Students who learn to identify three different kinds of word problems--and what strategies to use for each--do better on math tests than students who learn only one general-purpose model, finds a study in the February Journal of Educational Psychology (Vol. 99, No. 1, pages 115-127). Stopping to categorize a word problem before picking a plan to solve it may be especially effective for low-achieving students, says study author Asha Jitendra, PhD, a special education professor at Lehigh University.
Traditionally, students learned to solve math word problems by taking note of key words. For example, problems with the word "combined" or "together" often require addition. However, that strategy often leads students astray, as there are frequent exceptions to the rules. What's more, students scanning for key words often miss out on the big picture, says Jitendra. As a result, teachers have shifted toward general solution instruction (GSI) for word problems, a technique that emphasizes language comprehension and provides students with an all-purpose plan of attack: Read the problem, make a plan, solve it and check the answer.
Though GSI is an improvement over the key-word method, many students get stuck on the first step--they have trouble making sense of the problem, Jitendra says. So she and her colleagues developed schema-based instruction (SBI), in which students learn to first categorize word problems into a few different types and then apply a tailor-made plan to figure out the solution.
The researchers pitted GSI against SBI with 88 third-graders in a school with historically low test scores. The students were randomly assigned to learn how to solve word problems with GSI or through SBI.
The GSI students learned to solve addition word problems, then subtraction problems and finally two-step problems. The SBI students, in contrast, first learned to solve "change" problems, which can require addition or subtraction. What change problems have in common is that they tell a story such as, "Jane had four video games. Her mother gave her three more video games for her birthday. How many video games does Jane now have?" The SBI teachers taught the students to identify such problems and provided a diagram to help them organize the information.
Next, the instructors taught a strategy and diagram for "group" problems, where distinct groups combine to form a new group or set--calculating how many total students there are if you add together first-, second- and third-graders, for instance. Finally, the students learned to solve "compare" problems, in which they describe the relationship between two different numbers--figuring out how much older Sam is than John.
After nine weeks of instruction, the SBI group scored better on word problem tests than the GSI group. And several months later, the SBI group performed 112 points better than the GSI group on a statewide standardized test--they even beat the state's average score.
The SBI method may be effective because it gives students specific strategies for word problems, something that struggling students especially need, says Jitendra.
"Although GSI is a great approach, it is not very helpful for students who are low performing, because it does not focus on domain-specific knowledge," she says.
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