Introduction to Modeling in
math
What is Modeling?
• 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.
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
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?
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 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.
Provide Ongoing Formative
Assessment: Possible Strategies
• 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.
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 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?
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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