How to Teach Math Word Problems

In this hour-long, on-demand, interactive webinar from the Consortium on Reaching Excellence in Education (CORE), Dean Ballard, CORE’s Director of Mathematics, reflects on why students often have difficulty solving math word problems, reviews research around mathematical problem-solving, and models proven techniques for teaching math word problems to students.

Watch the video above and read below to preview the webinar and what Ballard discusses in it about how to teach kids to solve math word problems, and even more specifically, how to teach elementary math word problems.

How to Teach Math Word Problems – Understanding Students’ Struggles

Ballard admits that math text is often some of the most difficult reading material students interact with in K-12 classrooms. Math speak and text, he says, is an integrated and often confusing blend of words, symbols, visuals, semantic and syntactical challenges, academic and math-specific vocabulary. He references the following quote from Braselton and Decker (1994)  to back up that claim:

“Mathematics is the most difficult content area material to read because there are more concepts per word, per sentence, and per paragraph than in any other subject; the mixture of words, numerals, letters, symbols, and graphics requires the reader to shift from one type of vocabulary to another.”

 How to Teach Math Word Problems – Amplify, Not Simplify

 How can math educators help make math language, and specifically language in math word problems, more approachable and accessible? Ballard references advice to “amplify, not simplify” math text from Zwiers and others from Understanding Language and the Stanford Center for Assessment, Learning, and Equity at Stanford University. Zwiers’ recommendation states:

“Teachers can foster students’ sense-making by amplifying rather than simplifying, or watering down, their own use of disciplinary language.”

For example, when math educators simplify mathematics, they might continually refer to the numerator as the “top number” in a fraction. When they amplify instruction, math educators might employ the following techniques:

  • Ask students to clarify what they mean when they refer to “the top number” in a fraction.
  • Refer students to an anchor chart.
  • Have the class repeat the term “numerator” out loud while putting their hands over their head to associate the word with a visual.

How to Teach Math Word Problems – Teaching Math Word Problems to ELs

 How can English learners (ELs) be impacted by the difficulty of mathematical text, and how can math educators better accommodate them when teaching math word problems to students? Ballard refers to advice from Moschkovich (2012):

“Research shows that ELs, even as they are learning English, can participate in discussions where they grapple with important mathematical content. Instruction for this population should not emphasize low-level language skills over opportunities to actively communicate about mathematical ideas.”

How to Teach Math Word Problems – 6 Steps for Teaching Math Word Problems

There are many techniques for teaching math word problems to students. One of the techniques Ballard discusses in the webinar is a six-step method from the Institute of Education Sciences. These steps are:

  1. Identify the givens and goals of the problem.
  2. Identify the problem type.
  3. Recall similar problems to help solve the current problem.
  4. Use a visual to represent and solve the problem.
  5. Solve the problem.
  6. Check the solution.

Ballard also goes on to discuss and model many other techniques for teaching math word problems to students. He organizes these techniques into the following six categories:

  1. General Ideas
  2. Understand, But Don’t Yet Solve
  3. Using Visuals
  4. Getting Student Buy-in
  5. Scaffolding and Adapting Problems
  6. Identifying Problem Types

How to Teach Math Word Problems – Professional Learning

Learn more high-leverage teaching practices to help improve students’ math performance and academic success in CORE’s math professional learning. CORE’s professional learning services for mathematics guide teachers, math coaches, and administrators in best practices for increasing the rigor of math instruction while using high-quality, evidence-based math instruction techniques.

Video Transcript

I find that the math texts, explanations in books and word problems are some of the most difficult reading material students encounter in K-12 and maybe beyond. Although this statement is from 1994, it really does still apply today. Math speak and text is an integrative and often confusing blend of words, symbols, visuals, semantic and syntactical challenges, and lots of academic and math specific vocabulary.

According to Zwiers and others at the Understanding Language, Stanford Center for Assessment and Learning and Equity at Stanford University, teachers can foster student’s sense-making by amplifying rather than simplifying or watering down their use of disciplinary language. For example, simplifying would be to continually refer to the numerator as the top number in a fraction, whereas, amplifying would be to build on a student saying, “the top number” by asking, “Well, what do we call that?” Maybe refer to an anchor chart or have the class chorally repeat the term “numerator” and put their hands above their heads while they’re saying it, so they get a visual of that idea. There are different methods to increase awareness and understanding and use of academic language and these are example of amplifying versus simplifying.

We look here and research around English language learners, let’s take a moment to read this. I’ll pause while you do so. While we incorporate strategies to make mathematics and mathematical word problems more accessible to all students, the focus for students is still on the math. It’s not on the technique or the language and it’s important to remember that access and work with applications, word problems, and larger texts, are important parts of math education for all kids.

Here are six ideas from the Institute of Educational Sciences in a guide published online in 2012. It’s called Improving Mathematical Problem Solving in Grades 4 to 8. The IES conducts meta-analysis of research from which they draw conclusions and make recommendations, such as these six on the slide. Take a moment to look these over. I’ll pause while you get a chance to look them over. To let you know, all of these and many more techniques will be what we share throughout this presentation, within the six categories I mentioned earlier, that I’m going to review quickly in a moment. Again, take a moment to read this. This is probably one of the last quotes we’ll be reading today.

I want you to think about how this description of problem solving relates to how you see students solving math word problems and tasks. What level of thinking do the problems engage students in? What challenges do you see student having with word problems and tasks? I also want to notice the importance of students doing this type of work beginning in kindergarten, so it’s not we wait until middle school or wait until they get a strong foundation, knowledge or mathematics, and then they can start applying it. Students can start applying problems from kindergarten with the math they learn at that level, with problems that fit that math.

All right, so as mentioned here, again are the six categories under which I’ve arranged the techniques I’m sharing during this session today. With some of these techniques, I’ll simply describe the technique, with some I’ll show examples to illustrate and clarify them, and with some I’ll actually have you do a little bit of the math, utilizing the technique in order to experience it a little bit better.