89 Introduction to Understanding Problems in Math

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

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?

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