Estimated reading time: 3 minutes, 8 seconds

I’m on the right track, baby

I was born this way

–Lady Gaga

It was day two of my second year of teaching high school geometry, and already I had been called for a parent meeting in the principal’s office. I was a bit worried. What on earth could a parent have issues with already?

Mrs. X sat with her 14-year-old son across the desk from the principal. I shook her hand and took the chair next to her. The principal handed me a copy of my geometry class syllabus that I’d sent home with all of my students during the first day of class. Like every other class syllabus at this particular school, mine included class rules, the grading system, a list of general objectives and the obligatory notice that I’d be following all other relevant objectives outlined by the Commonwealth of Virginia.

“Mrs. X has some questions about your syllabus,” he said, turning the meeting over to her.

“I don’t understand what this objective is,” Ms. X said, pointing to her copy of the syllabus and then reading aloud: “‘Students will use their intuitive understanding of geometry to understand new concepts.’ What does ‘intuitive’ mean? Are you going to hypnotize my son?”

I instantly relaxed. Clearly, I was dealing with an over-zealous, perhaps under-educated parent, who had been listening to too much right-wing radio (which in the early 1990s was railing against witchcraft in the classrooms). I might think she was crazy, but I could handle this.

I calmly explained that all students come into my class with a basic understanding of shapes and the laws of geometry. I needed my students to tap into this intuitive understanding so that we could build on skills they already had.

In short: These kids already knew something about geometry, and as a professional educator, I was going to take advantage of that.

What I didn’t realize was that my heartfelt theory was not proven fact. But in April of this year, the *Proceedings of the National Academy of Sciences* published a study that does just that. Here’s the gist:

French researcher, Pierre Pica discovered that members of the Amazon Mundurucu tribe have a basic understanding of geometric principles–*even though they aren’t schooled in the subject and their language contains very few geometric terms.* In other words, geometry is innate.

In fact, Pica found that French and U.S. students and adults did not perform as well on the tests as their Mundurucu brethren. Turns out formal education may get in the way of our natural abilities.

“Euclidean geometry, inasmuch as it concerns basic objects such as points and lines on a plane, is a cross-cultural universal that results from the inherent properties of the human mind as it develops in its natural environment,” the researchers wrote.

Bla, bla, bla, and something about points and lines.

Not to toot my own horn or anything, but what this means is I was right all those years ago. We may not have been born with Euclid’s brain, but we do, at the very least, pick up his discoveries just by interacting with our world, rather than sitting in a high school classroom.

Actually, the philosopher Immanuel Kant said as much when he was doing his thing in the 18th century, so this isn’t a new idea at all. But many students (and parents) didn’t get that memo.

The bottom line: aside from uncommon processing and learning differences, there’s no reason that you can’t do ordinary geometry. More than likely, any obstacles you face are rooted in fear or stubbornness.

And I, for one, won’t let you get away with that.

Mary Helen Dellinger says

Geometry seemed to be the only math class in high school that I ever understood. And I think you are right – I did go into that class already possessing some basic understanding of it. The teacher helped by making it fun to learn, but I like it so much better than algebra – which could never seem to grasp.

Gina says

I wonder if there is a relation between Myers Briggs Type Indicator, Intuitive-Sensing, and the choice to pursue mathematics?

misanthropope says

david hilbert was very careful about the conflation of the standard ways of visualizing geometric objects, with geometry itself.

visual-spatial reasoning is an important component of intelligence, but it is not geometry. geometry comes from the pre-frontal lobes.

Laura says

Misanthropope,

I’d like to hear more about what you mean. Who is David Hilbert? And are you saying that the authors of this study were conflating visual-spatial reasoning with geometry? If so, I think that’s a fair point. Likewise, without visual-spatial reasoning, I think it’s fair to say learning geometry is difficult at best. While we can’t actually visualize a point, line or plane, visualizing something similar is quite useful.

Laura

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