Welcome to Mr. Nantais' Math Blog!

Hi everyone! I was introduced to a new concept which is another form of problem-solving strategy, known as the Japanese Bansho strategy. This was my favorite part of the lesson, and this lecture in particular I found to be particular important, especially for enhancing problem-solving capacities in students. Although I connected the Japanese Bansho strategy to some of the structured and non-structured problem-solving strategies we have learned in previous classes, I realized that there are some distinctive features with the Japanese Bansho strategy. Features such as discussing all parts of the problems through collaboration, arranging various solutions based on complexity, and the extensive need of justification in this strategy is what makes this technique distinguished. We were then split into groups to answer the following question: "There are 36 children in Mrs. Smith's class. There are 8 more boys than girls. How many boys? How many girls?". Below are the followi...

We have been discussing structured problem solving in mathematics classrooms. One of the core activities that helped understand the conceptualization of structured problem-solving was the growing dots problem. We were shown pictures of dots that were increasing in quantity, and we had to discover various ways to determine how to determine the number of dots in the 100th picture. Below is an attachment of everyone's work: I was initially surprised at how many different ways there was to approach such a basic problem. As I've mentioned in my previous blogs, I have been trying to challenge myself to get out of the habit into finding an algebraic solution and investigate other ways to solve problems using my problem-solving skills. Through our gallery walk, I learned that there are graphical, logical, visual and algebraic solutions to the same problem. My favorite part of the activity was realizing that we can even use techniques such as extrapolation (which you would th...

Hi everyone, and welcome back to my blog! This week's lesson focused on the importance of instilling problem-solving skills in high school math students. We focused on the differentiation between various problem-solving strategies that were established by Polya and Doxiadis. Our class discussion regarding problem-solving strategies really evoked many practical aspects of the teaching profession. Personally, I felt like our discussion helped me in my tutoring with high school students. I sometimes feel that I am 'stuck in my ways' when it comes to teaching certain material. However, this class in specific has really challenged me to seek different ways in explaining specific math concepts to students. For example, techniques such as drawing a picture, or writing out lists of possibilities for a solution are strategies that I will implement into my own tutoring practice, and in my future classroom. Thinking Mathematically emphasizes the importance of students 'being stu...

Hello everyone! This week was focused mainly on the differences between conceptual learning and procedural understanding in mathematics classrooms. Procedural understanding is the knowledge of a particular concept based off of memorizing or 'knowing' the steps of a specific problem. Where in contrast, conceptual understanding is actually knowing the meaning of a particular mathematics concept on a deeper level than just simply 'knowing' the steps. Attached are a few examples of the differences between the conceptual and procedural understandings of specific math concepts. Knowing the differences between these types of understandings is imperative as a future math teacher. In terms of theories such as Bloom's taxonomy, procedural understanding does not truly engage students to tap into their higher-order thinking skills as learners. In my opinion, procedural understanding is on the lower end of Bloom's taxonomy, as we are telling students to 'remember...

Hi everyone, and welcome back to my blog! Today's class focused on the mathematical processes involved in the Ontario math curriculum and connecting it to the ideology of a growth mindset, as opposed to a fixed mindset, in the classroom setting. We also briefly discussed the course content that is embedded in the curriculum documents to refresh our memory on what concepts are actually taught in the modern day high school classroom. I felt very confident about the topics of mathematical processes and the Ontario curriculum because I have been tutoring high school math for years now. Doing the discussion about linear, quadratic, exponential, rational, trigonometric and polynomial functions made me reflect on all of my previous tutoring experiences. It also allowed me to connect the curriculum to the mathematical processes. It made me question, how would I help a student with their problem solving skills if I was tutoring a grade nine applied student, versus a grade twelve calculu...

Hi everyone! My name is Jarrett Nantais, and I am a teacher candidate at Brock University, with teachables in mathematics and chemistry.  Mr. Nantais' Math Blog is a blog designed to incorporate reflective practices into the discipline of mathematics education. There will be lots of discussion about teaching and learning mathematics in general, and alternative ways to teach mathematics in a way that will engage students into learning mathematics. The main goal for this course is to gain valuable tools and resources that will help me teach mathematics at the I/S level. I am truly passionate about the topic of mathematics, and I want to find ways to share that passion with other students. I want to finds ways that will help students in finding that connection between the theoretical mathematics they learn in the classroom, and bring those math concepts into practical contexts. Also, as technology is emerging and becoming more prevalent in the classroom, another goal of mine...