89 Introduction to Understanding Problems in Math

Introduction to
Understanding Problems in
Math


What is Involved in
Understanding Problems
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Rereading the problem
Annotating words and numbers
Visualizing the situation
Converting visualizations into diagrams or mathematical
expressions
Assessing the reasonableness solutions


Key Elements of Understanding
a problem
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Learning how to solve word problems requires students to:

– understand the context
– develop a strategy to solve the problem
– build upon their ability to organize, create visual
representations, and use precise language

How Does Understanding
Problems Help Students?
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Helps students

– make sense of problems
– see that a problem is not just a jumble of words
and numbers
– deal with increasingly complex situations as they
move forward in their mathematical learning


Discussion Questions 1
1. Is there a systematic problem solving
process you use?
2. What strategies (e.g., thinking aloud,
organizing, modeling, visual representations,
precise language, and/or peer interaction)
do your students employ?
3. What aspects of problem solving do your
students struggle with?


How Can I Support Student Use
of Understanding Problems?

Use of Evidence-Based
Practices
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Provide Clear Explanations
Give Students Strategies and Models
Provide Ongoing Formative Assessment


Differentiated Instruction
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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 Process

– 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 Products

– 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 can you use CCSS Mathematical
Practices and the UDL principles to enhance
student comprehension in the problem
solving process?
2. How do you build differentiation into teaching
students to understand problems?
3. How have you used technology to
differentiate instruction?


Provide Clear Explanations:
Possible Strategies
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Use prompting questions and give students sufficient time to
understand and react.

– Ask students to present the directions or
explanations in their own words.
– Ask students to compare and contrast different
approaches


Use Varied Examples,

Materials, and Models: Possible
Strategies
• Use a process chart to guide students.
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Create a “gallery walk” to expand their repertoire of appropriate
models.
Show students how to embrace mistakes and errors as part of
learning.


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Provide Ongoing Formative
Assessment: Possible
Strategies
Ask students to explain
– what they are doing
– their use of pictures, diagrams, charts,
expressions, and equations
– if their process makes sense to them


Use Online and Offline Tools
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Manipulatives

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Interactive whiteboard

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Web-based applets

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Math drawing tools

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Calculators

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3D design software

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Graphing and charting software


Use Research-Based Strategies
and Tools
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To launch the lesson
During the learning task
As you bring closure to the lesson


Discussion Questions 3
1. What are some methods you have used to
effectively expand students’ understanding
of different solution methods?
2. How do you teach students to compare and
contrast different approaches to solving a
problem?
3. What technology tools have you used to
support formative assessment?


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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