Research Based Approaches to Word Problem Instruction
So if you have worked in special education for a while, you know how rough word problems (also known as story problems and about a million other things!) can be for students. In this post, I break down some of the research on what we know works.
Research to Practice: Word Problem Instruction
Word problems combine decoding, reading comprehension, mathematics computation, and mathematics problem solving in one, incredibly challenging bundle. To solve a word problem, students need to be able to 1) read the text of the problem; 2) understand what that text means and all of the vocabulary included in it; 3) engage in mathematical reasoning to figure out what to do; and 4) execute often complex computations accurately (Peng et al., 2018; Powell & Fuchs, 2013). Any one of these areas can pose a challenge to students. Combined and many students– especially those receiving special education services– are stumped. As a result, many students have IEPs with goals for word problems or problem solving. Without effective supports, year after year, students often make little growth in problem solving (Nelson & Powell, 2018).
Before we talk about what works, here are some notes on things that don’t work. When I found out about Polya’s four step approach to problem solving, I was like great! Something that works for students. Except it doesn’t. In general, heuristics, things like understand the problem, plan, solve, check, don’t help students who need help understanding the problem (Jitendra & Star, 2011). Another fail for me was key word strategies. That’s where you teach students tricks like all together means add or fewer means subtract. Apparently, key words not only don’t help students master word problems, they can actually trip them up because, for example, together can also mean multiply (Powell & Fuchs, 2018). Bottom line, heuristics on their own and key words aren’t going to help students master Common Core level word problems. Onto the good news!
I am going to cover, super briefly, one key strategy that works. If you really want to know what to do though, go check out Powell and Fuchs’s (2018) article on effective word problem strategies. It is available free and has worked through examples for how to use each of the strategies they discuss in your classroom– and the two ladies are two of the biggest experts out there on how to help students with disabilities excel in math!
The big strategy that they focus on in that article, and that other researchers have studied, is schema-based instruction. Rather than teaching students superficial tricks, in schema-based instruction (SBI), you help students understand the word problems conceptually. You do it by helping them learn to identify the type of problem they are being asked to solve and to use or create a diagram to represent the problem and understand what they are being asked to do (Xin et al., 2005).
With schemas, the words change across problems. You aren’t teaching students to look for specific words. Instead, you are teaching them to try to understand what is happening in the problem. Is the amount being talked about changing? Are you trying to compare two different values? Are you combining things? Powell and Fuchs (2018) focus on three types of additive schemas (which cover addition and subtraction) and three types of multiplicative schemas (which cover multiplication, division, and ratios). Other researchers use different terms for the different schemas– but what they all find is that if you explicitly teach these schemas to students, explicitly teach them how to look for and understand the underlying structures in word problems– students get better at word problems. The impact of these strategies on real students with disabilities is impressive (Fuchs et al., 2004; Jitendra et al., 2005; Xin et al., 2005).
While there are lots of problem types out there, a lot of the research has focused on just a few. First are additive schemas. These are schemas that underpin addition and subtraction problems. They include combine, compare, and change problems (Powell & Fuchs, 2018, p. 34).
Combine problems are ones with a few parts and a sum. They include problems like “Juan had 18 nickel and quarter coins. If 8 of his coins were nickels, how many are quarters?” and “Juan had 8 nickels and 10 quarters. How many coins does he have in all?” Both problems draw on the same schema– in one you know the sum and one part (and need the other!) and in the other you know the two parts (and need the sum!).
Change problems are ones where the number itself changes, where there is an amount at the beginning, an amount at the end, and some sort of change. One of these problems might be “I had $25 from babysitting and then I earned $10 more. How much money do I have now?”
So what do you have to lose? If you are tired of circling the drain on word problems, give schema-based instruction a whirl! You can use it with any word problems you like (including mine!!!)– it’s a strategy students can take with them when they leave your classroom.
- Fuchs, L., Fuchs, D., Prentice, K., Hamlett, C., Finelli, R., & Courey, S. (2004). Enhancing mathematical problem solving among third-grade students with schema-based instruction. Journal of Educational Psychology, 96 (4), 635-647.
- Jitendra, A. K., & Star, J. R. (2011). Meeting the needs of students with learning disabilities in inclusive mathematics classrooms: The role of schema-based instruction on mathematical problem-solving. Theory Into Practice, 50(1), 12–19.
- Jitendra, A. K., Harwell, M. R., Dupuis, D. N., Karl, S. R., Lein, A. E., Simonson, G., & Slater, S. C. (2015). Effects of a research-based intervention to improve seventh-grade students’ proportional problem solving: A cluster randomized trial. Journal of Educational Psychology, 107, 1019–1034.
- Nelson, G., & Powell, S. R. (2018). A systematic review of longitudinal studies of mathematics difficulty. Journal of learning disabilities, 51(6), 523-539.
- Peng, P., Wang, C., & Namkung, J. (2018). Understanding the cognitive related to mathematics difficulties: A meta-analysis on the cognitive deficit profiles and the bottleneck theory. Review of Educational Research, 88(3), 434–476.
- Powell, S. & Fuchs, L. (2018). Effective word-problem instruction: Using schemas to facilitate mathematical reasoning. Teaching Exceptional Children, 51(1), 31-42.
- Xin, Y. P., Jitendra, A. K., & Deatline-Buchman, A. (2005). Effects of mathematical word problem solving instruction on students with learning problems. Journal of Special Education, 39, 181–192.