The Math Misconception That Hurts Our Students


 
     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.

Growing Grade By Grade
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23 comments:

  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.

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

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  2. Thank you for sharing this post! Some students really do get down on themselves when they don't know everything quickly! I like your ideas at the end for ways to help alleviate frustration.

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  3. I find this to be a fascinating subject area. When I worked as a Director of Ed at a learning center, we would often find that missing memorization facts (of one kind or another) would hinder students in their future studies of Pre Algebra and beyond. But I've never considered that some of those very students might then have gained a misconception about math from there on out. It's a very interesting supposition. I'm so glad you share what can help with fixing the problem. I will be putting this idea in my inward teaching toolbox for future reference. Thanks so much!

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    1. Thank you, Christina, for your kind comments! I'm delighted that this post has been helpful!

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  4. Where were you when I was a student? LOL I never could memorize the addition facts and felt a failure in math from about 3rd grade on. Success was based on how fast you could pass the times test for addition facts and I could never get pass the 4's table. I still struggle with math to this day and wonder if you had been my teacher, I wouldn't feel like such a failure today. I joke with my friends when we discuss math problems, telling them that I taught kindergarten and only had to know how to count to 100. (Of course that has changed!) But by making a joke I'm just covering up my inadequacies about math. I hope today's children learn to measure their success with a different yardstick!

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    1. Thank you, Linda, for your kind comments. I totally feel your pain - I literally didn't learn some of my basic facts until - no joke - I was a teacher! I love your comment about teaching children "to measure their success with a different yardstick!" Best wishes!

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  5. I love how clearly you explained this. I was always comforted by the fact that I could "memorize" my way through math class...until I got into the more difficult classes and didn't have the tools to explore my way through it. This reminds me to be more open-minded with the "new math" my son is learning which seems foreign to me. I actually thought to myself the other day how much easier it would be if they just memorized things vs. making 10's, etc. Now I will be thankful he's being taught a strategy and to talk through things vs. simply recalling numbers!

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    1. I'm delighted that this post resonated with you, Lindsay! You're so right - your son will benefit from being taught strategies rather than simply recalling numbers. Best wishes!

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  6. What an important message! It's interesting how before I read this post I had never heard of this misconception and now that I'm done reading it, it seems so obvious! Thank you!

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    1. Thank you, Mary, for your kind comments! It took me years to see what was happening with my students and then, like you said, it seemed so obvious! Thank you!

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  7. I struggle with math (the numbers get switched up when I read them) so I always try to convey that to my students. I will work out the math problems on the board (I teach physical science and chemistry!) and sometimes they will have to come to the board to "help me out"! I have had a number of students tell me it make them feel better to see me work out the problems, too!

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  8. Kudos to you, Erica, for setting such a positive model for your students! Thank you for your comments - best wishes!

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  9. Hi Pat! I am new to your blog, but I'm so glad to have found it.
    The points you shared in this post are so true. Many of these are carried with us into adulthood.
    Looking forward to seeing more of your posts!

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    1. I'm delighted that you've found my blog, Berndette! It's true that we adults often have to carry baggage from childhood. I look forward to sharing more with you!

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  10. Great ideas! It is so easy to get caught up in math fact recall and forget that there is so much more to math!

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    1. So true, Mrs. Wilcox! The real fun can often be when we can problem solve! Thank you for stopping by!

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  11. I really agree with all of this. I finally learned basic facts by playing basketball with my brother. I had to answer the multiplication facts to make a shot. I am a somewhat kinesthetic learner. So. I share that with my students. And yes, if they can't memorize they often think they can't do. I am always behind on the pacing guide when I teach math because I take the time to talk, write, listen and explain. Kids can be so intimidated, as can I, by math. Our job is to help them find THEIR comfort level, not the district's or the publisher's.

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  12. I really agree with all of this. I finally learned basic facts by playing basketball with my brother. I had to answer the multiplication facts to make a shot. I am a somewhat kinesthetic learner. So. I share that with my students. And yes, if they can't memorize they often think they can't do. I am always behind on the pacing guide when I teach math because I take the time to talk, write, listen and explain. Kids can be so intimidated, as can I, by math. Our job is to help them find THEIR comfort level, not the district's or the publisher's.

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  13. Mickey, I'm glad that this resonated with you. You mention a great strategy for our kinesthetic learners, that of doing a physical activity while we learn. Like you, I was always behind on the pacing guide, and for the same reasons. You're so right, math can be intimidating when kids have the wrong perspective and I love your comment about finding their comfort level. Thank you so much for your input!

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