Building Critical Thinking in the Math Block


5 ways to reinforce real-life math applications

By Rachel Wilser

Let’s be real: teachers are under an inordinate amount of pressure. There’s an unreal amount of content to be taught each year, and most students start taking state mandated standardized tests as young as second grade. And we hear a ton about teaching kids to read, kids being behind in reading, kids not liking to read, and so on. Reading gets a ton of attention. But today, I want to give a little love to your math block, AND talk about how you can build critical thinking in your math block (which, bonus tip, is important for reading, as well as life).

Critical thinking is an essential school and life skill. How will you know if you’re overcharged at the store, or a restaurant if you’re not thinking critically? How can you decide if a news story or article makes sense or seems reasonable if you can’t think critically? You can’t assess pieces of information that people pass to you if you can’t think critically. In an era when we’re constantly bombarded with news, social media, and other images, critical thinking skills have never been more important. So how can we help kids build their critical thinking skills?

Here are 5 ways I build critical thinking in the math block. (For the record, my math block is 90 minutes.)

  1. Teach with tasks.
    What does this mean? A task is different from a traditional math (story) problem in two main ways. They have multiple points of entry for students at different levels, and they (usually) have multiple solutions. This is huge for building critical thinking, because it shows students that there are multiple ways to solve the same problem, AND that they’re all valid, AND they all work. Here are some examples of tasks I used in my math block with first graders: “XX played in a basketball game, and scored 10 points total. How many points did they score in each half?” (The goal here is for students to generate multiple ways to make 10.) “XX has a box of 28 crayons. Draw a picture to show what the 2 represents and what the 8 represents.” (This task tackles place value, and digits; students frequently draw a 2 and an 8, but that’s clearly inaccurate.) “XX baked 12 cupcakes for YY. ½ were vanilla, and ½ were chocolate. How many cupcakes were vanilla?” (This is a fractions problem that obviously has only one answer.) Teaching with tasks definitely takes a little more time, especially up front while everyone is getting used to the process, but the pay off is rich; students are able to analyze and problem solve in a much deeper way than when they solve simple word problems.
  2. Teach students how to work together, share ideas, and disagree respectfully.
    This is huge, again for school, and for life. Tasks are much less intimidating to students when they work in pairs, but in order for them to actually work they need some instruction first. They likely know broadly how to work together and share ideas, although you probably want to refine for them specifically how that will look during math. But it’s likely they’re not 100% sure how to disagree respectfully, and that’s where you come in: you can teach them what it looks like to disagree respectfully, because, per point 1, there are multiple correct solutions and students need to be able to explain their thinking and why it works. And their partners should know how to respectfully challenge them and/or to share a different idea that might also work.
  3. Give deliberately wrong answers, and ask students to find the mistakes or errors.
    If you do this, it’s essential up front that the answer is wrong. Don’t let them work under the false assumption that maybe it’s correct. Again, this is a great time for students to work together to find the error, either in logic or process.
  4. Have students write about math.
    This works simultaneously with several other steps, but writing about math is so important, and pushing kids to be explicit about their thinking/process. Often, with younger students especially, students want to write things like “I counted to solve,” or “I know the answer,” but that’s not really writing about math. It doesn’t tell anyone else how they really solved the problem. You want them to aim for something like “I drew a picture of 6 flowers, and added one at a time until I got to 10, so I know that the missing number is 4,” or whatever would be appropriate. We want them to be writing answers that show their thinking (so that other mathematicians can disagree respectfully).
  5. Incorporate puzzles and strategy games into math stations.
    When students work on puzzles, they are utilizing SO MANY skills at the same time; they are an amazing and super easy work station. (If you think your administrator might not be down for puzzles, print this free puzzle table skill set sign from Teachers Pay Teachers and display it by your work station. This is also a great place to utilize STEM challenges, as they will hit on many of the same skills and certainly work to build critical thinking.

We would be remiss as educators to ignore critical thinking in the 21st century, but you can build critical thinking skills outside of your literacy block. Start with any one of these five strategies to build critical thinking in your math workshop.

Image credit: George Martell/Bayard Inc, 2017. All rights reserved.

Rachel Wilser has spent the better part of a decade in classrooms around the country — in private, public, charter, elementary, and middle schools. Now, she chases twins and drinks coffee while planning her return to the classroom.

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