Lesson 1: The Mathematician's Plan and Purpose

Return to: Unit 1: What is the Mathematician's Plan?

Return to: Mini-course: The Mathematician's Plan: Promoting Thinking In Math

Continue to Lesson 2: What Does The Mathematician's Plan Look Like in Practice

Learning Objectives

Students will be able to identify all three steps of the Mathematician's Plan and explain the purpose of using the Mathematician's plan to solve math problems.

Do Now

Click HERE and type in the code 3HKN5A to answer the prompts below.

1. What does it mean to interpret a math question?

2. Have you ever made a plan to solve a problem? Why was it so helpful?

3. When you tell a student to "check your work", what does that mean you want the student to do?

Mini-Lecture

The Mathematician's Plan

This "chart" is student and teacher facing. It is the thinking that goes into solving a math problem. As adults, many of us complete these steps in our head without realizing it. These cognitive skills often can't be seen on paper however, with the help of the Mathematician's plan we can encourage this thinking as well as teach students how to show evidence of these steps on their paper. Below is the Mathematician's Plan.

    1. Read and Interpret the Question
      * Ask, “What is this question asking?”
      * Ask, “What is my plan to solve?”

    2. Use Your Plan to Solve
      * For multiple-choice, cover the answer choices and solve the problem before looking at the answer choices
      * Organize your workspace
      * As you solve, label your work 

    3. Check Your Work
      * Re-read the question and ask, “Did I answer the question” and “Does my answer make sense?”
      * If your answer doesn’t make sense, make a new plan and re-solve the problem

We will leave this idea here. In the next unit you will take the time to understand the student moves that occur within each step. For now, familiarize and memorize each step and its components.

The Purpose

"Proficient math problem solving is essential for success in school, on the job, and in the community, and the current mathematics curriculum reflects the critical importance of problem-solving skills." Problem solving skills go beyond math instruction. The Mathematician's Plan is a direct, procedural attempt at implementing some cognitive strategy instruction into math instruction.

"Even students who have acquired the necessary math skills often lack important problem solving strategies that would enable them to generalize the skills beyond the classroom." In general, math instruction has always focused on the content or procedural knowledge, which "centers on computational procedures and involves memorizing and following predetermined steps to compute answers". This is a disservice to children as it does not prepare them to use this knowledge. That being said, the logical next step is to infuse instruction with principled knowledge. This knowledge "focuses on the mathematical ideas and concepts that undergird mathematical procedures". (Krawec & Montague, p.126).

The purpose of the Mathematician's Plan is to incorporate the thinking behind principled knowledge in a way that is accessible to learn for both teacher and student.

Task 1

Directions: Complete this task to show that you know the steps involved in the Mathematician's plan.

1. Click to access the assessment and type in code VKVETA
2. Match the steps of the Mathematician's Plan

Task 2

Directions: Watch the video and think about the connections you can make between Dan Meyer's TED Talk, the study on Cognitive Strategy Instruction, and The Mathematician's Plan.

1. Watch the video HERE
2. Read the study HERE
3. Write your response to the video and study HERE and type in the code 6LYAGF

References and Resources

Krawec, J., Huang, J., Montague, M., Kressler, B., & de Alba, A. M. (2013). The Effects of Cognitive Strategy Instruction on Knowledge of Math Problem-Solving Processes of Middle School Students with Learning Disabilities. Learning Disability Quarterly, 36(2), 80–92.

Krawec, J., & Montague, M. (2014). The Role of Teacher Training in Cognitive Strategy Instruction to Improve Math Problem Solving. Learning Disabilities Research & Practice, 29(3), 126–134.