Looking back at the progression of my education in mathematics as far back as grade school in Germany there are some common learning patterns which I have been able to identify. Noticing common learning patterns in mathematics was something I only began to recognize in my current college pre-calculus/trigonometry sequence course.
During grade school learning arithmetic was something I didn’t enjoy. I lacked the patients to memorize times tables, and the persistence to compute long addition and subtraction. As a child I was more interested in art, and history.
During high school my interests began to shift towards programming and mathematics. Much of this was due to the fact that I wanted to learn how the digital tools I was using to create art worked under the hood. In high school I took Trigonometry, and enjoyed it. My high school offered a Web Design program which I loved. I ended up re-designing the schools web site, and launching my own web site. Throughout my early twenty’s I played in touring bands, while supporting myself in kitchens. I was full of haste, and needed adventure every night. However, in late 2013 something changed within me. I booted up my computer one day, and started working on 3D models again. My girlfriend at the time suggested I return to school to make my second attempt at a Computer Science degree.
Feeling confident and inspired by her I decided to take her advice, and am now 5 terms into my transfer degree at Portland Community College. Like many other returning students I placed into basic algebra (Math 60). This term I am taking my first 100 level math course. All of a sudden previous concepts, and theorems are coming together. It’s as if I broke some kind of barrier – a barrier where I see math not simply as a set of operators and operands, or loosely related theorems which allow me to graph some lines on a Cartesian coordinate plane. Instead I see mathematics as a set of tools which allow me to express my creativity in new ways. This new awakening has led me to think about how mathematics are learned in a structured and analytic manner.
I began by breaking the learning patterns into three main components. The first is the hardest of the three components. Let us call it the component of elementary knowledge, during this phase one learns the core symbols, and their meanings to complete basic and advanced computations. Another aspect of elementary component is memorizing key numerical patterns such as: multiplication tables, prime numbers, and patterns of squares to reasonable degree of magnitude. Although the elementary knowledge of math is taught to people at a young age, if not practiced common skills will deteriorate.
The second component is discovery and exploration. Discovery and exploration begin when a student is comfortable with the elementary concepts. For example, if I get an ‘A’ on a quiz or exam I allow myself to explore a new concept, or learn the usage of previously unknown notation. Another form of exploration which helps me become better with math is researching mathematicians. Consider compiling a list of four well known mathematicians throughout history. Then read about who they were, and what they contributed to mathematics. Based off of what you learned try to make connections about how their contributions affect current mathematics, and humanity.
Discovery is another important strategy to strengthen, and diversify current course material, or previously learned concepts. Discovery is all about breaking away from the linear approach of the required text book, and lecture guides. Once you have mastered a concept try to extract patterns. Furthermore, try generating your own problems based off of the learned concepts and patterns. By generating your own problems you will see what can and cannot be done with math. It is in some sense a natural way of testing a debugging your math.
One often overlooked key mechanism of discovery in mathematics is to make mathematics social. Try to connect with fellow students who are interested in mathematics and discuss concepts with them. If you are talented with mathematics offer help to students who are having difficulties with the coursework. Explaining what you know about math to someone who is having a hard time understanding will force you to know fully understand every detail about the given concept. Another interesting way to discover math is to ask uninterested students why they are uninterested in mathematics, it can teach you how to communicate math in an interesting way. Discovery and exploration are important. However, there are times where I have to pull my head out of the clouds, and focus on the material being taught.
The third component is application. I have heard the “When are we going to use this in real life?” question too many times. Through discovery and exploration these correlations should come naturally. However, I do understand that an art history major will have a hard time finding a future application for being able to solve quadratic equations, or apply transformations to functions. If your degree does not require math – apply the knowledge you are gaining to your life as a whole.
Mathematics has its applications in most aspects of life. Knowing math can prevent you from being stolen from, or even being physically hurt. Furthermore, it can allow you take control of your life, and help you stay organized, healthy, and safe. I hope this essay will inspire students taking mathematics on all levels to think critically about mathematics on a technical and social level. Now go grind some equations, and write a 1000 words about it afterwards.