Summer PD: No More Keywords!

Show a child some tricks and he will survive this week’s math lesson. Teach a child to think critically and his mind will thrive for a lifetime.

(Quote Reference) 

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. 

The Problem

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. 

In order for students to become successful at solving word problems, they must become proficient at identifying what’s happening in the problem situation. Students can do 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. This is the power of using the operation situations. They allow students to see the problem as a whole, like a scene from a movie, and match an operation to the picture. 

While it looks like there are a lot of situations, there are really only six-- two addition, two subtraction situations, one multiplication, and two division 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.  

You'll notice that some of the situations have a missing component within the operation side of the number sentence, such as with What's the Change (Joining), What's the Start, and What's the Part. Sometimes, students must use an inverse operation to obtain an answer. For example, joining situation #2 is an addition situation, i.e. two groups of spiders are joined together. However, because the second group is an unknown, the problem sets up as 5 + __ = 11. Students then have to subtract to find the answer. Yes! This is an early algebra concept. However, when students are presented with problems like these, they will determine the correct path and eventually see subtraction as the most efficient way to find the missing information.

The illustration above shows the multiplication situation and the two division situations. In the multiplication situation, equal groups are counted until a total is found. Problems illustrating a multiplication situation involve finding the total amount in a certain number of equal groups. In the division situations, a total amount is divided into a specific-size group or a specific number of groups. Problems illustrating a division situation will involve finding how many groups or how many in each group.  

Give it a try! 

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. 

2. Need an anchor chart idea? As the students encounter different problem types, record the word problem and the problem type on a labeled operation poster, like "Addition Problems". Keep adding to the anchor chart throughout the school year.

Looking for more? You can find a complete version of my Operation Situation pack with the full-size illustrations of the operation situations in my Teachers Pay Teachers Store. Click here to see it now! 

Sound Off! How do you teach your students to analyze word problems? 

References: 

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.