Posted Sept. 1, 2021
ARTICLE FAST FACTS
“Making Word Problems Meaningful”
Author: Melissa A. Gallagher, assistant professor
Department: Curriculum & Instruction
Co-authors: Laura Ellis, Travis Weiland
Journal: Mathematics Teacher: Learning and Teaching PK-12
Publication date: Aug. 1, 2021
Topic: math education, reading comprehension
Overview: The article discusses how teachers can help their students better understand and solve math word problems with literacy strategies.
INTERVIEW WITH THE AUTHOR
What is the purpose of the article?
The purpose is to really help teachers see how they can leverage literacy strategies that students are already using and help them see math as a place to make sense and comprehend in the same way they comprehend stories. We do this by focusing on four key literacy strategies: visualizing, retelling, making connections and asking questions. If we teach kids right from the very start, “What is the problem asking? How do you make sense of it?”, then we might be able to avoid problems in later years.
How did your own experiences in education contribute to this article?
Gosh, I have so many stories. But I’ll focus on one. I was working with a sixth grade group of kids. We were trying to get them to better understand and make sense of word problems. So, the problem was, you had a Starbucks gift card. Maybe the card had $10, and your favorite drink was $1.85. How many drinks do you have left that you can buy?
It could be looked at as a repeated subtraction problem or as a division problem, but it had the term: “How many do you have left?” in it. One of the students said, “Well, ‘how many left’ means subtraction, so I have to take $10 and subtract $1.85.” Helping her try to make sense of that and break out of the “key word mentality” was really challenging because she wanted the answer to be $8.15 because she had subtracted, so she must be right. I think we can really do a disservice to our students when we teach them to use key words to figure out what to do with word problems.
How is this article unique?
People have been researching word problems, problem solving and how students solve problems for probably a century. I think what’s unique about this piece is the focus on integrating literacy strategies and problem solving. The audience of this article is teachers, and I’ve not seen anything similar published in any of the National Council of Teachers of Mathematics journals in the past.
What were your most significant discoveries?
Teachers often are so focused on helping students find the right answer that they don’t always listen to where students’ challenges are. So, are students visualizing the problem incorrectly and misapplying the procedure, or are students making a different connection? If the teacher just says, “No, that’s the wrong answer,” then the student won’t know where they went wrong, but also the teacher won’t understand if they just were using different reasoning because they were making different connections. The key takeaway for teachers is to leverage what students already know and can do to help students make connections to make sense of problems.
What are the broader social implications of this article?
We know that understanding fractions predicts how students succeed in algebra. If you take algebra in eighth grade, you’re predicted to earn much more money each year once you graduate. So, if we’re disadvantaging students from getting on that track because we have a test that’s based on word problems, and we haven’t given them access to those, then we’re holding people back from the very beginning.
Why is this subject important to you?
When people make decisions in the real world, if they’re not using math to make those decisions, then they’re making poor decisions. For instance, people who argue that the COVID vaccine is only 94% effective but only 1% of people are dying and think, “I actually have a better shot with my own immune system than with the vaccine,” don’t understand conditional probability and dependent events. They don’t understand the math, so they don’t understand how the vaccine will help them be more protected from the virus.
Whether you’re buying a house or deciding on a car loan, people try to put one over on you with numbers all day long. I want all my students to go out into the world fully capable of figuring out, “What is the best home loan for me? Should I take out student loans, or should I work before I decide to go to college?”
What advice do you have for teachers?
As teachers, we oftentimes find a procedure that we feel works, and then we turn it into a highly structured routine. We take all the joy out of the mathematics when we do that. So, in the article, we really encourage teachers not to push all four reading comprehension strategies with every problem that kids solve. We really want it to be done purposefully to help kids think about and make sense of the problems.
What will you research next?
Laura Ellis, a co-author on the paper with me, tried out some of these strategies in her classroom and found them successful. Now, we’re interested in testing this more systematically, so she’ll be implementing it in two fifth grade classes at her school. We’ll be seeing how it affects students’ confidence in their word problem solving ability and their actual achievement in solving word problems. We’re hoping with nine weeks of instruction they’ll start to internalize these strategies on their own.
— By Lillian Hoang
— Photo courtesy of Melissa A. Gallagher