Consider the following word problem: There are 125 sheep and 5 dogs in a flock. How old is the shepherd? (contributed by Robert Kaplinsky) How might you expect your students to respond? Now, view the YouTube video below. The video documents how a group of eighth-graders responded to the same problem.
While the results of this video are quite shocking, this kind of formulaic thinking when it comes to solving word problems is all too common. In fact, when another mathematics educator tried a similar activity with her first graders, her results were just as astounding. (See the original post here.) So, what’s the problem here? Our students have been trained to look for keywords, or clues, to what operation they are expected to perform to solve a math word problem. While I completely understand that teachers have perfected the use of keywords over the years in order to provide a strategy that would prove successful both in the classroom and on standardized tests, the use of keywords does not require students to think critically about a problem or allow them to make sense of the situation.
With this thinking in mind, I was not surprised to find a plethora of pins related to using keywords on a recent search through Pinterest. The picture below shows a list of all the words that I found– many of which, I disagree with the placement or inclusion of. As a teacher, I can’t imagine what it would be like to help my students memorize all of these terms. How are they going to learn them– with a weekly quiz? I think not.
Van de Walle and Lovin (2006) and Van de Walle, Karp, and Bay-Williams (2012) provide four reasons to remove the use of keywords from our work with students:
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. Add to that the use of multiple-meaning words and our students can become quickly overwhelmed and confused.
Consider the following problem: Julie left $9 on the table. Her brother left $6 on the table. How much money was left on the table? (Find more “Keyword Fails” here.) Use of the word “left” might indicate to some that the solution to this problem is obtained with subtraction; however, this is an addition situation because two quantities are being joined together.
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.
When students begin to view problem situations in this way, they can identify the bigger picture and make connections between problem situations and the necessary solution strategy required to solve the problem.
3. Many problems, especially as students begin to advance to more sophisticated work, have no keywords. Consider the following problem: Dominique had 10 flower petals. Four were green and the rest were orange. How many orange flower petals does Dominique have? Because this problem does not contain keywords, students who rely on this approach will not have a strategy on which to rely, which will most likely result in a new word, like “rest” being added to the subtraction word list.
4. The use of keywords 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 because they will miss the intermediate steps needed to lead to the final result.
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. Students can accomplish this by visualizing the situation and creating a mental picture of the actions that are taking place. Once they understand the actions, students can then connect them to symbols.
After students have had experience with a variety of problem situations, some patterns will begin to emerge as students begin to recognize recurring themes, such as joining, part-part-whole, separating, comparing, equal groups, sharing, and measuring. Throughout the year, teachers can record the different situations students encounter on an anchor chart. Then they can replace that old, out-dated math keywords poster with the brand-spanking new operation situations poster.
- Download my “Analyze Word Problems with Operation Situations” chart here or click on the image to the right. (Note: The chart is meant to be a guide for teachers to use when you create word problems or select the best ones to use with your students.)
- Grab a set of visual operation situations posters from my Teachers Pay Teachers Store to learn more about the operation situations with a set of colorful posters that visually explain each of the operation situations on the chart. Click here!
- 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.
Sound Off! What strategies do you use to emphasize making sense of word problems with your students? Respond in the comments below.