# Bringing Clarity to Math Instruction and Understanding

02/06/2024
Learn how to understand and clearly teach mathematics instruction based on current mathematical strategies and standards.

Over the past few months, I’ve been supporting educators like you and noticing a recurring theme. Many teachers and learners are struggling with the different approaches to mathematics instruction. Frustrated educators have told me, “I didn’t learn this way,” and aren’t always sure how to help students understand mathematics based on the current strategies and standards. If this is you, or if you know someone in this situation, here are a few tips to help build your understanding and your students’.

1. It’s Not New Math
Nothing has changed about the mathematics you learned. Two plus two still equals four. Three times eight still equals 24. And the same fractions, decimals, and percentages are still equivalent. So why does it feel so new? To answer this question, we don’t have to look any further than the Standards for Mathematical Practice (SMPs), specifically practice number two, Reason Abstractly and Quantitatively. Proficient mathematicians don’t just memorize procedures—they understand number and operation relationships well enough to manipulate them during problem solving. There’s a stark difference in expectations from math learners in the past, so it feels different or new. Think of it this way—you’re not just teaching students how to do math, you’re helping them understand why how you do math works. Why does two plus two equal four? Why does three times eight equal 24? Why is one-fourth equal to .25 and 25 percent? Asking yourself why will help put you in the mindset of how to approach instruction.

2. Show What You Know
As math teachers, we’re no strangers to the words “show your work.” Students respond to this command by usually writing out the steps they used to solve a problem using numbers and symbols. But showing what you did and what you know are two different things. Think about the student who shows their work, is unaware of an error, and is adamant they are correct because they followed all the steps correctly. In situations like these, it’s beneficial to have students use a different representation to show what they know, not just what they did. Creating a drawing, building the problem with manipulatives, writing a story to put the math in context, or verbally explaining their thought process are all alternatives that help students better show what they are thinking rather than just what they did. So, pull out those manipulatives, which leads us to the next tip.

3. Let Go and Let Them Explore
Students will shock you with how much they understand mathematical ideas. Much of what they learn in school, they already have some fundamental understanding of—addition, subtraction, multiplication, division, etc. In school, we help them formalize their understanding but often at the expense of ignoring prior knowledge. To better build on what they know, we must allow them to explore math and share their thinking. This also helps students develop number sense, which cannot be effectively fostered by algorithms. Even in higher grade levels, students need the space to try things, make mistakes, figure out why things don’t work, and discover alternative ways to represent their understanding.

4. Do It Yourself
Finally, the best tip I can give you is to do the math yourself. I know you’ve already passed the grade level you’re teaching and have been teaching for years. But we’re all lifelong learners, right? If there’s a specific strategy or model you don’t fully understand, practice and play around with it. Not sure how to use a double number line or divide using fraction models? Connect with a colleague in your school or online. You’ll find that many of the strategies are not as complex as you might think.

For example, I had a teacher share with me that she didn’t understand why students were being taught to “add to subtract.” She felt it didn’t make sense and was too complex for her students. I asked her to remember a time, long ago, when she paid cash for something at a store. When the cashier gave her change, I asked if the cashier subtracted from the \$20 or counted up to \$20 from the total price. Of course, the cashier counted up. I told this teacher that’s “adding to subtract,” and suddenly, it made sense to her.

## Creating Proficient Mathematicians

In the end, remember that we want to create strong, proficient mathematicians—not just good calculators. Math standards, as well as the SMPs, are there to provide a foundation for the shift in math instruction, but you must dive in and explore yourself. The better understanding you have, the better you can support your students.

Want to hear more from Jesse? Tune into the Extraordinary Educators™ Podcast