Hugo teaches math

My topic on microteaching will some kind of card game, I am still deciding between blackjack or poker.

When we were first deciding on which art piece to choose we had everyone pick 2 of their favourites and we would pick one that everyone agreed on. Our decision led us to the piece by Margaret Kepner. Her spiral contained 400+ numbers and I didn't know how to recreate it without drawing it by hand. Fortunately, Kyle was able to write a code in LaTeX that made life much easier. Original At first, I thought the concept(prime numbers) behind the art was a little too simple. But there was much more to understand, such as the different types of numbers (happy, triangular, lucky, etc.). Also the Ulam Spiral, which was the inspiration for her piece, was very interesting to learn about. It was more complex than I expected! Replica When we were to put our own spin on the spiral, we had to think of 3 different types of numbers we could use instead of prime/happy/triangular numbers. We did some research on different types of numbers and ended up with going with prime/lucky/perfect...

"Brothers and sister have I none, But that man's father, is my father's son!" The first thing I noticed was that clearly stated in lines 1 and 2, was that the speaker is an only child. I think the confusing part of this word problem comes from lines 3 and 4. Next my strategy was to 'simplify' line 4, "my father's son". Since the speaker is an only child, "my father's son", would refer to HIMSELF(the speaker). Now with that information I replaced line 4 with 'myself'. "Brothers and sister have I none, But that man's father, is myself !" This makes more sense now, "that man's father is myself" must mean that the man  is the speaker's  son. The problem makes sense if you consider a group of 3 people; grandfather, father, and son. In this situation, the speaker  is the father, and the 'man'  is the son.

My first approach to this problem was to start off with a sketch of the lockers after the first 10 students. It looked something like this: The line represents lockers that are closed and the O represents lockers that are open. After seeing this table, I thought the solution would be related to prime factorization or prime numbers. This is because the number of time a locker switches depends on how many factors that locker number has. I did not see the pattern, so I decided to create a MATLAB code that would show the results for a set of 100 lockers. for i=1:100              < Sample size of 100 lockers (This could be increased to 1000, but kept it smaller for now)    N=i;                           K=1:ceil(i);                   D(i)= length(K(rem(N,K)==0));        <  Finds out how ma...

Positive experience: Hi Mr.Wong, I hope you are well. I just wanted to thank you for the positive impact you had on my education. You were not only friendly and approachable, you also explained difficult topics with ease. You were a laid-back and easy-going teacher, and were always patient whenever we had struggles. Even though I was a shy student, I never felt uncomfortable in your classroom. You not only had a positive impact on my education, but also a positive impact on my life. Negative experience: Hi Mr.Wong, how are you? I wanted to tell you about my experience in your Math 10 class. All the material that you taught me I have never used in my life, it was useless! I always felt as if you favoured the smarter students and neglected those of us who struggled. Your class was boring and I was always dozing off. You were always busy and never seemed available for help when I was having trouble with math. From both these experiences, I hope that I leave a positive impact not onl...

The earliest positive memory I have of math is when during a tutoring session when I was around grade 1. I vaguely remember scoring a perfect on my test and getting to write my name on the star board. From that point, I remember being very confident in my math abilities throughout elementary. My parents would say I had a 'talent' in math. I believe it was around grade 7 where I started learning about integers and I was struggling. This was the first time I had ever struggled with a math concept. I remember having to redo the test around 2 or 3 times until I finally understood the material. This led me to understand that even though I was strong in other math areas, there were some topics that I would not grasp.  I believe that failure has humbled me as a student and gave me a new perspective on math education. As I got into high school, I quickly realized that I was not the only one who was good at math. There were many other students who I thought were much smarter than me. ...

Representation is a strong tool to help understand mathematical concepts. Representation comes in a lot of different forms. For example, drawing a rough sketch to solve a word problem, or plotting points on a graph to see how a function looks. One of the author's main convincing point in his argument is the experiment Tchoshanov performed in Russia. To be honest, I do not find the results of this experiment surprising. I believe that a student who is able to put his thoughts(sketches) on paper combined with strong analytic skills will excel greatly compared to students who are only strong in one suit. An example of a mathematical representation would be the blocks used for teaching kids how to count. Kids are able to count quickly if they learn to represent 10 blocks as the 1 long stick, or to represent 100 blocks as the big flat piece. Another example they use is the different ways of presenting a set of 20 dots. On the left, the 20 dots are scattered and in no particular pat...

Richard Skemp describes instrumental understanding as 'rules without reason'. When he was giving such examples in math, it made me think of my time as a student in high school. I remember learning trigonometric identities and using them to solve problems, but I didn't understand what  they truly meant. I did not understand where  they came from and why   we used them, I only understood how  to apply them. This is the main difference between what Skemp describes as relational vs. instrumental understanding. Relational understanding answers why,  whereas instrumental only answers  how . Skemp tells us of these mathematical mis-matches, where the student's goal is to understand instrumentally, while being taught by a teacher wants them to understand relationally. Up until grade 10, I was one of these students who only had a instrumental understanding of mathematics. I had an amazing teacher who taught us in this relational way of understanding. This teacher ...

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