Chapter 3: From Patterns to Algebra to Critical Thought

The traditional mathematics classroom, although never my absolute favourite, worked for me. Jumping through mathematical hoops became routine by the time I reach Brock University. For most math/physics/chemistry questions at the high-school level, I had a simple yet effective method for "retrieving" the correct answer:

1) Write down the information given. I always called this my "What do yah know?" section. 

2) Write down what the question is actually asking for in the end. This was my "What are yah tryin' to find" section. 

3) If it applied to the question, write down anything you needed to solve to go from given information to the solution. This was my "What do yah need to know to get there" section.

4) Use the information given to select the proper formulas required for the question. This was my very cleverly named "What formula are yah usin'?" section.

5) Solve all equations required to isolate the final answer. This is my "K done" section.

Jumping through Mathematical Hoops: Image created on Microsoft paint

More often than not, this was my fool-proof rinse, wash, repeat cycle for any math related question. Using this method taught me how to efficiently solve mathematics equations without ever really understanding the concepts behind them. Why would I want to learn more than I had to? I retrieve the correct answer and received my mark, and that was good enough for me. Of course there were exceptions to the rule throughout my high-school career, times where I really had to put the work in to understand an abstract concept in order to get the correct answer, but for the most part it was steps 1-5.

I thought to myself "Wow, I could probably just get through my entire Chemistry and Mathematics undergraduate program doing this". 

Cut to Thistle Hall room 245 (I think). It was late September, early October the first year of my undergrad. Everyone in the MATH 1P05 class was eagerly (or nervously) waiting for their name to be called to the front to collect their marked midterm 1 test. 

It was late September, early October the first year of my undergrad that I realized I could no longer play the game. University claims that they increase critical thought in their students, and I honestly believe in that claim. Whether it was math, chemistry, history, or education, I always found myself critically analyzing my every move. In university, I really put in the work to understand what I was doing, why I was doing it, and what effect  would it have on surrounding factors. It was a huge paradigm shift in the way I approached any problem, whether it be on paper or in my personal life. 

You're probably wondering where I'm going with all of this...

This week in class, we looked at the use of manipulatives and patterning to express linear relations. The concept blew my mind. It made me look at the concept of linear relations in a whole new way. I was trying to use patterning in my head to model a million different other concepts at once. My entire life, I literally trained myself to look at a problem from one and only one perspective. I thought I was being efficient, but aside from retrieving the correct answer, the only thing I became efficient in was mathematical ignorance. 

This activity made me truly understand the importance of:

a) using manipulatives in the classroom

b) teaching a concept through several perspectives

Using these two methods will allow all students to connect and engage with the curriculum material in a way which suits them best. As educators, we need to challenge the students who think they know the answer to look for it again without their set of "rules". I think this is the key to helping students really understand how/why something works at an early age. The world demands critical thought...this is how we provide it. 

Thanks for reading, 

Kevin Lavallee