My Geometry Class Insight

My Geometry Class Insight

Curtis Kelly

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We’ve all had them, those kids that seem way ahead on the line of brain development–the smart ones–and then, those, well, kids way behind–the ones who just don’t get it.

Teachers of young learners are particularly aware of that difference: That kid just doesn’t get it. The learning situation might involve sounding out words with a four-year old, algebra with a 7th grader, or grammar rules with a junior high-schooler. So, what do you do? You take some extra time and explain it in a way that anybody could understand. Carefully. Perfectly. Slooooowly. You break it down into simple steps, and go through them one by one. It is so simple. There is no way that kid couldn’t get it by now, and the kid nods weakly that he does. Then, you go back to the main task and he fails again.

That is when you cut your losses. You figure he will never get it. You wonder why he is even in this class. Maybe he is a slow, or that thing teachers are never supposed to think: maybe he’s not as smart, the nice way to say “stupid.” And both assumptions–slow and not as smart–are absolutely right. But there is more to the story, which I will get to.

Well, guess what? I was that boy. I took a required geometry course in the 10th grade. We studied geometric theorems and proofs, but no matter how hard I tried, I just couldn’t get it. All my peers were doing well, spinning out proofs for the theorems one after another, but I was floundering. So, I dropped out of the class, something that was quite radical for a high school student back then.

Then something inexplicable happened. I took the class again a year later, with the same teacher, same materials, and same theorems to prove. But this time I got it. I really got it! I was a whiz and, with far less study than the first time, I got one of the highest two scores in the class.

Let me say that again. The first year I did not get it. Then the second, I did. I did not have any family or health issues the first time through. I did not have a girlfriend that I broke up with. I did not get insights on geometry from some other class. So, what happened? Same learner; same situation; completely different results. Actually, one thing was different, just one: the year in between.

That made all the difference. I was a year older.

But why? Piaget gave us part of the answer back in 1958 in his systematic Theory of Cognitive Development. Whereas we used to think any smart person could learn anything if given enough training, Piaget found that this was not the case. Biological development plays a role, too. A 7-year old can understand that water poured from one glass into another with a different shape does not change in quantity. A six-year old can’t. The ability to understand this develops in the Concrete Operational Stage (7 to 11). In the Formal Operational Stage (12 to adulthood) youths become able to engage in the kind of deductive, syllogistic thinking needed to solve scientific problems, which, in my case, was making proofs for geometric theorems.

Despite criticism and refinement by other researchers, known as Neo-Piagetians, such as Kurt Fisher, Piaget’s theory is still considered valid. In addition, the massive ABCD study is providing terabytes of data to help us look even more closely at gradations in brain development.

That explains brain development and cognition, but does it mean that those who are “slow” in development are just plain “slow” mentally as well?

That set me to wondering. A few years after my geometry class, I became an avid fan of the science writer, Stephen J. Gould. I noticed one thing he kept saying over and over: A basic rule of ontogeny (growth) seen across species is that higher-level brains take longer to develop. For example, chimp brains, which look just like human brains, develop along the same track as human brains up until about three years old, where maturational development stops. While an adult chimpanzee never develops processing abilities beyond the three-year old stage, humans keep on developing well into adulthood, allowing us to develop abilities they cannot: collaboration, language, and higher-level abstract thought (Tomasello, 2014).

So, it occurred to me, if the link between development speed and higher cognitive abilities is true across species, might not it also be true within a species?

The evidence says it is. Increasing cortical thickness, which comes with maturation, is associated with higher levels of intelligence in humans, but with a caveat. The higher levels of intelligence are only reached if brain development is prolonged [source]. According to J. Giedd, a researcher at the U.S. National Institute of Mental Health:

The brain regions used to think, plan, and reason mature two years later in those kids with high IQ scores….A child who is not reading or doing math like his peers may end up doing even better than them years down the road. (Savage, 2006, para 2)

While all brains reach the same level of development by 19, those brains that took longer to get there show the highest levels of intelligence.

Think about that and the implications. Those kids that we think are “slow” (unaware of how right that word really is) are the ones Giedd says become the smartest. If so, what a terrible injustice we are perpetuating, an injustice I’m going to call “Better Brain Punishment.” We group learners by age, not maturation, and compare their test scores to differentiate the smart from the not smart. Interestingly, the “not smart” group includes Speilberg, Edison, Disney, Lincoln, Darwin, Gates & Allen, Dyson, Rowling, Zuckerberg, Einstein, Newton, and so many more, all of whom had trouble in school. 

We punish the slow ones. It is a principle our entire educational system is based on, and if you think about it long enough, one that should bring tears to your eyes.

When I was the only kid in my Geometry class who didn’t “get it,” my peers thought I was dumb and I thought so, too. A year later, I did get it, but by then, it was too late. I had already been judged. In today’s world, performance in school carries huge stakes for youth, and Better Brain Punishment might be further tilting the playing field. We might be shutting out the smartest. Or worse: I don’t consider myself particularly smart, but, for most of my life, I had to struggle against a recurring low self-image. Here we see the dark side of self-efficacy

"Here we see the dark side of self-efficacy."
Curtis Kelly
TT Author

So, what can we do? Just knowing what we have discussed here is a good start, and telling other teachers can help as well. But maybe the best counter is telling parents. Parents tend to be more direct in their punishments, and more than anyone else, they need to be told that a kid who has trouble “getting it” is probably just a late bloomer, and that, in itself, might be a sign of higher intelligence.

We have a chance to cross a bridge, my friends, to becoming wiser educators. We have a chance to make right the wrongs our predecessors have inflicted. Just telling the kids-who-can’t-get-it that the smarter ones often take longer might flip the mindset. Just showing them that you cherish them as much as any other might give them the power to persist. We now know that, instead of just one or the other, abilities come from a combination of nature and nurture. We cannot stop nature; but we can shape it with the nurture!

Curtis Kelly (EDD), the first coordinator of the JALT Mind, Brain, and Education SIG, is a Professor of English at Kansai University in Japan. He is the producer of the Think Tanks, has written over 30 books and 100 articles, and given over 400 presentations. His life mission, and what drew him to brain studies, is “to relieve the suffering of the classroom.”

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