Lesson 1: Student Thinking Behind Each Step

Return to: Unit 2: How Can I Use the Mathematician's Plan in My Classroom?

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

Continue to Lesson 2: Analyzing Student Samples

Learning Objectives

Participants will analyze student thinking behind each step of the Mathematician’s Plan.

Do Now

Think back to a student you’ve had or even yourself as a student. Which of the three steps of the Mathematician’s Plan do you think is the hardest for students to accomplish. Take the poll HERE and use the code KP8F29.

Mini-Lecture

Nowadays math is not as simple as memorizing algorithms and computations. Students have to think deeply about the questions being asked. "Math problem solving is a complex skill that requires students not only to calculate an answer but also to comprehend and integrate the problem information, generate and maintain mental images of the problem, and develop a viable solution path" (Krawec, 2013).

Krawec identifies four steps of the problem solving process.

1. Problem Translation: the student must "comprehend what the problem is saying"
2. Problem Integration: the student must "mathematically interpret the relationship among the problem parts"
3. Solution Planning: the student must "determine which operations to use and the order"
4. Solution Execution: the student carries out the planned computations"

These four steps are very closely linked and represented in the Mathematician's Plan.

Although the Mathematician's Plan is broken into three seemingly easy steps, there is a lot of thinking involved on the students end within each step. We will take a second to analyze each step and the thinking involved behind it.

Step 1: Read and Interpret the Question

There are two questions students ask themselves during this first step:

• What is the question asking?
• What is my plan to solve?

Let's first dive into What is the question asking? Students have to read the entire question and extrapolate the main question it is asking them to answer. In order to do this students need to understand what is happening in the story. Some students may make a mind movie, draw a picture, pull out important information or create a diagram.

Then students must ask themselves What is my plan to solve? This requires students to take their understanding of the question and apply it to math. Students may understand the actions in the word problem but then have to make the connection to mathematical understandings. A student makes a plan to solve by determining the steps they must take to answer the question.

Step 2: Use Your Plan to Solve

There are three parts to this second step:

• Organize your workspace
• As you solve, label your work
• If it is a multiple choice, solve before looking at choices

First, organize your workspace requires students to divide their workspace in a way that leaves room for all steps. This is a metacognitive skill that allows students to practice organization. Students are held accountable to follow their plan by organizing their workspace.

Next, students label your work so that all numbers can be traced back to the question. Students must understand the numbers in context in order to label them correctly. They must also have an understanding of why they are performing a certain step, and how their result fits into the context of the word problem. It allows graders to determine if a student truly understands the word problem.

Step 3: Check Your Work

There are two steps:

• Re-read the question and ask, "Does my answer make sense?" and "Did I answer the question completely?"
• If your answer doesn't make sense, make a new plan and re-solve

First, students must reread the entire question, not just their answer. Most students check their computations to ensure no mathematical error is present, however they often do not reread the question in its entirety. This step allows students another opportunity to ensure understanding of the question. Students will then make a new plan if errors have been found or if the answer doesn't match any answer choices.

Task 1

Directions: You will be picking a step of the Mathematician's plan and determining what you would be looking for in student work in order to deem it an exemplar.

1. Click HERE
2. Follow the directions on the slides

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.