Welcome to Summer PD! Because many of us devote time during the summer months to look for opportunities for professional growth, I will be presenting an 8-week summer PD blog series this June and July. Join me each Wednesday for a new topic! Happy Reading!
The focus of this week’s Summer PD is the dangers of using keywords to solve math word problems. This article presents arguments against the use of keywords and offers a new strategy to refocus students’ learning on critical thinking and sense-making.
Van de Walle and Lovin (2006) and Van de Walle, Karp, and Bay-Williams (2012) provide four arguments against the use of key words:
1. Keywords can be dangerous! In fact, they can be used in ways that differ from the way students expect them to be used and lead students to an incorrect solution strategy path. Consider the problem in the illustration below. If students misunderstand the phrase “6 more” to mean that Caty has six more baseball hats than Derek, they will incorrectly respond with an answer of 16 rather than 4.
2. The use of keywords focuses on looking at the words in isolation and not in the context of the problem. “Mathematics is about reasoning and making sense of situations” (Van de Walle & Lovin, 2006, p. 70). Students should analyze the structure of problems in context not just dissect them for keywords.
3. Many problems, especially as students begin to advance to more sophisticated work, have no key words. Consider the problem in the illustration below. Because the problem does not contain key words, students who rely on this approach will not have a strategy on which to rely.
4. The use of key words does not work with more advanced problems or those with more than one step. Therefore, students who do not attend to the meaning of a problem while solving it will be unsuccessful in completing the problem.
Tina Cardone, author of “Nix the Tricks,” a guide to avoiding non-conceptually developmental short-cuts, suggests having students think about the words of the problem as a whole and focus on what is happening in the problem in context. Additionally, she suggests that the use of student-drawn illustrations will help students understand the problem and make sense of the words before completing computations. (Grab a copy of Tina’s book here.)
Math Makes Sense
Instead of using keywords, I would like to encourage the use of the operation situations.
The illustration above shows the two addition situations. In a joining situation, sets are being joined together. Problems illustrating a joining situation involve looking for the total or one of the addends. Similarly, problems illustrating a part-part-whole situation involve looking for the whole or one of the parts.
The illustration above shows the two subtraction situations. In a separation situation, a group is separated and something is left behind. Problems illustrating a separation situation involve finding what’s left or what changed after separation and the initial amount before the change. Problems illustrating a comparison situation involve comparing quantities and looking for the larger amount, the smaller amount, or the difference.
Here are some ideas to move your students from keywords to the operation situations:
1. Use basic word problems from a grade-level resource or textbook as a sorting activity to allow students to practice visualizing the situations and matching them to an operation. Be sure to have students identify the situation when they provide the operation.
- Van de Wall, J. A., Karp, K. S., & Bay-Williams, J. M. (2012). Elementary and middle school mathematics: Teaching developmentally. Boston, MA: Pearson.
- Van de Wall, J. A. and Lovin, L. H. (2006). Teaching student-centered mathematics: Grades 3 – 5. Boston, MA: Pearson.