The Most Important Thing Your Child Should Know About Math

In a study at Columbia and Stanford (Blackwell, Trzesniewski, and Dweck, 2007), researchers looked at the math performance of students in seventh grade, divided into two groups: an intervention group and a control group.

Both groups received some enriching academic activities, as well as some instruction in study skills. So one might assume that both groups’ math scores would improve over time, just from that. Apparently the control group’s did not.

The intervention group’s scores, however, did improve. What they received that the control group did not, was the message that their math skills could grow through effort and learning. They were taught that the brain is strengthened through mental effort, and that intelligence can thereby be nurtured and developed.

Students in the control group, on the other hand, did not receive any information about their intelligence being malleable.

When the students’ mathematics grades were measured again at the end of the research study, the control group’s grades had declined, while the intervention group’s grades had increased. Clearly, it made a difference for students to find out something about how the brain works, and how that affects their own learning and mastering of a subject. If you believe your intelligence is fixed and there’s nothing you can do about it – that you’re just naturally and forever “not good in math” because of natural limitations – then you’re likely to view your efforts as futile and your difficulties as failure. Your pessimistic premise will tend to discourage you from making wholehearted efforts or adopting a meta-perspective that helps you approach the task one step at a time.

If, on the other hand, you frame your learning endeavour as exercise for your brain, to get it into good shape for higher performance, then you will be able to see your struggles not as failures but as necessary steps on the path to building your brain’s neuro-cellular network and increasing your intelligence. When you have faith that incremental brain “training” can lead to becoming a math “champion,” then you can more easily see your difficulties in a context of practice rather than as proof of a lack of aptitude.

So… is the most important math lesson actually a biology lesson about how the brain works? To be honest, I don’t really know specifically how the idea of brain-based development of intelligence was presented to the intervention group.

They may have been taught about neuroplasticity and neural pathways, or they may have simply been given an analogy comparing brain “training” to bodybuilding. What I do know is that the students didn’t improve in math just because they had new information about how the brain is malleable. I believe they improved because that new information gave them three important things:

  • permission to be in process
  • increased faith in their own ability to understand and learn the material in an incremental way
  • a reason to believe that they are capable of growing in intelligence rather than limited to “how they were born.”

Could they have acquired that faith and belief without the (more or less scientific) explanation of how the brain works? I would imagine that some of them already had faith in themselves, even before the lesson about the brain. But I would also imagine that some students who didn’t have that self-confidence had nevertheless already been given words of encouragement that conveyed the same thing – it just didn’t convince them.

So in the case of 7th graders like those in the study, it’s possible that pep talks are not enough and their belief in themselves needs to be based on something “objective” like brain research, rather than on something they see as subjective, like what Mom and Dad believe they can do.

It’s hard to say, from the study, whether or not the same applies to younger children. Can parental encouragement by itself convey the message just as believably as “scientific fact” when the mind is less mature?

If a “You can do it!” talk, with patience for the learning process, doesn’t seem to be enough for your own young child, you can explain the way the brain works with an easy-to-understand analogy. It could be the “muscle-building” analogy – maybe using Olympic athletes as an example: how they have to keep trying and trying until they “get it” and then they get better and better the more they practise, and still keep training every day to keep in shape.

Or it could be the “beaten path” analogy: how the bits of knowledge have to travel around your brain and connect to each other through the right path, and if there is no path in the right spot, it has to be made – like when you leave the beaten path in the woods to make your way through the wilderness to where you want to go. The more often you go back and forth between the beaten path and the new spot of interest, the more your new path becomes well-worn itself, until it, too, is a beaten path that is easy to travel.

Regardless of how you present it, the most important thing a child needs to know – and really believe – about math, is that struggling with it doesn’t mean they’re “bad at math” or stupid or a failure. It simply means that they’re in the process of training their brain ‘muscle’ (so to speak), shaping a new brain-cell pathway, and growing their knowledge and intelligence one step at a time. Let them know it’s the way everybody in the world has to do it: there isn’t a genius on earth who wasn’t once a baby who knew nothing.

And if they don’t believe you because you’re presenting it as just a parental “I believe in you!” speech, back it up with the “objectivity” of science. It might just make a difference in how much patience they learn to have in the process, and how much faith and belief they learn to have in themselves.


Originally published in the OFTP Members' newsletter, Home Rules, in 2007.

© Marian Buchanan, 2007

Marian joined the Ontario Federation of Teaching Parents a couple of decades ago, around the time PPM131 was being negotiated. Her unschooled son is all grown up now, but she remains involved in the homeschooling community through her volunteer work with the OFTP as well as running several homeschool-related websites, including the Canadian Home Based Learning Resource Page, University Admissions in Canada, and the Homeschool Media Network. She also offers a few downloadable activities for children through her Kids and Caboodles site.


Topics: How People Learn, Teaching Tips