Teaching Word Problems—A Different Kind of Reading Comprehension
I have worked with elementary and middle school teachers for more than two decades, and a common lament is, “My students don’t know how to solve word problems. They get anxious, they give up, they just don’t know where to start.” When I question them a bit more, a common portrait of student frustration and failure tends to look like this.
First, they might begin reading the word problem, but they quickly shift to looking for numbers in the problem and then guessing how they might be used to calculate the answer to the problem. If they’re third grade students, and they are starting to learn about multiplication, they often simply multiply the numbers in the problem, get “an answer,” and move on to the next problem.
Recently, many of these teachers have tried the CUBES strategy, but with little success. This method involves:
- Circling the numbers in the problem
- Underlining the question
- Boxing the key words
- Evaluating and eliminating unnecessary information
- Solving and checking
My colleagues and I examined strategies like these for a national expert panel on problem solving in grades 4–8, and we found there was no substantial, empirical evidence for them.1 These approaches are simply too broad, and in the case of the CUBES strategy, they are likely to mislead students into the wrong answers. Consider the following two problems. CUBES encourages students to put a box around the key words. Notice in these two problems the different meaning of the word more. Putting a box around more does little to help students solve the problem.
Mia got $15 for her birthday this year from her parents. Then she got $5 more from her aunt. How many dollars did Mia get for her birthday?
Mia got $15 for her birthday this year from her parents. That is $5 more than her parents gave her last year on her birthday. How many dollars did her parents give her last year for her birthday?
It is natural to classify how many students struggle with word problems as an issue of “reading comprehension.” Some researchers, particularly in special education, even suggest the core issue is one of vocabulary. Most certainly, some words used in textbook word problems are foreign to some students—laundromat, discount, hourly wage. But teachers can change these words in the problem or pre-teach them if necessary.
The deeper issue is there are several types of word problems, and they require different approaches. Helping students be successful in geometry problems where there are very few “words” is different from word problems involving whole number operations. Let’s focus on the latter, particularly addition and subtraction word problems.
First, it is critical educators understand that at the heart of problem solving is determining the relationships between quantities. That’s essential. Second, addition and subtraction word problems have basic, underlying structures:
| Action Problems |
|
| Relationship Problems |
|
The first problem involving Mia, her parents, and her aunt is an Add To/Join problem, and it is relatively easy. The second problem about Mia and how much her parents gave her this year and last year is much more difficult. It is Compare problem. Understanding the relationship between how much money she was given this year and last year requires the learner to determine that Mia received less money last year than this year. It is also reasonable to solve this problem with either addition (5 + __ = 15) or subtraction (15 – 5 = __).
The 3 Read Strategy
A promising method for teaching students these kinds of addition and subtraction problems (and many more types of problems) is through the 3 Read Strategy2. The three steps in the strategy move students from understanding the context of the problem to looking for relationships between quantities, to a final step of generating mathematical questions.
1st Read: Comprehend the Text
Teacher reads the problem stem (without the question) to students without the numbers and without reading the question.
“What is the situation about?”
“What is taking place in the problem?”
“How might I model this problem?”
“What operations might be involved in the problem?”
2nd Read: Comprehend the Mathematics
Teacher or student reads the problem stem (without the question) with the numbers.
“What are the quantities in the problem?”
“What do they mean?”
“How are they related?”
“How might I adjust my model of the problem?”
3rd Read: List All the Possible Mathematical Questions
“What mathematical questions can we ask about the situation?”
“How would we find the answer to the question?”
The 1st Read allows teachers to employ an emerging, promising practice in problem-solving: Acting out the problem to give students a better sense of the meaning and context of the problem. A key part of the 2nd Read is students develop a representation of the problem. This might involve chips, number bonds, tape diagrams, or a simple line drawing. Concrete or semi-concrete visual representations reinforce the relationship between the quantities for students. The 3rd Read allows students to refine that representation before they compute the answer. Here is a tape diagram of the second problem involving Mia and the money she got on her two birthdays.
| This year | $15 | |
| Last year | ? | $5 |
My colleagues and I have found in our professional development work that teachers find the 3 Read Strategy extremely helpful. It is relatively easy to implement, and over time, students begin to use the steps on their own to solve similar problems. Moreover, it is useful across a range of problems, from multiplication and division to ratio and proportion and algebra problems.
Try a sample of Dr. John Woodward’s TransMath, a comprehensive math intervention curriculum that targets middle and high school students who lack the foundational skills necessary for entry into algebra and/or who are two or more years below grade level in math. Get your sample here.
References:
1Woodward, J., Beckmann, S., Driscoll, M., Franke, M., Herzig, P., Jitendra, A., Koedinger, K. R., & Ogbuehi, P. (2018). Improving mathematical problem solving in grades 4 through 8: A practice guide (NCEE 2012-4055). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. Retrieved from https://ies.ed.gov/ncee/wwc/PracticeGuide/16
2The 3-Read Protocol. (n.d.). Retrieved 6 18, 2019, from SFUSD Mathematics Department: https://www.sfusd.edu/departments/mathematics-department-page/math-teaching-toolkit/math-teaching-strategies/signature-strategies/three-read-protocol
