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

Chapter 2: The Importance of Verbs (Week 2 Reflection)

What is a verb? Verbs express actions and states of being, and are arguably the most important part of a sentence. Without verbs, a sentence would just be a bunch of words! Lets try:

What a verb? Verbs actions and states of being, and arguably the most important part of a sentence. Without verbs, a sentence just a bunch of words!

See? Important.

This week, we discovered that the grade 9 mathematics curriculum has no shortage of verbs. During the first portion of our activity, we highlighted all of the verbs within the specific expectations of a mathematics unit. This took quite a while, even with breaking the unit into sections for each of us in the group. In order to visualize the occurrence rates of each verb, our group graphed the results (see the figure below). This activity "highlighted" just how many, and how often each verb was used.

Visualizing the "verb count" was overwhelming, and led to the questions of "why?", "what does this mean?", and "What implications does this have on me?".

Why? Well, it should be rather obvious that the writers of the curriculum place a significant importance on verbs. They are there to provide educators with guidance.

What does this mean? During the debriefing portion of the lesson, we discussed how verbs describe the route of engagement to the curriculum  for students. Again, they are there to guide teachers through the curriculum and how it should be accessed by the students.

What implications does this have on me? This notion really resonated with me. When reading the curriculum documents in the past, the verbs tend to be almost subliminal as the content jumps to the forefront. For example:

"Determine, through investigation, the relationship for calculating the surface area of a pyramid"

For the me in the past, this may have simply read "teach the students how to calculate the surface area of a pyramid", which is completely wrong. Think of all of the different ways that message could be interpreted. What if I had just given a traditional lecture on how to calculate the surface area of a pyramid, then passed out a work sheet with several questions asking them to solve the surface area of various pyramids. What would the students determine? Where is the investigation? What relationships would they be able to determine? Most, if not all of the actual intentions of the expectation are lost by skimming the document for "content".

Final Reflection. The verbs describe how the students should be taught, not just what they should be taught. This lesson really opened my eyes to the importance of analyzing the curriculum documents, not just to understand what I am supposed to teach, but how my students should be engaging the content.

Chapter 1: Introducing Kevin Lavallée

      Hello everyone...My name is Kevin Lavallée and I am a prospective educator in the Concurrent Education program (Chemistry and Mathematics, I/S) at Brock University. Although chemistry is my first teachable subject, this blog will mainly be written through the lens of a math mind. Before I describe why I chose mathematics as my second teachable, I wanted to present you all with a quote from Ken Robinson, a British author, and an expert regarding education in the arts. He said "We don't grow into creativity, we grow out of it. Or rather, we get educated out of it". Although he speaks to the education of arts, I believe that this statement can apply to the education of mathematics. Ever since I could remember, mathematics has been an outlet for me to express my creativity. Whether it meant trying to solve a question in a different way from my classroom neighbour, or developing a game out of my math homework, or optimizing the size of the tree fort I could build given the limited supplies I found in the dumpster at lumber store down the road, I always found a way to give what I had learned in the classroom a creative purpose. Although my "Math Story" revolves around creativity, I find that most other's do not. Referring back to what Ken Robinson said, I believe that a significant portion of mathematics students have had their creativity educated out of them. They believe that math is a right-or-wrong, yes-or-no, factual subject with no room for imaginative thought. Well, I believe that there is room for creativity in the mathematics classroom, and I believe that it is up to mathematics educators to make their students believe it too. Identifying and understanding this notion only progressed my passion for creative mathematics, and as a result the subject was a natural choice for my second teachable. 
      As a prospective mathematics educator, my biggest fear is incorporating the entire mathematics curriculum while attempting to develop a fun, creative, and relevant mathematics classroom. I hope that this course will help me gain practical knowledge and experience to ensure that creativity is not lost at the expense of the curriculum, or vice versa. This blog will serve as a tool to track my progress throughout this journey! Thank you for reading!
-Kevin Lavallée