Mistakes in the Math Classroom

Many students grow up believing that being good at math means being fast and always getting the right answer. In reality, research shows that making mistakes is one of the most powerful ways students build deep mathematical understanding and confidence as problem solvers.

Hi, my name is Susie Fahrer, and I am the Executive Director of Rainbow Community School and Omega Middle School. Today, we’re going to drop into the concept of successful mathematical instruction and self-concept.

Rethinking What Success in Math Looks Like

One of the things that I recall when I was younger in elementary school, and like many students I see today, I was under the impression that successful mathematics, and successful students, and successful mathematicians were folks who were fast, always accurate, and really picked things up quickly. They were the ones who finished their pages of mathematics first.

As I matriculated, that sometimes prevented me from feeling particularly successful as a mathematician because I was slower. I often had to write out my thinking, and I sometimes made mistakes.

So what I’ve learned over the years, particularly as I became a math educator, is that I could fall in love with mathematics when I let go of the idea that math is only about speed, accuracy, and efficiency.

Building Deep Mathematical Thinkers

When we really think about what we want to build within our mathematicians, we actually want students who understand concepts with depth and understand how to problem-solve when they don’t get an accurate answer.

Efficiency and speed are often something that can be built over time and can be helpful, but that is not how we want to define success. We want students to be deep mathematical thinkers and problem solvers.

How Rainbow Supports Mathematical Understanding

Here at Rainbow, one of the ways we support that is through some of the programs that we use for mathematics instruction.

For our students in kindergarten through fifth grade, we use a program called Singapore Math. While it is designed typically to be used for schools that have significant periods of time for mathematical instruction, we adopted it because we recognize that the use of this program, with its approach that begins with building concepts, concrete representations of mathematical concepts, moving to pictures, understanding the representations of the concept, and then moving to abstract, with the use of number and algorithm, is really profound in building the types of mathematicians that are effective problem solvers and can attend to more complex computations in their future years of instruction.

Applying Math to Real-Life Situations

Equally, we find that as our students matriculate to middle school and engage in a program called Connected Math, they’re taking these really deep, foundational skills as mathematicians and being asked to apply them to real-life context situations.

This supports a deeper understanding of how mathematical concepts apply to everyday life, whether that means understanding how to calculate a percentage on a restaurant bill for tax purposes, creating budgets for groceries, or understanding measurement and time.

These are hands-on, everyday mathematical concepts that can increase in complexity. Our students are understanding why they are important and how they will be used.

Supporting Advanced Math Learners

For students who have a really high level of math proficiency and achievement, they are able to move to a program that is efficient and maybe even a little bit quicker with their math instruction.

However, they are also able to face those complexities and those mistakes with a sense of rigor and curiosity.

Learning Through Mistakes

Recent research suggests that, as mathematical instructors, we want to be able to provide environments for our students to learn through mistakes.

Not only does this give students the opportunity to analyze a mathematical problem and really understand the stages and steps and find places of typical error, but it also debunks the myth that a strong mathematician is always going to be accurate.

A strong mathematician understands that when a mistake is made, they have the tools and the capacity to unpack it and find out how to fix it for the future.

Supporting Mathematical Thinking at Home

I hope this inspires some different ways to think about what successful mathematics can look like for your child. Attached, you’ll find some ideas on how to build mathematical engagement with young people.

As always, we invite you to come and visit our school and see our mathematics classrooms in real time. If you’re already here, talk to your teachers about how mathematical instruction is being crafted for your child and build a partnership with them so you can support those conversations at home.

We’re excited to partner with you around mathematics and all types of instruction here at Rainbow.

Hope you have a wonderful day.

Learn More

Continue exploring ideas from our Director’s Kaleidoscope series, including topics like executive functioning, student autonomy, and project-based learning.