The Problem with Problem Solving
Making Math Count in WHPS
Students usually struggle with problem solving because they don't understand the problem. Let's explore strategies to take the problems out of problem solving.
So how do we get students to slow down and move from "answer getting" to real problem solving? We need to improve reading comprehension in math. Here are some ideas from Math in Practice: A Guide for Teachers by Susan O'Connell.
Understand the Problem
We want to know that when children read the words, they understand the words. For many years we have asked students to underline the question, but underlining the question doesn't mean students understand what is happening in the problem. After reading the problem, students retell or restate the problem in their own words. A graphic organizer used in retelling a story, can help with retelling a math problem. Students tell what they know at the beginning of the problem, what action happened during the problem, and how the problem ends. This sounds a lot like reading comprehension strategies.
Visualizing the problem may help students understand it. Students can act out what is happening, use objects to show the problem, or use a math tool like a part-part-whole mat to represent the problem. Sometimes, gathering data into a chart or table or using a number line, will help students visualize what is happening in the story.
Multiple reads will allow students to process what they are reading in order to better understand the problem. One strategy is called Three Reads. First, students read for the gist of the story. They can paraphrase without numbers and explain the story. As students show understanding of the story, add the question and the numbers to complete the story. The second read is to understand what the problem is. In this read students are identifying what they need to solve. The third reading is for gathering the details needed to solve the problem. In this read students identify information needed to solve the problem.
Focusing on reading the story without numbers will help students view problems in a different way. They are seeking understanding of the situation and the problem. Students should be thinking about how the information they have can help solve the problem. The focus shifts from right answers to solving problems.
Identify Necessary Information
Sometimes students need to find conditions in the problem. A condition is data that doesn't appear with the other data, but affects the outcome of the problem. Consider this problem:
Molly's Pastry Shop baked these tasty treats:
120 candy cane cookies
125 gingerbread men
55 apple pies
65 pumpkin pies
Molly rolled out the crusts for the pies. The apple pies each needed 2 crusts. The pumpkin pies only needed 1 crust. How many crusts did she need to roll?
The number of crusts needed for each pie is a condition that affects the solution.
Identifying missing data is also critical to identifying necessary information. Sometimes the important data is not in the problem, but can be found from the information provided in the problem. This leads to a two-step problem. Students need to think about what information will help them find the missing data, and what data is unnecessary to solve the problem.
Develop a Plan
- What is a good plan for solving this problem?
- Should I add, subtract, multiply, or divide?
- Should I make a table to help me see patterns or relationships?
- Would a picture or diagram help me simplify the problem?
- Could working backward help me find the solution?
- Would organizing the data in a systemic way help?
- What other strategies might help me solve this problem?
Try the Plan
Check for Reasonableness
- teacher moves
How does this lesson support differentiation in the classroom?
What instructional challenges does the teacher face and overcome in the lesson?
Can this instructional approach be taken in other grade levels in a similar way?