1. Chapter 3 Teaching Through Problem Solving
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2. Teaching Through Problem Solving
Most, if not all, important mathematics concepts and procedures can best be taught through problem solving
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3. Problems and Tasks for Learning Mathematics
Begin where the students are
The problematic or engaging aspect of the problem must be due to the mathematics that the students are to learn
Require justifications and explanations for answers and methods
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4. A Shift in the Role of Problems
Away from:
Explain, practice, then story problems
One way (the teacher’s way)
Show and tell approach with the student as a passive learner
Problem-solving problems as a separate activity
Expecting explicit directions for how to solve problems
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5. The Value of Teaching Through Problem Solving
The focus of the students’ attention on ideas and sense making
Develops the belief in students that they are capable of doing mathematics and that mathematics makes sense!
Provides a context to help students build meaning for the concept
Allows an entry point for a wide range of students
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6. The Value of Teaching Through Problem Solving (Continued)
Provides ongoing assessment data that can be used to make instructional decisions, help students succeed, and inform parents
Allows for extensions and elaborations
Engages students so that there are fewer classroom discipline problems
Develops “mathematical power”
It is a lot of fun!
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7. Examples of Problem-Based Tasks
Procedures and Processes
Students develop procedures via a problem-solving approach. They are engaged in the process of figuring out mathematics, not just accepting procedures blindly.
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8. Selecting or Designing Problem-Based Tasks
Multiple Entry Points
Provides the opportunity for students to work on the problem using their own ideas at their own level
Allows for more than one correct way to work the problem
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9. How to Find Quality Tasks and Problem-Based Lessons
A Task Selection Guide
How is the activity done?
What is the purpose of the activity?
Can the activity accomplish your learning goals?
What must you do?
Good tasks: check out
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10. How to Find Quality Tasks and Problem-Based Lessons (Continued)
A standards-based curriculum provides an increased emphasis on learning through problem solving
Traditional textbooks can be used to adapt a non-problem-based lesson by using the best lessons or using the main ideas of the chapter
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11. Four-Step Problem-Solving Process
Understanding the problem
Developing a plan
Carrying out the plan
Looking back
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12. Teaching in a Problem-Based Classroom
Let students do the talking
How much to tell and not to tell
The importance of student writing
Metacognition
Disposition
Additional goals
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13. Teaching in the Problem-Based Classroom
How much to tell
Mathematical conventions
Carefully suggest alternative methods
Clarification of students’ methods
And not to tell
Establish teacher- preferred methods
Teacher thinking
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14. Teaching in the Problem-Based Classroom
Importance of student writing
— a reflective process
— can be a rehearsal for the discussion period
— can serve as a written record that remains long after the lesson.
Tools for writing
— text editing
— wikis
— blogging tools
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15. Teaching in the Problem-Based Classroom
Metacognition—being aware of how and why you are doing something
Disposition—attitudes and beliefs about (in this case) mathematics
Attitudinal goals for student
— gaining confidence
— taking risks
— enjoying doing math
Attitudinal goals for teacher
— build in success
— praise effort and risk taking
— listen to all students
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16. A Three-Part Lesson Format
Before: Getting Ready
Activate useful prior knowledge.
Be certain the problem is understood.
Establish clear expectations.
During: Students Work
Let go! Avoid stepping in front of the struggle.
Listen carefully.
Provide appropriate hints.
Observe and assess.
After: Class Discussion
Encourage a community of learners.
Listen! Accept student solutions without evaluation.
Summarize main ideas and identify future problems.
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17. A Closer Look at Text Books
Examine a chapter of the book.
Determine grade level.
Find the standards that correspond.
Compare the intent of the standard (Objectives) with the lessons.
What modifications could you incorporate?
(See pgs of Van De Walle book)
Copyright © Allyn and Bacon 2010