Automathography for “Math Is Personal” (based on previous mathographies for graduate school and student teaching).
I attended middle school and high school in a small suburb or the San Francisco Bay Area with high-performing public schools where math was heavily tracked. As a blanket statement, I was not as good at math as most of my friends. Admittedly, some of my friends memorized the periodic table and programmed music in their free time, so they aren’t the most objective measure of “average” mathematical knowledge. Still, they often understood things about math that I did not. They were also passionate about math in a way that I was not – while I went to class, did the work, generally understood and did well enough, they were petitioning to skip courses (or just skipping them, to the chagrin of the administration), taking advanced online courses, and competing in math competitions.
I remember liking 8th grade Algebra (it was systematic and logical) and 11th grade Calculus (it was also systematic and felt higher-level) and not caring as much for 9th grade Geometry (it was too abstract and proofs were too much writing and confusion). Surprisingly, my geometry score on my teaching certification test had fewer red flags than my algebra score. I don’t know if this is due to the passage of time or a change in understanding.
I specifically remember learning how to calculate the derivative and second derivate of an equation (from a math teacher who, while good, was not considered particularly strong at our school). Not only did calculating derivatives make sense arithmetically, it made sense as a real world concept – I was calculating the rate that something was changing (or the rate of change of the rate of change), not just plugging numbers into an equation. On the other hand, I liked Algebra – while more systematic and abstract than Calculus, it was logical and (somewhat) easy to understand. It felt like doing a mind-teaser that was tricky, but not impossible. I think I would like statistics a lot as it tends to be very applicable to “the real world” – however, my knowledge of statistics (from college) is a bit shaky.
Back to high school – although I liked Calculus, I opted not to take math my senior year, instead taking a course at a local community college over the summer so that I could free up space in my schedule senior year.
Four years later, I graduated from college with a Bachelor’s in Product Design (an interdisciplinary major combining Mechanical Engineering and Studio Art), but the mixture of both majors meant I didn’t know either major very in-depth – including some of the math that I wish I had internalized a bit more now. I was also still burned out from high school and didn’t pay as much attention as I wish I had now.
Though I might not have been the strongest math student, I soon found that I was interested in education, especially in low-income communities. My junior year, I tutored local high schoolers from through Upward Bound. I remember loving working with and interacting with students (though I don’t remember doing much math tutoring).
My actual appreciation for math began at my last job, 6 years after graduating from college. The nonprofit where I worked recruited recent college graduates to work as teaching assistants in high-need high schools. During our first year, we focused exclusively on Integrated Algebra. My co-worker, the Site Director for Math, said that math was the easiest subject to pick up for college graduates (even those who weren’t math majors). He said this somewhat flippantly as he’s good at math (and teaching math and coaching math teachers) and tends to gloss over the details in conversation. Around the same time, my boss also mentioned that research showed that only 15% of youth from low-income communities would graduate from college in six years. Those 15% would be the ones with the most rigorous academic high school courses. He also said that success in algebra was one of the best indicators of academic success. While these numbers shocked me a bit at first, they made sense. I saw this, even in the high performing schools I attended: friends who did well in algebra generally did well in geometry and algebra II/trig (or at least took and passed them). Friends who struggled in algebra were turned off to math and, while they usually continued taking courses, they generally didn’t do well and opted out as soon as possible (taking algebra II instead of algebra II/trig).
On a more personal level, I was beginning to work more with Excel and statistics in my job as the Operations Manager. Being a “data-driven” organization meant that we tracked data, calculated it, and then made decisions based on it. Now, I had to know how to relate our numbers and our data to our organization – not just to each other, but to last week’s numbers and to future projections. I also had to explain to my boss and other stakeholders what the numbers meant and what actions we should (or shouldn’t) take, based on these numbers.
Jargon-heavy B-school talk? Perhaps, but all of a sudden math was very, very relevant to my life. And I loved it. While running weekly reports for recruitment and program, I could look at numbers, figure out what they meant, figure out why they were different from what we expected, and recommend a course of action to get to where we wanted to be. I struggled a bit with the finance side of things – while I could generally make the numbers fit in the right places, I didn’t have an accounting background and wasn’t sure how to work the software or run or interpret the reports. After inadvertently leaving out a $100,000 check (oops) in our monthly finance report, we got help from a bookkeeper who helped me navigate the software and enter things correctly so that we could keep track of our finances in real time (including how much we owed and how much we were owed). I struggled with finance to the end. While I know there’s a narrative/story that the numbers are trying to tell, I was still trying to figure out how to easily decipher and share that.
That was how I found myself applying to graduate school, 12 years after opting out of math during my senior year of high school. Although I thought about teaching high school English, I decided to apply to math programs, knowing that math was a gateway course (among many others) to college.
Through graduate school, I student taught in three Geometry classes at an urban comprehensive high school, which had a heavy focus on groupwork and actually tried pretty seriously to detrack its math classes (all incoming students were placed into geometry, regardless of whether or not they’d taken algebra; we tried to provide the necessary support in class with mixed results). It was interesting to see how students related to math; some looked at it (as I once had) in very procedural ways while others were almost scared to do it. Many of the students who claimed to be very bad at math said they’d “always been bad at math”. I also began to see that math was about more than just measurements and calculations – we tried to make concepts and reasoning a big part of the course as well.
Given these experiences, here’s what I value and believe about math (subject to change, as always):
Math describes the world around us (if you know how to interpret it).
Everyone can learn math.
Everyone can teach math.
Neither learning nor teaching math is easy – they require a lot of work, as do most of the worthwhile things in life.
The “smart kids” are often able to make math look easy, which can be discouraging to the rest of us. The smart kids do, in fact, struggle with math, but either make it look easy or just manage to hide it from the rest of us.
Many students are scared of math. Partially from watching the smart kids be really good at math, partially because they think they haven’t been as successful at math in the past. Possibly because math is not always taught in a way that is easy to interpret.
The more you can break math down into small steps, the better people tend to understand it. It helps people who are struggling with math make connections they wouldn’t see otherwise and it keeps people who are good at math from making sloppy mistakes.
I’ve noticed that my friends who were “good at math” tended to be fearless about math – they just went at problems (whereas other people would stop, get confused, and give up). I’m not sure if this was because they were more confident or because they had a better handle on what they were doing. But they never just gave up without trying several times.
Here’s what I’m curious about:
How do you “catch students up” when they’re behind? (either a couple units or a whole course)
How do you build up students’ confidence in math?
Do you need different kinds of math to be ready for college versus to be ready for a job?
How does building relationships tie into math education?
How does one effectively teach math to English Language Learners? To a math classes with many, many different ability levels?