Last year I did a pre-calculus demo lesson. The last time I had anything to do with trigonometric equations was around 1994. I, like most other people on the planet, came to the decision that I was just not a "math person". Granted, I probably spent way too much time playing Green Day's Dookie and playing Super Metroid to actually study math, but I still felt like I just didn't have the "math gene".

I felt that way until grad school when I discovered the joy of statistics. Once I did well at math in gradute school my internal narrative changed. I was no longer "bad at math" I was now "good at useful math but bad at thinking about abstract concepts."

Overcoming limiting beliefs

My confidence in statistics did not help me when the head of the math department asked me to teach about trigonometric identities. My immediate reaction was panic. My brain said "I can't do this! I haven't touched this crap in 30 years! And I don't do well at learning useless abstract garbage! And he wants me to do it in two days! WTF!"

I let that emotional response play out for a bit and then I told myself "Ok... here is the challenge: learn a concept well enough to teach it to a group of high school juniors in the next two days".

I modified the techniques that I learn in the book, Getting Things Done, to help me figure out how to best attack this challenge

I looked at my constraints:

  • I have a full time job that I still need to do and children I need to raise.

I looked at my available resources:

  • I have YouTube, some math textbooks, and a buddy in the math department that might be able to spare a lunch hour.

I set conditions on myself:

  • I will devote 2 hours a day of the most intense concentration I can to learning the topic well enough to teach for 45 minutes.
  • I will know that I have the concepts down if I can solve all the odd number problems on page 299.
  • I will know I can teach this well enough to get by if I can draw and write out my process for solving these problems.

I determined what I counted as a success:

  • Success is explaining the concept of the unit circle and demonstrating 2-3 problems on the board and then helping students solve problems.

The class went fine. Nobody stepped in and corrected my errors mid sentence. I went in to see the head of the math department after teaching to get some feedback. He told me that my work was fine but I didn't use some proper terminology in my explanations and I jumped around a lot on the board as I solved problems.

The math department head told me that he wouldn't consider having me teach upper level math next year but that I had demonstrated enough clarity of thought that he would be open to me teaching the lower levels of math.

I felt a bit dejected but I realized that whatever mistakes I made were likely inevitable. It makes sense that he wouldn't want me to teach a pre-calculus class - I couldn't devote 2-4 hours a day every day to learn the pre-calculus concepts and devote additional time to figuring out the intricacies of how to teach these concepts optimally.

In showing that I could quickly grasp and articulate the higher level math I had demonstrated that I could teach lower level math well by logical extension. In proving that I could lift a very heavy and intense weight I proved my ability to sustain carrying a much lighter weight over a long distance.

Math Anxiety and self perception theory

Approximately 93% of sampled adults claim somewhere between low to high math anxiety, with approximately 33% of the US student population sampled self reporting high levels of math anxiety. One of the biggest stumbling blocks for many people keeping them from finishing their associates or bachelors degree is the math requirement to get through Algebra I. For many students math class is a "Significant barrier to completing a degree".

I think a big part of why this barrier is so difficult to overcome for so many people is because of the idea that Daryl Bem termed "Self perception theory". Self Perception Theory postulates that people observe their own behavior and from that they conclude what attitudes must have caused the behavior.

In other words; when someone fails a math exam they tell themselves "I didn't work hard to study. The reason I didn't work hard to study is because I hate math. The reason I hate math is because I'm not good at it. The reason I am no good at Math is because I don't have a math brain."

Clearing out your mental RAM

I think it is probably really good for people to go back and try and teach themselves a concept that they just completely didn't get back in high school. We are all carrying all kinds of childhood baggage and corresponding beliefs about our own abilities and potential because of that. Even people who got straight A's in high school probably did that by avoiding certain subjects.

Our brains are wired to go to pleasure and to avoid pain. This makes total sense from an evolutionary perspective. But what happens when our brain associates a mental thought process with pain. It creates a kind of panic and fear that blocks our thinking through things.

When we are adolescents our rational brain is not fully developed. The differentiation of its neurons and development of synaptic connections in humans extend to the 3rd decade of life. In other words, your brain seems to be stuck with the script you wrote when you were a kid and struggling with feelings of inadequacy.

That's the main reason why every adult should study whatever they hated back in high school.

The only way for our brain to stop panicking when we think about those subjects and other mental challenges is if we show both our rational and emotional brain that while those subjects represented a kind of "danger" when we were kids they no longer represent a danger.

Being able to concretely change that message would probably pay enormous dividends for just about everyone.

Former mediocre students would discover that they aren't actually bad learners. Think about how many people might consider developing new skills or learning new concepts if they no longer thought that their brains just didn't "get it".

Or consider the student who got great grades in the sciences but thought that reading Shakespeare was just a stupid waste of time. Maybe at age 30 they might be able to find some beauty in the words that they simply couldn't value at age 15.

How might the student who had a perfect GPA but absolutely hated PE benefit from spending a month doing push ups? Maybe they might begin to appreciate the physical discipline that the hard ass gym teacher was trying to help cultivate.

How I would go about doing this personal challenge?

I'd choose a single topic within that discipline. I'd look for what are considered the fundamental concepts within that discipline. In Pre-Calculus it would be the principles of trigonometry. So as I did for this lesson I chose that concept.

  • I'd give myself a short timeline to grasp that concept.
  • Then I'd set the conditions for proving to myself that I understand the concept.
  • Then the last part would be that I would need to demonstrate that understanding in some capacity.

The beauty of this is that the psychological effect of overcoming the fear seems to be rather quick. Whether it is true or not once you have solved some small part of a problem that overwhelmed you when you were younger it no longer has the same psychological hold on you as it did. So if that is all that you need to get out of this topic then my most sincere congratulations on clearing a decades old psychological hang up! I can't wait to see what lies in store for you as you approach the world with that unconscious fear no longer weighing you down and affecting your choices.

I can't think of anything that you can do that is more psychologically positive and quickly enacted than attacking a subject that you hated back in your formative years. It will do you a world of good!

Sketching a Pigmy Hippo with monster

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