Math problems are a frequent source of frustration for teachers and students alike. Mathematical Practice #1 states that students will “make sense of problems and persevere in solving them.” Let’s break down that definition into practical steps teachers can take to help students develop this habit when solving math problems.
What Does It Mean?
The standard states that “mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution.” There are several key words and phrases to reflect upon in that sentence. First, students are responsible for “explaining to themselves the meaning of a problem.” In order to do that, students must have a strategy for making sense of a problem. Second, students must find “entry points” to help them on their way to solving the problem. Breaking down the problem, sentence by sentence or sometimes even phrase by phrase, is one way to teach students this aspect of the practice. They do this through a careful analysis of the problem – the data given, the clue words used that indicate an operation and the final question to the problem.
Typically students solve math problems in one of two ways. They either ask for help immediately, or they look for a similar problem and pattern their approach from it. Arguably these are weak strategies. Students use them because they work (someone usually does help them when they ask for it) and they don’t have any other strategy to use in its place. It’s not that students don’t want to be able to solve math problems more independently…it’s just that teaching students a variety of ways to solve such problems has not been a consistent part of their math instruction.
An Alternative Strategy for Solving Math Problems
So, how do we provide our students with an alternative strategy? There are no doubt countless ways to do this, but I’ve started using a graphic organizer that is very similar to the one we use for writing essays based on the well-known Four Square method. I like using this organizer for two reasons. First, it’s familiar to my students. They don’t have to tackle a challenging word problem while at the same time learn a brand-new organizer. This approach reduces their stress levels and allows them greater focus on the problem itself. Also, it gives them a step-by-step method of developing the habits outlined in the longer definition of the practice – explaining the problem, looking for entry points to the solution, and developing a plan.
Begin by explaining to students that you will teach them a step-by-step strategy for making sense of word problems. If you also use the Four Square method during writing, you can connect it to their understanding of that graphic organizer. Display a math problem to solve, such as the following:
Chloe read 17 pages on Monday, 23 pages on Tuesday and 19 pages on Wednesday. In all, how many pages did she read this week?
Then take them through each box in the graphic organizer. First, operation. Students need to be able to translate words such as “in all” and “how much more” into mathematical operations to perform. Second, students record the numerical information given in the problem. Third, using what they’ve discovered in the first two steps (operation and numbers), students then write an equation to solve the problem. Finally, students answer the question (including a label as appropriate). I like to have my students re-read the problem again after they have a solution to answer that question and ask themselves, “Does it make sense?”
Strategies Take Time to Master
I have included a link to a PDF version of the graphic organizer (click on the image). However, don’t feel you have to make a paper copy for every word problem. Instead, teach your students to draw it in their Math Notebook or on a dry erase slate. Gradually transition them to using the steps in the organizer mentally. That’s the purpose of a graphic organizer – to articulate the steps in a strategy and provide a visual scaffold for using it. Your goal is to have students use the strategy mentally and fluently with a variety of math problems. You will need to model this many, many times…probably more times than you might expect. Strategy instruction is not a “one and done” process. It would also help if you taught your students to recognize clue words/phrases in math problems that indicated a math operation. Here is a link to a PDF by Melissa S. Moreno that is a wonderful resource for doing just that.
A Broader Context
Although, this first mathematical practice never directly uses the word “math,” I think it can easily be transferred to other contexts in which the values of resilience and perseverance are encouraged. If you think about it, this first practice is really a critical life-skill that we all must learn to do well if we want to live productive, happy lives. So, persevere and watch your students grow in confidence and competence when it comes to solving problems. It won’t be long before solving math problems will be an enjoyable experience.