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.

Students are often presented with a story problem and they immediately start guessing what operation they should do to the numbers. I call it the "pluck and poke" method of problem solving. They pluck the numbers out, poke them in an equation and say they have a solution. The problem is the answer may not be related to the problem. The students may not understand the problem they are trying to solve.


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

First, students must understand the problem. To help them focus on reading and understanding, leave the numbers and the question out of the problem. Let students read, retell, and visualize the story with no numbers. In place of numbers use words such as a group or some. This helps students slow down and consider the story part of the problem. Students can focus on what is happening, rather than "how many" it is happening to.


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.

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Identify Necessary Information

Information needed to solve a problem is not always readily apparent. Important information may be buried in a sea of information, making it difficult to identify the most important information. Once a student knows what the question to be solved is, then he or she can identify and find the information that is helpful in solving the problem.


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

Here is a list of questions that will help students make 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

Give students time to try their plan. Let students work in partners and discuss progress with each other. If you see students becoming frustrated, jump in and ask questions that lead students to possible approaches as they share their thinking. Be careful not to guide too much. You want to honor students' opportunities for discovery of a process that leads to a solution. The goal is to promote perseverance with students as they tackle challenging problems.

Check for Reasonableness

Throughout the problem solving process, students need to ask themselves, "Does this make sense?" When students have an answer, they need to consider if this answer makes sense for this problem. Students may use rounding to determine if the answer makes sense. If students understand the problem and know the numbers, they should be able to check for reasonableness.

Summary

As you look at the steps to problem solving above, you may notice understanding the problem is the first essential element to successful problem solving. That's because the numbers and equations are meaningless without understanding. Deep understanding is what leads to a successful solution that goes far beyond an answer.
In the video below, the teacher never gives the numbers. The students choose their own numbers to solve the problem.
In the video above notice:


  • structure
  • engagement
  • 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?