Introduction to Understanding Problems

in Math

What is Involved in Understanding Problems

• 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

• 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?

• 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

• Provide Clear Explanations• Give Students Strategies 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, multi-level 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

• 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.• Create a “gallery walk” to expand their

repertoire of appropriate models.• Show students how to embrace mistakes

and errors as part of learning.

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

• 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 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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