Teaching Problem Solving in Guided Math Groups: Part 1

Posted on September 10, 2010. Filed under: Math is a Language | Tags: , |

Problem solving is an essential part of learning to do math. During the next few posts I want to talk about some key elements in teaching this process standard. NCTM defines problem solving as “engaging in a task for which the solution is not known in advance.” The math research maintains that contextualizing problems within our everyday lives is what helps students to make connections and learn in a natural way. Moreover, students must have a variety of strategies to approach problems, including diagrams, looking for patterns and various other strategies.


I remember a few years ago, NY state sent out a memo to all testing grades to NOT USE THE KEY WORD STRATEGY. Although many of us often teach the key word strategy (as in this word means….) math researchers say not to use it! Actually to heavily avoid it! Yes, I’m talking about all those key word posters we have hung up in our classrooms across the U.S:)  We teach our students that when they see “altogether” and “in all” to add and when they see words like “left” and “fewer” to subtract (Van de Wahl, Karp & Bay-Williams 2010). These do work sometimes, in many of the simplistic story problems in textbooks (Svlentic-Dowell,Beal & Capraro, 2006). However, they aren’t a good strategy for the real world and even for more complicated story problems. Many researchers and math educators have advised against teaching them in this way (Burns, 2000; Sowder, 1988).


1. They can be misleading, especially if students aren’t taught to read, visualize and think out the entire problem.

2. Many problems have no key words. So then, what do students do? They often get stuck!

3. It teaches bad practices. It teaches students not to think and reason, just find that word and solve it. We must teach them “a sense-making strategy.”

In conclusion, I think more than teaching students key words, teach them to think.

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3 Responses to “Teaching Problem Solving in Guided Math Groups: Part 1”

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Could you explain the idea of a “sense making strategy” a little more? I confess that I teach my children to rely on those keywords.

Van de Wahl is really referring to having students think out the problem in a way that it makes logical sense. So to have them visualize the problem, interpret the problem and then come up with a strategy that makes sense given what they have thought about instead of just defaulting to whatever words might be in the problem. Does that help? Also, having students draw out the situation when possible allows them to make sense of the problem. It can be so revealing to have students “translate” the problem into their own words and explain it outloud. Furthermore, always getting them to ask at the end, “Does this answer make sense?” and of course talking about “what it means to make sense” – so often we assume students understand basic concepts like this when they don’t.

What you suggest is so true, teachers can use those key words sometimes, but not as a strategy for bigger problems. What if the problem is not worded that way? Also, these “clue words” are used in practice for the standardized testing. Many of the problems on multiple choice tests are geared toward finding the one operation and that’s why teachers make it a practice in their classes. I like to use these Strategy of the Month posters throughout the school, such as Drawing a Diagram, Looking for a Pattern, Solve a Simpler Problem, etc. Each of the posters also poses a problem for the students to solve. (Gr. 1/2 has a problem, Gr.3/4 etc). The students submit their solutions to me and we discuss the strategies they used to solve the problem. The middle school teachers have the students post their solutions and justify their strategies. The hard part is getting teachers to realize their students are doing more mathematics when they are solving these monthly problems than if they are solving a one-step multiple choice problem for a test. Where’s the balance?? Any thoughts??

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