Math Art Project 2020

 Here is a link to our Math - Art Project

https://docs.google.com/presentation/d/1JPwtfn_BX-FqC5VVc9jGBdT3OuA1om4EBGh2FOwiLlQ/edit#slide=id.g9b5c589a29_0_21

Response to Mathematical understanding and multiple representations article

 

In the article, Pape and Tchoshanov (2001) argue that internal and external representations should be utilized to develop student's understanding of mathematics (p.118). They define internal representation as "abstractions of mathematical ideas or cognitive schemata that are developed by a learner through experience." (p.119). These are the mental images that learners have in mind, and draw relation to personal experiences. External manifestations of mathematical concepts can be represented by visuals such as graphs, tables, diagrams and charts. External representations also include numerals, and algebraic equation. I believe visual representations of mathematical concepts would be helpful for students in understanding the mathematical concepts. They give a clearer sense as to what the content is, and they make math problems less dull. Visual representations also make concepts notable and deepen the memory in the learners minds because I often find students pay more attention to visuals than just plain words. 

Verbal representation was shown in Figure 1 on page 119 in the article, but the authors do not provide an example for how it works. In verbal representation, students use words to relate math symbols and ideas. This type of representation can be useful in word problems by deciphering the given  information and what is being asked to find. 

Example of how the verbal model works can be found in this link. 

https://www.target.k12.mt.us/cms/lib7/MT01000812/Centricity/Domain/68/math_iwthout_numbers.pdf

Favourite and least favourite math teacher and letters from students in 10 years

 

My favorite math teacher was my grade 12 math teacher. I thought she was really smart because she has a dual degree in English and mathematics. She was not only the head of the math department at our school, but she was also one of the MYP coordinators. I really liked her because her way of teaching was very organized. She explained everything thoroughly, and I understood everything she was presenting in class. The amount of homework load she assigned was just about right, and the tests were fairly designed. I have developed my interest for math in her class and I look up to her as a role model for the type of math teacher I want to become. 

My least favorite math teacher was my instructor for a second year university course. Maybe it was his first time teaching that course, my classmates and I felt like he didn't how to teach. We felt like the assignments we had to do had no relation to what was taught in class. I felt puzzled throughout that course and now when I look back, I can't remember what I have learned exactly. I only remember we were asked to do assignments using python and latex, but I never learned any of that in previous courses nor in that particular class. I felt like I had no idea what was going on in that class and I had a time passing that course. 

Hi Ms.Liu,

My name is Bunny and I was one of your students in your math 10 class. I really love your class because it was full of fun and engaging activities. My interest for math has developed ever since your class. I used to think math is boring and there are too many things I don’t get about math. I still remember the times I approached you for extra help and you were always there. I really appreciate the support you offered outside of class time and it showed that you really care about students. Your lectures really built up the foundations of math which were beneficial for my other classes. You would explain concepts and steps clearly and it was such a pleasure to have you as a math teacher. 

Hi Ms.Liu,

I was one of your students in math 10 from ten years ago, not sure if you would remember me, but I didn't really like your class that much. Although you did engage some activities in class and you assigned math projects, I just didn't think those were relevant to what we had to learn. I wanted to learn something that would better prepare for entrance exams. You could have just given us more worksheets to practice problem solving so we could do well on tests. I mean, I am doing Arts now, and I don't think math is that important in my life. I have my phone with me all the time, and whenever I need to do math, I just do it with my phone. I just think all the hassles from your math class with those projects and assignments were not so important. Why did we even bother?

Reponse to group discussion on Skemp's article

 

I like how this group mentioned one way to improve the negative attitudes of math anxiety is to make "quizzes easy at the beginning of class to keep up with content and build confidence". In our group, we talked about how we as secondary teachers are one step behind because a lot of students would have had negative experience with math at their elementary ages. By the time they are in high school, they already have this preconceived mindset that math is difficult and they don’t like math. That's why I think It is important to build up the interest and motivation for students to keep their focus and interest in math.

Solving The Locker Problem

 

First, I try to decipher the probelm by creating a table with the locker numbers and the student numbers up to 10.  By the time I finish the number 10, I can start to see a pattern. 

Numbers 1, 4, 9 have CLOSED lockers, and they are perfect square numbers.

Numbers 2, 3,5,6,7,8,10 have OPEN lockers. I can see that 2,3,5,7 are prime numbers, and 6,8,10 are even numbers. I begin to wonder what is in common between these two sets of numbers. Then, I notice that they both have even number of factors. As I go back to look at the Prime numbers,  I notice that they have odd number of factors. From there, I can conclude that, locker numbers with odd number of factors are CLOSED, and locker numbers with even number of factors are OPEN. 

Note that the first locker is remains CLOSED. 

Sept 14, 2020 Skemp's Article Response

 

 

When I was reading the first page of this article, I thought I was reading some article on language learning because it starts by talking about the French word Faux Amis. It made me pause for a little, and I went back to check whether this was the reading for one of my math-related classes. I stopped again when Skemp introduces the concepts of "relational understanding" and "instrumental understanding". I always thought "understanding" is just "understanding“ and I did not know that it separates into two different concepts. After reading Skemp's article, I now have a little more understanding on the two types of understanding, and I believe the type of understanding have is instrumental. Later when Skemp went on to talk about applying relational and instrumental in teaching mathematics. I paused to wonder which method should math teachers use? Although Skemp concluded that teachers should "make a reasoned choice" depending on the situation (p.11), I believe most teachers would choose instrumental mathematics over relational mathematics. If we are talking about students in elementary to high school, I would prefer instrumental mathematics because students would have to assessed through tests and exams in order to advance to the next level. Both students and teachers may not want to make the effort to discuss the content behind relational mathematics. I believe relational mathematics would be more applicable to students in the post-secondary level

TESTING