solving word problems that is based on common underlying structures
Teach number and operations using a developmental progression.
Step 2: Give Students Strategies and Models

When possible, include alternative visual representations and discuss the similarities and differences between the representations. This will help your students to move more easily from one representation to an alternative they prefer. It will also help them recognize limitations in one visual representation that may not appear in others.

Vary the shapes and orientations of representations so that students focus on the important features only as they learn about the objects and situations represented (see UDL Checkpoint 3.4: Maximize transfer and generalization).
Ways to vary representations Fractions should be represented not only by circle (“pizza” or “pie”) diagrams, but also by rectangles, sets of objects, arrays, lengths (such as fractions of an inch or centimeter on a ruler), and locations on a number line.
 Geometric objects should not always be shown using regular figures. A quadrilateral should not always look like a rectangle or parallelogram. Triangles should not always have the same orientation (for example an equilateral triangle with a horizontal base always on the bottom).
 When you introduce a visual representation for a task, explain the connection between the problem and the representation. Use the same language with the representation that the problem uses.
IES Recommendations
Intervention materials should include opportunities for students to work with visual representations of mathematical ideas and interventionists should be proficient in the use of visual representations of mathematical ideas.
Help students recognize that fractions are numbers and that they expand the number system beyond whole numbers. Use number lines as a central representational tool in teaching this and other fraction concepts from the early grades onward.
Source: IES Practice Guide: Developing Effective Fractions Instruction for Kindergarten Through 8th Grade
Instruction during the intervention should be explicit and systematic. This includes providing models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review.
Help students understand why procedures for computations with fractions make sense.
Source: IES Practice Guide: Developing Effective Fractions Instruction for Kindergarten Through 8th Grade
Step 3: Provide Ongoing Formative Assessment

Show your students a specific representation—a graph or table—that is missing an important feature (see UDL Checkpoint 3.2: Highlight patterns, critical features, big ideas, and relationships). Ask them to identify the missing feature. For example, they should be able to identify when a graph has no scale indicated on an axis, or that the quantity represented by the axis is missing.

When students get stuck as they try to interpret a visual representation, ask questions that guide their thinking (see UDL Checkpoint 3.3: Guide information processing, visualization, and manipulation). Questions may help you to discover the source of a student’s confusion. Prompt the student to focus on the information the visual representation provides.

Consider each student’s needs and learning styles when you decide which actions to take to move students closer to the learning goals. Give students time to ask you questions, share their thinking, and respond to the feedback you provide.
Key questions to elicit student thinking Why do you think that?
 How do you know that is correct?
 How does that picture represent the problem?
 Can you explain your answer?
 Is there another way you could do that?
IES Recommendations
Instruction during the intervention should be explicit and systematic. This includes providing models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review
Mr. Simpson’s 5th grade class is in the middle of a fractions and mixed numbers unit. In this lesson, students will learn about adding and subtracting mixed numbers using visual representation strategies.
This practice guide presents five recommendations to help educators improve students? understanding of fractions. It features strategies to develop young children?s understanding of early fraction concepts and ways to help older children...
A 2003 design effort by ED working with educational technology and research experts recommended focusing the study on software products used to support reading and math instruction. The study team set up a competitive process and worked with ED...
The purpose of this study is twofold. First, the researchers sought to assess the effectiveness of two instructional strategies, an explicit schemabased strategy and a traditional basal strategy, on onestep addition and subtraction word...
This study investigated the differential impact of the structured peer tutoring and group reward components within a reciprocal peertutoring (RPT) intervention to enhance mathematics performance for students at risk for failure. Participating...
This study examined the effectiveness of the explicit translation strategy method that explicitly teaches fourthgraders to translate word story problems into mathematical equation form. The study also explored the impact of providing students...
The study compared the effectiveness of concreterepresentationalabstract (CRA) and representationalabstract (RA) instructional sequences in teaching mathematics to middle school students with mild to moderate disabilities. Students in the CRA...
The Curry Center for Technology and Teacher Education at the University of Virginia is developing materials to help preservice secondary mathematics, social studies, and science teachers (PSTs) learn to incorporate technology appropriately into...
The PowerUp WHAT WORKS Team at the Center for Technology Implementation, has conducted extensive reviews of the literature on mathematics teaching and learning. View our bibliography for a collection of references on evidencebased math practices...
The PowerUp WHAT WORKS Team at the Center for Technology Implementation, has conducted extensive reviews of the literature on the use of virtual manipulatives to support student learning in mathematics. View our bibliography for a collection of...
This study compared student achievement in solving liner algebraic functions using a concrete torepresentationaltoabstract (CRA) sequence of instruction and a repeated abstract explicit instruction model. Six classes of students were randomly...