Unit 3: Student Strategies for Solving Word Problems

Back to: Case Study: Word Problems in Mathematics

Mini-Lesson used for Case Study: Word Problems in Mathematics: Teaching/Student Strategies to Comprehend Word Problems by Victoria Keller

Aims & Objectives

This case study of Unit 3 focuses on strategies that can be used in helping students that are experiencing difficulty with solving word problems. These methods are meant to promote students' ability to think about their own thinking through reflection (metacognition) and to break apart word problems using steps to find the underlying questions within the problem in order to solve the word problem (scaffolding).

The key objective for the unit is to differentiate various student strategies to create effective lesson activities and evaluation.

Methodology

The assignment for the unit is to, "Write the procedures and evaluations for your problem solving lesson." While coming up with the best methods for my lesson, I felt that combining both the metacognitive and scaffolding strategies from the Teacher Strategies for Students Solving Word Problems unit will lead to better personal understanding on how to attack mathematical word problems. Students will benefit from doing this activity with the teacher to learn how to combine the 6-step strategy to solving math word problems and the 3-step meta-cognitive "Say-Ask-Check" strategy. I will not expect them to do this in-depth process for every word problem in the future, but these are important skills to work on and for students to become aware of. Students are already aware of the "CUBES" strategy brought up in the unit Student Strategies for Solving Word Problems

Here are the procedures and evaluations for my lesson:

"Procedure" - Start the class off by asking the students to, “Write in six steps what you personally do to solve math word problems.” This will be a “Do Now” that will go right into the six-step process needed to solve word problems. Students will share their personal steps and compare among their classmates.

- Explain to students that six steps should be taken while solving word problems, carefully explaining the purpose of each step:

1. Read the problem carefully

2. Construct a representation of the problem (What is being asked, what is relevant and irrelevant, etc.)

3. Decide how to solve the problem

4. Execute the necessary calculations

5. Interpret the outcome to form the answer

6. Evaluate/Check the solution

- Go back and bring up the “Do Now” task they did. Ask students to now compare their steps with the new ones they recorded. “Which ones did they miss? Do they know what process they just did by thinking about their own thinking?”

- List the meta-cognitive components that students need to do during each step of solving word problems. Provide examples and carefully explain the importance of each one of these components:

1. Self-Instruct: State to yourself the purpose of the step to create awareness (The “Say” Step)

2. Self-Plan: Ask yourself what needs to happen to complete the step (The “Ask” Step)

3. Self-Monitor: Execute the plan and check for accurate successful completion (The “Check” Step)

- Explain to students that these three components must be used for each of the six steps to guarantee all areas of the word problem are accounted for. As a class, go through a mathematics word problem using the meta-cognitive and scaffolding steps. The students will work in their desk groups to come up with the meta-cognitive steps, then we will go over them as a class to make sure we are all completing the steps correctly. Call on students to explain their meta-cognitive steps. Students will be given a worksheet that has the given math word problem as well as the scaffolding and meta-cognitive steps expected to be completed.

- Students will be allowed to take this worksheet home with them to use as a reference while completing the homework worksheet. Students are expected to turn in both word problems completed for next day's class period. Refer to the worksheet below for the homework word problem.

"Evaluation of Students"

- Students will be assessed on completion of both worksheets and correctness of the math problems.

Findings

I found the Metacognitive Strategy List and the CUBES Method graphics in the unit helpful for preparing me to giving different options to students on how to attack the word problems I will present to them. I was unable to get a clear visual of the QAR Method graphic, even when it was clicked on and attempted to zoomed in. For next time, I would recommend finding a larger version of the file or provide a link to that larger version. I did not get anything out of that method due to being unable to view it.

As for the created lesson, the "Do Now" activity was a great way for my students to really concentrate on what individual steps they do to solve word problems for mathematics assignments. Many of the students had difficulty coming up with six steps, but that was mainly due to them combining their steps. A few of them forgot to include "Checking your answers" as a step, so that is something these students became more aware of after this lesson was completed. I can tell the students were going in depth with the word problems due to using previous strategies brought up in the past, such as stating "What you Know" from the word problem and using the CUBES method to break down the word problem. They mentioned plenty of times that they felt the process was very repetitive and that they do not like doing all the writing for a mathematics problem. We were able to get through the whole first word problem as a class, so they had a completed layout of how to complete the full word problem using both the scaffolding and meta-cognitive steps. This was helpful for students because they all walked out of the classroom with a reference for how to complete the homework word problem. The evaluation was for eight total points, four points per worksheet. The only issue with the evaluation was that one students forgot to bring in both the class reference word problem and the homework word problem. Other than that one, all students brought both worksheets in the next day and received full credit for completion and correctness.

Conclusions

For the mini lesson, the QAR Method graphic needs to be larger in order for people to get the full use out of it. If it is not there for educational use, then it just creates distraction for the student. For my lesson, it is important that I walk my students through an example of how to use the strategy to attacking word problems in order for them to have a reference while completing the assigned homework problem by themselves. The only thing I would change for next time is to evaluate their classwork word problem before they leave in order to make sure each student wrote every step down and to give them credit before they lose the worksheet. Thankfully, all but one student presented the fully completed classwork and homework word problems, but there are no guarantee's with future assignments. Students showed me deep breakdowns of the problem-solving process through the use of the meta-cognitive steps, which led to accuracy in solving the questions presented to them. Students will not have to do this process for every mathematics word problem in their futures, but it is important for them to notice the steps needed to guarantee correctness.