Introduction to Modeling in math

• Modeling is a strategy to represent the important structures of problems so they can more easily be explored and solved.

• Students use physical or virtual manipulatives to act out and think through problems.

What is Modeling?

Key Elements of Modeling

• Students use objects--and computer versions of objects--they can see and move to engage in problem solving through sight, touch, and kinetics.

• Examples of objects include:• Base-ten blocks• Colored chips or tiles• Fraction strips• Cuisenaire rods• Geoboards

How Does Modeling Help Students?

• Provides concrete experiences from which they can generalize.

• Promotes their mathematical thinking.• Gives them a variety of tools to draw upon.• Deepens their conceptual understanding.• Builds their confidence in tackling problems.

Discussion Questions

1. What models have you used in your classroom for which mathematical concepts?

2. What are the advantages and disadvantages of the virtual models you have used with struggling students?

3. How could you use a model to help your struggling students make that abstract concept more concrete?

How Can I Support Students' Use of Modeling?

• Provide clear explanations• Use varied examples, materials, and models• Provide ongoing formative assessment

Use Evidence-Based Instructional Practices

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

Differentiated Instruction

Teacher-Dependent Ways to Differentiate

By ContentDifferent levels of reading or resource materials, reading buddies, small group instruction, curriculum compacting, multi-level computer programs and Web Quests, audio materials, etc.

By ProductActivity 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 ProcessTiered products, students choose mode of presentation to demonstrate learning, independent study, varied rubrics, mentorships, interest-based investigations

Student-Dependent Ways to Differentiate

By ContentDifferent levels of reading or resource materials, reading buddies, small group instruction, curriculum compacting, multi-level computer programs and Web Quests, audio materials, etc.

By ProductActivity 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 ProcessTiered products, students choose mode of presentation to demonstrate learning, independent study, varied rubrics, mentorships, interest-based investigations

Discussion Questions

1. How does modeling support the Common Core State Standards Math Practices?

2. What types of difficulties do your students have, and how can different types of models support their learning?

3. What role does the content of a lesson have in differentiating instruction?

Provide Clear Explanations: Possible Strategies

• Describe, demonstrate, and let students practice using each kind of model.

• Explain the connection between each model and problem.

• Use language/terms from problems to keep students focused on what models represent.

Use Varied Examples, Materials, and Models:

Possible Strategies• For each problem, share a range of appropriate models

students can choose from.• Think aloud as you choose models to help students

know when/why to use certain in ones.• Model how to use virtual manipulatives.

• To assess students’ understanding, ask them to explain why they choose certain models.

• Watch for and help those who choose models that are too complex or simple for the task.

• Ask struggling students which strategies the class has learned that might be helpful.

• Give students time to respond to feedback, ask questions, and share their thinking.

Provide Ongoing Formative Assessment: Possible

Strategies

Use Online and Offline Tools

Tools Online Offline

Manipulatives X X

Interactive whiteboard

X X

Web-based applets

X

Math drawing tools

X X

Calculators X X

3D design software X X

Graphing and charting software

X X

Use Research-Based Strategies and Tools

• To launch the lesson• During the learning task• As you bring closure to the lesson

Discussion Questions

1. What do you consider when you decide which model is appropriate for a particular problem?

2. What are the advantages and disadvantages of using virtual vs. physical models?

3. What types of formative assessment have you found to be particularly useful when checking for students’ understanding of models?

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).

This document contains information from other public and private organizations that may be useful to the reader; these materials are merely examples of resources that may be available. Inclusion of this information does not constitute an endorsement by the U.S. Department of Education of any products or services offered or views expressed. This publication also contains hyperlinks and URLs created

and maintained by outside organizations and provided for the reader's convenience. The Department is not responsible for the accuracy if this information. Further, the programs/models/resources featured on this site have not been extensively evaluated by CTI. This website was created and is maintained by American Institutes for Research (AIR) through funding from the U.S. Department of

Education, Award # H327G090004. For more information, send an e-mail to PowerUp@air.org.