When an early elementary student can recite all of the single digit multiplication facts, a typical response is “wow, that kid is really good at math!” I was that student. I could finish the 2-minute multiplication fact exercises with time to spare, and I could recite formulas within hours of seeing them the first time. I could also (almost) flawlessly re-enact any algorithm our teacher showed us in class that day. It was in college that I learned that memorizing all these facts, formulas, definitions, algorithms, and more is not all that is involved in mathematics. It was a hard lesson. I realized that even though I was good at memorization, I had to do more than that to do the mathematics I was now facing. Even then, memorization and recall of information played a huge role.

A student writes down information while looking at a paper hanging on the wall.

When an early elementary student can recite all of the single digit multiplication facts, a typical response is “wow, that kid is really good at math!” I was that student. I could finish the 2-minute multiplication fact exercises with time to spare, and I could recite formulas within hours of seeing them the first time. I could also (almost) flawlessly re-enact any algorithm our teacher showed us in class that day. It was in college that I learned that memorizing all these facts, formulas, definitions, algorithms, and more is not all that is involved in mathematics. It was a hard lesson. I realized that even though I was good at memorization, I had to do more than that to do the mathematics I was now facing. Even then, memorization and recall of information played a huge role.

Why is memory so important in learning and doing mathematics? It’s important to make a distinction between memorization and memory. Memorization is a mental process by which we store information, and is only one piece of a larger puzzle we reference as memory. Memory consists of three components – short-term, active-working, and long-term. The short-term memory is really short, 2–3 seconds. It serves as triage for the brain, asking “What do I do with this information? Do I use it and forget about it? Do I need it now? Should I save it for later?” Many are familiar with long-term memory, which is often equated to the hard-drive on a computer where information is stored and just sits waiting to be summoned for use. Active working memory is the aspect often least familiar to people. Our active working memory receives information via our short-term memory and pulls information from our long-term memory to synthesize and connect the dots to form new information that we tuck away into long-term memory for use another time. Our active working memory also suspends one or more pieces of information while we manipulate other data and then pulls it all back together for more synthesis. This is an over-simplification, but it’s the gist.

In mathematics classrooms, long-term memory is often given the most regard. We ask students to memorize facts, symbols, vocabulary, algorithms, formulas, and so much more. We also ask them to remember what they did in previous lessons. Involved in this ask is not just the storage of those facts, but the recall of them when the situation calls for it. This is where the active working memory gets involved. The short-term memory accepts incoming, external information, determines its relevance and feeds what’s necessary to the active working memory which then recalls other necessary information from the long-term memory and does its best to make sense of it all. When we say “my brain hurts” or “my brain is full”, it’s about the active working memory trying to keep track of all that’s going on.

A student counting nickels while seated at a desk.

At any of these points, if there is a misfire with memory, a student may get labeled (and may believe they are) “not good at math” when, in fact, it’s their memory that is having trouble. They might be skilled at reasoning about the mathematical ideas and solving problems if they could only remember pieces they need. While storing and recalling information are helpful abilities, challenges in these areas don’t have to be a stumbling block for learning and doing mathematics.  There are many tools that can help a student overcome this obstacle, especially with current technology. Providing written resources (formulas, fact tables, etc.) can be one form of support, as could be providing a calculator, along with many more. Even AP (Advanced Placement) tests provide a formula sheet and allow calculators so that students can focus on reasoning about the mathematics and not spend precious time struggling to remember. And, while the capacity of the active working memory is not infinite, it can be exercised and improved given experiences that support and strengthen it. In the meantime, when the goal is to learn new concepts, it can be helpful to not push a student’s memory too far, offering them memory-specific supports such as written instructions and calculators so they can use their active working memory for other information.

Memory in all its forms plays a very important role in mathematics, but challenges with memory don’t have to be the reason someone is not successful in the subject.