07 March 2015

Everything I Needed to Know, I Learned in my High School Calculus Class

During my last two years of high school, I had to take Precalculus and subsequently Calculus with a teacher named Mr. Bormann. Those two years assuredly prepared me for college and instilled the discipline and drive to learn outside of school which has carried me to where I am today.

I owe a lot to those two years and to Mr. Bormann. The unfortunate thing is that during those years, I didn’t see it like I do now. I disliked Mr. Bormann from the very first day just because he replaced one of my favorite teachers which wasn’t fair to him.

I wanted to write about what caused me to dislike him and how his class ended up preparing me for the rest of my life.

A Small Town

I grew up in a little town of Iowa called Algona. The population was 5,741 at the 2000 census.

The Algona School District is the home of the bulldogs and small like the town it inhabits. My graduating class from Algona High School (AHS) of 2009 consisted of 86 students.

The town and school were small enough that it meant the population was more homogeneous than it should have been. There was a lack of diversity in interests as well as many other aspects; it was nearly impossible for me to find someone that had a similar passion for computers and programming.

It was this reason that finding someone that had similar interests and understood me was such an important thing in my life.

High School

My freshman year at AHS I got to meet the physics and precalculus teacher at the time. His name was Mr. Hines and he was known as not only a brilliant teacher but as someone that made class really fun.

My first two years were filled with “Mr Hines did this…”, “In Hines’s class…” types of stories about classes with Hines and the funny and great things that happened in them.

In addition to teaching those classes, he also was in charge of the Computer Club for AHS. You wouldn’t have doubted this if you had to step into his classroom. It had computer towers and monitors stacked all over. There was a box full of hard drives and various other parts. He loved computers but I think he loved using them for pedagogical purposes more than anything.

It wasn’t uncommon to be talking about a subject only for him to relate it back to computers with an analogy. Every discussion was an opportunity to learn something new with Mr. Hines.

I heard about computer club from a sophomore friend at the time so I decided to go to the first one to see what it was like in the hopes of learning and meeting some people.

Computer Club

It was a great little club that had a lot of upperclassman that I looked up to. We’d spend a few hours after 3:30pm every Thursday to discuss the tech news, build some computers, talk about a Linux distro, or even things vaguely related to computers.

The community and belongingness was what was important. It was the closest thing I could find to being around similar people at least in that small town that I was stuck in.

The first year was definitely the best. While the senior class my freshman year had a lot of people that attended, the junior class had only a few that showed up. This meant that by my sophomore year, the Computer Club attendance dropped pretty dramatically but it didn’t hinder me from going and hanging out with Mr. Hines.

It was the days where not many people showed up that I really got to know him and talk with him.

Mr. Hines

I got to know Mr. Hines really well and really looked up to him. He was a very smart guy that had a ton of curiosity about the world.

I couldn’t wait for the following year where I could have him for two classes as I was going to take Physics with him as well. It was going to be the first time that I had a teacher that I felt “understood” me and what I hoped to do.

However, during the second half of my sophomore year, Mr. Hines mentioned that he was going to be leaving the school district and moving to Mason City to pursue teaching there instead.

When he mentioned that, I was absolutely crushed. I felt that I got along with him the most out of all of the teachers that I had met yet. It wasn’t fair for him to move to a different school district like that.

Junior & Senior Years

As my junior year approached, I wondered a lot about who would take over teaching for Mr. Hines. There was a bit of hope that it would be someone with similar interests that I could learn from. I assumed that the more like me that the teacher was, the better it would be for me.

On the first day of school, I finally got to find out who would be taking over teaching Precalculus.

His name was Mr. Bormann and he was quite a bit different than Mr. Hines.

Precalculus & Calculus Class

Mr. Bormann’s classes (as far as I could tell) were very different than how it was in Mr. Hines’s classroom. Since Mr. Hines’s classroom was so full of computers, there wasn’t much room for other things to be organized. So his desk was always full of various papers, pop bottles, and other things to compensate for the lack of space. When you walked into Hines’s class, it just felt like a carefree environment.

This carried over to the students attitude because when Hines wasn’t talking, the students usually were. There was always a buzz of chatter that occasionally got too loud.

Mr. Bormann’s classroom had a much different feel. It was always tidy and nothing was ever a mess. His books were lined up and things were put away.

In addition to the classroom differences, Mr. Bormann carried himself differently. He had a lot discipline and was more serious. As I came to learn, he was this way through high school and college when it came to football so it was only natural that it carried over into his teaching.

I came to learn later on that he was softer than his exterior but that definitely didn’t show in the classroom.

When you walked in, if there was any discussion going on, it was always just a handful of people. It was never loud and rowdy.

Classtime was even quieter once Mr. Bormann started talking. You would have to be slightly nuts to risk talking to your friend because it wouldn’t be wise to disrupt class.

Mr. Hines was one of the most laid back guys I had met. He just let everything fly unless someone was being hurt or something was being damaged.

Mr. Bormann was the opposite. He had a tight reign on everything happening and never let things get out of control.

Despite these differences, it was a good place (at least for me) to learn.

Learning Everything I Needed

One of the most important things I learned from his class was (ironically) how to learn on my own as well as how to study.

