Solving Math Story Problems

Written by Guest Blogger Dr. Gene Tavernetti.
Gene has been involved in education for over thirty years. He has served as coach, teacher, counselor, administrator, and consultant. He is the author of Teach FAST and Maximizing the Impact of Coaching Cycles. Dr. Tavernetti holds a core belief about children and adults: Given the right environment and proper support, everyone can improve and succeed. We, at FactFreaks, share that belief.
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Do your students struggle with story problems? Are you searching for a new strategy or trick? I'm sure that you've run across the multitudes of various strategies that claim to teach students how to solve story (also known as word or application) problems. What is disenchanting about the many strategies, tips, and tricks, many of which are found in textbooks, is that the authors provide these strategies as an ala carte menu of offerings as if there were no cohesive agreement regarding problem solving.

But that does seem to be the case. Most subjects, with the exception of math, have an agreed upon framework or protocol for solving problems, with only small variations in the various disciplines. In content areas other than math, students are taught to use some form of the scientific method to solve problems:

• Identify the problem
• Determine what is already known about the problem (has this, or something similar, occurred before)
• Generate a hypothesis
• Conduct an experiment
• Review the data

The good news is that this methodology is so common it is constantly observed in our everyday life! Think about the last time you went to your doctor with a malady. Your interaction with the doctor likely followed this structure. The doctor asks, “What is wrong?” (Statement of the Problem) Next, “Have you or anyone in your family had this, or something like this, before?" (Identify the problem) "What were you doing differently when you first noticed this?” (Determine what is already known) After several questions like this, the doctor may say, “I have seen something like this before” or “Let me do some research on that." (Generate a hypothesis) From the collected data, a diagnosis is made, a treatment is recommended (Conduct an experiment), and a follow-up appointment is made (Review the data).

The most time consuming, and I argue, the most important components of the process are the first two steps; identifying and gaining knowledge about the problem. A student should continually re-visit their initial questions, which identified the problem and determined what was already known, multiple times throughout the process to stay focused on getting the correct answer.

Use of the scientific method is ubiquitous in our daily lives and is, in fact, a largely intuitive process. We observe a crying baby. We ask when has this happened before? Maybe the diaper is dirty, so we change the diaper but the baby is still crying. Maybe she is hungry, but when offered food she won’t eat. Imagine that the crying is due to pain but we decide to stop asking questions and just put her in her crib and hope she falls asleep. The first two steps are so crucial, that if we stop gathering data and skip to the wrong conclusion without generating a hypothesis, we will get the wrong answer.

This process continued correctly - identify the problem, determine what is known, generate a hypothesis, conduct an experiment, and review data - is simply common sense. We use it everywhere except when we teach students to solve story problems. To be fair, I have read about teachers using this framework, but in my twenty years as an instructional coach I have never observed it. Instead of teaching students a process to identify the problem, instead of teaching them a structured systematic process to reflect on whether they have encountered similar problems, we observe teachers directing students to use disparate strategies that lack the coherence of the problem-solving framework. Strategies such as finding the numbers in the problem, looking for clue words or phrases such as “all together”, “remain”, “how many groups?”, are strategies that may work for some problems but will fail for others.

These disparate strategies do not lead to deeper understanding of the problems by the students, and they rob teachers of the opportunity to gather discrete formative data that could guide further instruction. If a student is unable to solve a problem, we need to find out where they are getting stuck. Are their reading skills less than what the problem is requiring? Is it a lack of knowledge of the necessary math to solve the problem? Do they not recognize a pattern from previous problems? Are they unfamiliar with the context of the problem? (Have you ever noticed how many story problems involve shopping in various types of stores? What percentage of students in your classes have shopped in an office supply store for school supplies?)

How then, can (and should) we relate the problem-solving framework used by other content areas to math? The first thing to do is teach the framework to the students. Students should be able to describe the process and identify where they are in the process when solving story problems. The framework should be a roadmap, a protocol for every problem.

Please note that as in the example of diagnosing a physical ailment, the first part of the problem solving process, identifying the problem and determining what is already known, takes the longest time. Teachers have argued that some students are able to solve story problems without the cumbersome processes listed above, asking why should we make them do all the work suggested to solve a problem they are already capable of doing? Two simple answers: First, learning the problem-solving framework and becoming proficient in using the methodology, will serve the students when they encounter a problem that is more complex. Second, when students are providing answers to practice problems, don’t you require them to show their work? What is unreasonable about asking them to show their work when solving story problems? Nothing, it's not only reasonable, but a necessary part of the process.

When a student uses this framework there is no guarantee that they will be able to solve the story problem. But what is guaranteed is that by following this framework, teachers will be able to identify sticking points more accurately because of the additional formative data collected. And that is a strategy that will actually help students solve math story problems.