The Importance of Memorization and Other Math Misconceptions
Many of us were taught that once we memorized our math facts, the rest would fall into place. If only it were that simple! Memorization is actually a complex process that asks a lot of our brains–including the ability to recall in times of stress, like taking a test, seeing a flash card, or even being called on.
At McLean, we’re all about understanding how brains learn best–which is why we use multisensory strategies and the Concrete-Representational-Abstract sequence of instruction, or CRA. With this method, students are first exposed to a math concept with manipulatives (concrete), move to pictures (representational), and finally to algorithm (abstract). So, say we’re teaching basic addition to our first graders, we would start by handling physical objects–for example, five yellow blocks and two red to demonstrate that, together, they add up to seven. Next we’d introduce a picture of five squares plus two squares–visual representation of the same concept. By the time we get to the abstract–5+2–we have created a context for understanding.
It’s a math misconception that you can just jump in at the abstract level and learn math that way. All the flashcards in the world won’t force your brain to memorize something out of context. Flashcards are at the abstract level – since really they’re just symbols of the numbers–with no inherent meaning attached to them. Sure, that might work for some students, but it’s only because their brains are able to make that connection from the concrete to the abstract on their own. And even for those students, a clear understanding of the sequence will serve them well at higher level math and in other subject areas. Flashcards do have a place, but they should be the last step in the learning process–after you have a context and a clear understanding of a concept. And rather than use them in a rapid-fire style, I’ll often make them into a game, like Concentration, where if you don’t get the pairing right, you move on–no blame, no shame. Our brains are wired for fun, so I like to integrate this into as many lessons as possible.
The ability to change things up and slow things down–and to work in small groups, or one-on-one–can mitigate the stress response so many students experience with math. As those of us who work at McLean know, the emotional component to learning is so much bigger than most people realize. Taking the time to sit with a student, to talk through a problem and its solutions, makes all the difference.
Because a lot of our students struggle with working memory, we have many techniques and tools to support them. In situations where the pressure to recall might prevent them from progressing through a math problem, we will encourage the use of a multiplication chart, for example, since we’d rather see them put their energy into the process. You can be a brilliant mathematician and use a multiplication chart! Just like you can be a brilliant writer and not know how to spell. I say it to my students all the time: the ability to retain and recall math facts has nothing to do with how smart you are. Knowing that can help them feel less stress, which makes them more available to learn the facts–and gain more confidence.
Another math misconception is that technology makes learning math easier. In fact, starting at the concrete level is more important than ever because technology has eliminated a lot of the hands-on experiences that once fortified our learning–like working on the family farm in what my students would call “the old days,” when people calculated crops and math was a natural part of each day.
But perhaps the biggest misconception about math is that there’s a right and a wrong way to do it. That’s actually a very limited view. I remind my students daily that math is a process and you have to make mistakes because that’s where the learning happens. When doing a puzzle, you don’t just pick up the perfect piece right away; you try different things and see what works until it clicks into place. Math is like a puzzle waiting to be solved, and it might take a few tries; and even if you don’t understand it now, we’ll come at it another way and figure it out.
My wish for all my students is to understand that math is an integral part of life, a way of communicating and understanding the world. There’s a lot of joy in that! And that’s a math fact worth memorizing.
– Sarah Baxter, Lower School Math Specialist