I’ve done it. You’ve done it. We’ve likely all done it at some point…used a “trick” to help us find the answer to a math problem. And, like magic, we have no idea why we got the right answer. It was just there!
Much like teaching algorithms without conceptual understanding, teaching keywords as a primary strategy for solving word problems is not only problematic, it’s harmful. It undoes logic, intuition, and reasoning. Rather than trying to really understand the situation, we pull out the numbers, find a word or two to indicate the operation, and voila, we have a solution.
If the keyword strategy for solving word problems was really that simple, we wouldn’t even have to read the word problem. We would only have to pick out numbers and words and then operate. However, just like the rest of life, it’s just not that simple. Key words are inconsistent (e.g., “more” can mean to add, subtract, or multiply, depending on the context) and, often, nonexistent (sometimes they aren’t even present in a word problems). Sure, they work in contrived situations when “experts” write them to conform to a formula. But trying to apply an over-simplistic strategy such as key words will let us down in real life far more often than it will help us.
So, if using a keyword strategy won’t work, how else might we go about solving word problems?
Here are three strategies I’ve found to be highly successful. If you find that you, or the teachers you work with, are falling into the keyword trap, please share these strategies – they really work!
- Bet Line: Present a word problem, revealing only one line at a time. First, present the title of the word problem and ask, “What do you bet is going to happen in this math story?” After listening to a few predictions, reveal the first line. Then ask, “What do you bet is going to happen next?” After listening to a few more predictions, reveal the next line. Continue asking “What do you bet is going to happen next?” after you reveal each line until it’s time to reveal the question. Ask, “What do you bet the question is going to ask?” This has been, by far, the most productive process I’ve used to help children really understand the structure and flow of word problems. Want to learn more? Check out this article from NCTM.
- Target the Question: Post one reading passage each week. The passage should include several quantitative bits of information that can be used to answer a question. Then, each day, post a different question that can be answered using some or all of the quantitative information in the reading passage. This helps students see that you don’t know what to do with a word problem until you know the question. And different questions will require that you “do” different things each time. For a commercial version, check out the Lone Star Learning website.
- Write Me a Story: Asking students to write their own word problems is a powerful way to help them grapple with the structure and syntax of story problems. Begin by providing an equation such as 24 x 6 = 144. Then, leave it up to the students to find a context that makes sense for the number set and operation you gave them. They need to be sure to include a statement of context, a quantitative scenario, and a question that makes sense. You can differentiate for students by giving them different numbers and operations. You can also make this more difficult by asking students to include additional information that won’t be used to answer their questions. You might also ask students to write multiple word problems that use the same equation.
So, there you go — three ways to move beyond a keyword approach for solving word problems. Next week, I’ll share an amazing template that provides students with space for working out their word problem solutions…so stay tuned!
Please join the conversation. What are your favorite ways to help students grapple with word problems? And please let us know how it goes if you use one of the strategies mentioned above!
Kimberly Rimbey, Ph.D., works with teachers and leaders to develop system-wide change in mathematics teaching and learning.
PS – If you’ll be in the Phoenix, AZ area at the end of October, please consider joining us for the Beyond Math Blocks Teacher Institute. This unique opportunity is designed to support K-5 teachers and coaches as they reimagine mathematics teaching and learning. Learn more by clicking here.