Teaching through Problem Solving

Discussion Board Assignments

Unit Four - Mathematics as Problem Solving

One of the 7 key roles of the teacher when “teaching through problem solving” is using think-alouds to model how a problem is tackled. However, think-alouds are definitely more commonly used in literacy instruction as compared to the instruction of mathematics. In many cases, teachers of mathematics demonstrate how to solve a problem through “worked examples”, but often miss the opportunity to make their thinking visible through a think-aloud process. Adding a “think-aloud” strategy to a teacher’s repertoire of strategies can “bump-up” their practice and increase their impact on student learning. Experiencing planning a “think-aloud” supports mathematics leaders to not only recognize the practice, but also to know the “how to” necessary to support teachers as they embed the “think-aloud” strategy in their instructional practice.

Read/Review

  1. From The Guide to Effective Instruction in Mathematics, K - 6, Volume 2: Problem Solving and Communication read/review the following sections:
  2. The Teacher’s Role in Teaching Through Problem Solving - pg. 26
  3. Providing Appropriate and Challenging Problems - pg. 26 - 29
  4. Supporting and Extending Learning - pg. 29 - 31
  5. Encouraging and Accepting Student Strategies - pg. 31
  6. Questioning and Prompting Students - pg. 31-33
  7. Using Think-Alouds - pg. 34
  8. From Visible Learning for Mathematics: What Works Best to Optimize Student Learning, Grades 1 - 12 read/review the following section:
  9. Making Learning Visible Through Appropriate Mathematical Tasks -
    • What Are Worked Examples and When Are They Appropriate pg. 113 - 116
    • Mathematical Talk and Metacognition & Strategic Use of Vocabulary Instruction pg. 119 - 123

Experience

  1. Select or develop through revision an “appropriate and challenging problem”.

Here’s how:

  1. Select a Grade (1 - 8)
  2. Identify a concept (rather than a skill or procedure) from the overall expectations in the math curriculum that students in that grade need to develop
  3. Select a problem that addresses the concept to be developed. This site may be helpful with linking overall expectations to a problem. https://ca.ixl.com/standards/ontario/math

B. Plan a Think Aloud

  1. Read/review the “Think Alouds” section in The Guide to Effective Instruction in Mathematics, K - 6, Volume 2: Problem Solving and Communication - pg. 34
  2. Read/review the Think Aloud - A Problem Solving Strategy for Mathematics document
  3. View the Think Aloud Template and read the comments about its suggested use. Then, Click here to add a copy of the Think Aloud Template to your “My Drive”. Use it to develop your solution to your chosen problem and to make your “thinking visible” by annotating your thinking and decision-making processes.
  4. Post (by including your completed template as an attachment) to your discussion group.
  5. Provide feedback to others in your group by using the feedback questions:
    • What did you like and why?
    • What would you change and why?
    • What questions do you have?