Studying in high school was a rare occurrence and something I just didn’t have to do much of. I paid attention in class, I turned my homework in on time (albeit after much procrastination), and never missed school. Surprisingly, those 3 things took care of most of the worry and made high school incredibly easy.

Precalculus was a bit of the same. I could tell quite soon that it wasn’t going to be that challenging since I liked math so much.

Even though it was just as easy, I wanted to make it a bit more difficult for myself.


I was a spiteful teenager at the time and disliked that Mr. Hines was gone and that a teacher that I didn’t see eye-to-eye with was teaching.

I made a pretty immature and naive decision to channel this spite by doing as little of in class activities as possible. This included not taking notes and not doing anything that wasn’t absolutely required.

This irked Mr. Bormann because it went against his nature of hard work and discipline. A number of times he would recommend that we all write a particular equation down or a helpful pointer for a topic down. A few times when he saw that I never did, he’d ask why I wasn’t doing so.

However, unbeknownst to him, I would actually go home and every other day devote an hour or so to reading about the same topics from Stewart’s 5th edition Calculus book.

I saw this as an opportunity to learn more about a topic on my own yet have pretty low risk if I wasn’t good at learning without an instructor.

This attitude and practice made it easier to pick up other math and programming ideas later on. I was a big fan of Project Euler and liked to explore the problems on the site. The problems usually had a relatively easy brute force method of solving them, but they also had a more optimized way of solving it which usually involved math.

It was fun to delve into these topics which we didn’t have time to look at in depth at school. This also was a great way to improve my programming as that was something I was working a lot on at the time.


I had always liked math but Precalculus and Calculus cemented the fact that I wanted to continue to learn more about it.

One of Mr. Bormann’s big goals beyond learning the material was college preparation. In anticipation for this, he decided that there wouldn’t be a mandatory end of the year exam given in the class.

Instead, we were given the choice to either take his exam or take the Calculus AB Advanced Placement exam offered by College Board and inturn, receive an automatic A on the final. This was because it took months for the results to be returned and it would be the middle of the summer before we knew how well we did.

Beyond the obvious incentive of the automatic A, the additional perk was that if we did well on it, it had the potential to eliminate the need to take Calculus I at university. Nearly everyone took the AP test.

The weeks prior to the test, I was pouring over the various preparation material that Mr. Bormann had given us. In fact, the picture at the top of this blog post that shows up (on desktop) when you hover your mouse over my picture is of my cat when I was studying for the test.

It was the first time that I truly had to study for an exam. It set the foundation for my study habits in college.

The whole test, preparation, and waiting for the results reminded me of Harry Potter and of his O.W.L.s.

When the day came to see the results, I was pretty nervous but for the most part excited to finally see that my hard work had paid off that last month of school. I got to skip Calculus I and went straight to Calculus II in college. Plus based on getting to know the other students, I had a stronger base than most when it came to the basics of Calculus.


In addition to not taking notes, I also spent my in-class time learning as much as I could about my TI-84 Plus Silver Edition which was my calculator at the time. By the time I graduated, it was a well known trope that I spent a lot of time on that thing and that the manual for my calculator never left my side and was heavily worn.

The calculators had a rather primitive language called TI-BASIC that you could write programs in. The programs that I wrote started off simple like the classic number guessing game to more advanced things like a program that got passed around from student to student called “ULTIQUAD” because it would ask for A, B, C and then use the quadratic equation and it would either spit out the values if they were rational, or show the simplification if they were irrational or complex.

Eventually I went onto more advanced things like my own version of Pong, Snake, and a fun little (naive) interpreter that made it easy to manipulate mathematical functions as values.

TI-BASIC was just a convenient way to program when I didn’t have a computer around. At home, I spent my time learning how to program on OS X with the de facto Objective-C book by Steven Kochan and followed it up with Hillegass’s book on Cocoa.

By my senior year, I had written a few different OS X applications for myself and even made one for one of my other favorite teachers.

Objective-C was the first language that I learned but it made it easier to learn others. I spent time to read the classic K&R book on C programming, learned Python from the Lutz book, and picked up Perl when I had downtime at my high school job.

All of this extra work learning various languages lightened the load when I got to college and decided to major in Computer Science. While the students that hadn’t programmed before were struggling with the syntax and semantics of languages, I got to ease past that and focus on the problem solving.


Mr. Bormann had a phrase that he used to remind us of (especially during the later Calculus class) and it went something like this:

This isn’t supposed to be easy.

He’d say it when people were trying to grok a harder topic and just couldn’t wrap their heads around it. He also said it whenever anyone complained.

It was a phrase that stuck in my head when I would be stuck on a hard problem at university or trying to implement something while working.


It’s weird to think about what might have happened if Hines had stayed to teach. I might have still went on to learn a lot, but maybe I wouldn’t have had a similar drive with the discipline.

Or maybe I wouldn’t have gained the ever-necessary study habits that helped me succeed in college.

Either way I do know that I’m ever grateful for Mr. Hines helping me those first two years when I was an awkward teen without much aim in life.

But I’m ever more grateful for Mr. Bormann for stirring up the desire to want to prove something to myself, to him, and to others. It instilled the skills and knowledge that I needed to succeed after high school when things got so much more tough.

It’s just a shame that I did all of this without explaining it all to Mr. Bormann or showing him that I really appreciated what he did.

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