Overcoming Math Anxiety: Why Understanding Beats Memorization

The way we approach learning math often contributes to math anxiety. Most students learn math through memorization—practicing the same types of problems over and over, mimicking steps without truly understanding why those steps work. The result? Gaps in understanding may surface when students are presented with questions of similar difficulty but different in style or nature.

Many math teachers assign worksheets filled with repetitive questions that require identical procedures. For example, a typical worksheet on one- or two-step equations, commonly used in junior math courses, might include problems like:

While practice is important, over-assigning identical questions can be counterproductive, as it may encourage students to work robotically rather than thoughtfully. They follow steps mechanically, without truly understanding why those steps work. The issue becomes apparent the moment students encounter a question with even a slight variation. For example, consider a question like:

Even though this new equation follows a very similar solving process, many students I've worked with suddenly feel lost. A minor change — such as introducing a fraction — turns what should be a familiar task into a brand-new problem in their eyes. While fractions are a common stumbling block in mathematics, the key issue is that students are often not as confident in applying familiar processes when they encounter them in a new form. This shows that while a student may master the approach for a specific type of question, they may struggle with variations due to a lack of fundamental understanding of the content, limiting their ability to adapt to different problem types.

As teachers, our goal is to find the right balance—encouraging a sufficient amount of math practice while nurturing critical thinking skills, so students can confidently problem-solve and adapt when faced with new challenges.

I remember a story from my math methods university class where my instructor made a striking point: he didn’t find much value in a student who could quickly compute 7 × 15 from memory, but struggled with 7 × 17. His reasoning was simple: 7 × 17 isn’t a completely new problem — it’s just 7 × 15 plus two additional sevens.

What I’m trying to illustrate here is that Student B may not solve 7 × 15 as quickly as Student A, but with a deeper understanding, they are able to reason through the solution for 7 × 17 and, presumably, tackle other multiplication problems more effectively. This illustrates the difference between a student who simply memorizes and regurgitates answers versus one who deeply understands the finer details of the content.

If a student is trained to memorize without an emphasis on understanding the underlying key concepts, they are more likely to encounter gaps in their knowledge when faced with abstract mathematics. These gaps can contribute to math anxiety, as students struggle to adapt to slight variations of the same concept.

Unlocking the Power of Math: Understanding Over Memorization

To truly tackle math anxiety, students need to shift from a mindset of memorization to one of comprehension. The key to this shift is practice with purpose. While repetition is important, it’s essential to engage with math in a way that connects the dots. Instead of just repeating steps, students should actively ask themselves, "Why is this step necessary?" and "How does this connect to other concepts I've learned?"

For example, once students understand the relationship between numbers—like recognizing that 7 × 17 is just a simple modification of 7 × 15—they gain the flexibility to solve problems in multiple ways. This shift from memorization to understanding strengthens students’ problem-solving skills and allows them to approach more complex questions with confidence.

When students move beyond simply replicating steps because they're told to and begin to understand how concepts connect, math becomes more than just a set of rules—it becomes a practical tool for solving real-world problems. As they grasp the reasoning behind each step, math becomes less intimidating and more approachable. This understanding helps them tackle challenges both in and outside the classroom, building confidence and reducing anxiety.