The Math Misconception That Hurts Our Students

     Math can sometimes seem like countless skill-based concepts that we must make sure children internalize. A misconception can really throw a kink into the works. I believe there is a math misconception that is never taught but is far too often “learned” by far too many children. This misconception can significantly impair their overall performance and damage their attitude toward math. This misconception could be stated as,
“Since we have to learn (memorize) basic math facts,
we have to do all math mentally.”
     What children seem to do is transfer the necessity for quick mental recall of basic facts to the entirety of math. The 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.” Believing this is so damaging to children and their ability to grow mathematically.

     How do kids develop the “all math is mental math” misconception? This mistaken belief is born just about the time that children grasp the concepts of combining and taking apart. Well-meaning teachers and parents start to focus vast amounts of energy on learning (memorizing) 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 and may never catch up. What’s worse, they may develop an “I’m not good at math” mindset or, worse, “I hate math” mindset.

    How does this “all math is mental math” misconception hurt students? Beside the frustration and negative attitude that can result, 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. This poor habit of not recording our mathematical thinking further hampers 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 (rounding, predicting, estimating, drawing, analyzing, collaborating) that don’t require math facts seem not to matter. Every math lesson becomes a mathematical mine-field where the lucky ones who know their basic facts will shine and the unlucky ones who don’t may 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 vital 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…and, to be honest, the way I taught early in my career, 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 teach what I have learned to my past students. What I can do is to take every tutoring, consulting, and mentoring opportunity to allay my students’ frustrations. My dialogue includes 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 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.
     I wonder if other teachers have experienced this misconception among their students. I’d love to hear how you correct it as you support your students.
Pat McFadyen
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  1. Thanks, Pat, for sharing these important ideas. I, too, was one a student who trekked through the "minefield" of math. I appreciate your insights.

    1. I feel your pain, Marcy! I'm glad this resonated with you!


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