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Teach Except Child. Author manuscript; available in PMC 2018 Sep 10.
Published in final edited form as:
Teach Except Child. 2018 Sep; 51(1): 31–42.
Published online 2018 Jun 7. doi:  10.1177/0040059918777250
PMCID: PMC6130842
NIHMSID: NIHMS961836
PMID: 30210179

Effective Word-Problem Instruction: Using Schemas to Facilitate Mathematical Reasoning

In a fourth-grade general education classroom, Mrs. Blanton posted her math lesson’s objective: Students will solve division word problems. During her instruction, Mrs. Blanton says, “In a word problem, the word share tells you to divide.” Mrs. Frank, a special education teacher, provides small-group instruction to Mrs. Blanton’s students with learning disabilities. During Mrs. Frank’s intervention time, she showed students the word problem of the day: On Wednesday, the coffee shop had 108 customers. The bookstore had 65 customers. How many more customers did the coffee shop have on Wednesday? Mrs. Frank reminds her students to use the Math Key Words Poster hanging in her resource room. The poster indicates that more means addition.

Many general and special education teachers across the U.S. teach word problems by defining problems as a single operation (e.g., “Today, we’re working on subtraction word problems”) and linking key words (e.g., more, altogether, share, twice) to specific operations (e.g., share means to divide). Unfortunately, teaching students to approach word problems in these ways discourages mathematical reasoning and frequently produces incorrect answers. In Table 1, we list eight common key words, identify the operation typically associated with each, and provide word problems that illustrate how reliance on key words can result in incorrect answers. Neither of these approaches—defining problems in terms of a single operation or linking key words to specific operations—has evidence to support its use.

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