When I was growing up, math seemed like a bunch of disjointed ideas that I was supposed to know - and I usually didn't. When I started teaching, math seemed like a bunch of skills that I had to almost shove down my student's academic throats.
I was fortunate to get some great math training as a beginning teacher. It helped me not only understand where I was weak but also to understand where kids can miss out. I discovered early on that with all of the
concepts to learn in math, a
misconception can really throw a kink into an already overwhelming job.
I believe there is a math misconception that is never taught but is far too often “learned” by many children. This misconception can significantly impair their overall performance and damage their attitude toward math. This misconception is:
Since we have to memorize basic math facts,
we have to do all math mentally.
Children seem to transfer the need for quick recall of basic facts to all parts of math. Their belief is, “I should be able to look at 3 x 5 = ? and instantly spit out the answer. Therefore, I should be able to look at:
and instantly spit out those answers, too.” It is tremendously damaging to children and their ability to grow in math when they believe this.
How do kids develop the “all math is mental math” misconception?
This misconception is born just about the time that children grasp the concepts of combining and taking apart. Well-meaning teachers and parents start to focus tons of energy on learning, usually by memorizing, all basic addition and subtraction facts. As we move on in math, we add multiplication and division facts to the task. Children who struggle even a little bit with this task can start to fall behind in math. They may develop an “I’m not good at math” mindset or worse, an “I hate math” mindset.
How does this “all math is mental math” misconception hurt students?
Besides the frustration and negative attitude that can develop, students also miss the importance of talking about and writing about their math. They think that the only good math is mental math, so why should I write it down? I’ve seen kids who thought writing down their math thinking was actually a weakness. I've seen others who would write down their thinking...and then erase it! This poor habit of not recording our mathematical thinking can seriously hamper math growth.
I have seen so many children over the years begin to pull into a shell as the need for efficient recall of math facts hampers the rest of their math performance. All of the other essential math skills, like rounding, predicting, estimating, drawing, critical thinking, analyzing, and collaborating that don’t require math facts don't seem to matter.
Every math lesson becomes a mathematical minefield where the lucky ones who know their basic facts will shine and the unlucky ones who don’t will suffer acute embarrassment and chronic frustration. I was actually one of those unlucky students – it took me years to develop efficient recall. I never understood how my struggle fed right into the “all math must be done mentally” misconception until I became a teacher – a math teacher, of all things – and was able to recognize and verbalize the problem.
So basic math facts aren’t important?
Don’t get me wrong! As a long-time math teacher, I am all about mastering basic math facts. They are essential tools for so much that we do in math. Along my journey as a math teacher, I discovered that there are infinitely better ways to teach the concepts and learn the facts than the way I was taught. To be honest, the way I taught early in my career was terrible, but that’s another blog post.
What can teachers do to correct this misconception?
I wish that I could go back in time and directly re-teach what I've learned to the students I've let down in the past. But, I can't. What I can do is to take every tutoring, consulting, and mentoring opportunity to ease my students’ frustrations. Some excellent strategies are:
1. We can change our dialogue to include comments like these. Maybe you can think of others that would work.
- Math is so much more than basic facts.
- Basic facts are the only thing in math that needs a quick recall.
- Learning basic facts can take time. In the meantime, we can still do math successfully.
- You can write about and talk about math without knowing the answers right away.
- Arithmetic is simple computation. Math is solving problems using many math tools, not just basic facts.
- Writing about math is what great mathematicians do.
- If you know most of the answers right away, the math is too easy for you.
- Math is meant to be worked through.
- Fast math is not always good math.
2. We can recognize and praise students who talk about and write about their math.
3. We can display good examples. Even students who don't yet feel confident in math can produce good work samples.
4. We can make grades dependent on explaining our thinking. Some children are highly motivated by grades. If you make displaying and explaining part of the credit for each problem, students will be more apt to show their thinking.
I wonder if other teachers have seen this misconception in their classrooms. I’d love to hear how you correct it as you support your students.
