Dishes Problem

 I had a hard time trying to solve the dishes problem without algebra because I am so used to using algebra when solving problems like this, so initially I tackled it with algebra. Following this I realized that the number of guests would have to be divisible by 2,3, and 4 so I made a list of all the numbers divisible by 2,3, and 4. The numbers would be 12, 24, 36, 48, 60, 72, and so on. From this list my next thought was to take each possibility and divide it by 2,3, and 4 and add up the answers. My final answer was that 60 guests were there because 60/2+60/3+60/4 = 65.

I think that it does make a difference to our students by offering problems from a variety of cultures. It can help students feel more included and heard. It can also help students see how math is presented in different cultures and societies. As well, it can help students be more interested in the problems we are asking them to solve. While this problem does not really involve any part of Chinese culture, it would be important to teach students about Chinese history in mathematics to go along with the problem.

Word problems and its imagery does matter. Word problems that are more applicable to our student’s everyday lives will help them be more interested in math!  

A Mathematician's Lament Blog Post

One thing that Lockhart mentioned that really resonated with me was that we are teaching our students to be “trained chimpanzees” (Lockhart, 2009), we are pumping our students full of algorithms and training them to study just for tests. Our students do not understand why math works the way it does or the reasoning behind why we study mathematics in the first place. This is like what Skemp said about the difference between relational vs instrumental mathematics. Our school system focuses on instrumental learning more than relational learning when we need a balance of both.

One thing I disagreed with was the idea that our curriculum is completely wrong and should be abolished. While our students are more likely to learn algorithms from the curriculum that we are presenting to them, it does not mean that they cannot learn critical thinking and problem-solving skills from the curriculum. There are aspects to our curriculum that are vital to teach to students wish to pursue STEM in university, we need to provide students with a basic understanding of mathematics before they can start approaching more theoretical aspects of mathematics such as a proofs and real analysis. A potential solution to this problem could be to introduce more theoretical aspects of mathematics in high school by moving some of the “basic” content down to the middle school level.

 

Works Cited

Lockhart, P. (2009). A Mathematician’s Lament. New York; Bellevue Literary Press.

Skemp Blackboard

 

Locker Problem Blog

 

To solve the locker problem I first drew out 10 lockers because 10^3 is 1000, so using a sample size of 10 seemed reasonable. My process was to evaluate what the first 10 students did and then see if I noticed any patterns. The pattern I noticed was that all perfect square lockers (1,2,4,9,16,...) were closed while the rest were open. From this I concluded that non perfect square lockers will be open and perfect square lockers will be closed.  

I think all the perfect square lockers are closed because they have an odd number of factors. For example, 1 has 1 factor, 4 has 3 factors (1,2,4), 9 has 3 factors (1,3,9), 16 has 5 factors (1,2,4,8,16), etc. Because they have odd number of factors, each perfect square locker will be touched an odd number of times and hence will be closed.  

Favourite vs Least Favourite Math Teachers Blog Post

My favourite math teacher was my grade 11 math teacher for pre-calculus. He was a very encouraging teacher, and a teacher who saw my potential and pushed me to pursue my dream of becoming a math teacher. Before I started his class, I knew I wanted to be a teacher, but I didn’t ever consider becoming a math teacher, and he really pushed me to do so! Additionally, he was also a patient teacher, he accommodated all students in his classroom. He encouraged us to understand why mathematics works and the reasoning behind why we study math. Following graduation, he mentored me and had me come back as a volunteer in his classroom where I got my first taste of what teaching could be! He showed me the ins and outs of teaching and really helped me realize I belong in the classroom.

My least favourite math teacher was my grade 7-9 math teacher. He was a very discouraging teacher, especially to those students who were not the best at math. He would often yell in the classroom and belittle students who did not understand the content. When I went to him for one-on-one help, he would often get upset and yell when I did not understand the content. He consistently told me that I was bad at math and that I shouldn’t do anything involving math in future, and I believed him because I looked up to him. His teaching style was not one that worked for me, and he made me dislike mathematics and believe that I was bad at math.

Overall, from my math teachers I learned that I need to be encouraging and motivating for my students. I do not want to be a teacher that the students fear, rather I want to be a teacher that encourages my students to persevere through their struggles.

Skemp on two approaches to teaching and learning mathematics Blog Post

 The idea of teaching instrumental vs relational mathematics made me rethink how I was taught when I was in high school. I feel that I was taught instrumentally and for that reason I knew the algorithms behind the mathematics but not why those algorithms worked. I think it is important to teach relationally so we can help develop our students critical thinking skills and help them overcome the idea that mathematics is the act of memorizing algorithms and repeating them on assessments. I also thought the idea of teachers teaching beyond the simple “here is an example, now practice” was interesting, to tackle teaching instrumentally we must take an inquiry-based approach in the classroom. Students learn best by doing and figuring out things for themselves, if we as teachers fall into the routine of just showing students how to do the problems, they will never grow their critical thinking skills. Another point in the article that made me stop was student’s response of “because area is always in square centimeters,” (Skemp, 1978) I too remember stumbling on that thought when I was in school because the concept of area was never truly explained to me. Helping students understand where concepts come from is crucial to their learning.

I agree with the issue Skemp raises because it is important to help students understand why mathematics works. Even though the students may not understand in the moment why we are talking about concepts not necessarily related to the topic at hand, they will understand in the future when they understand why mathematical concepts work. I speak from experience when I say, learning instrumentally hindered my ability to understand mathematical concepts at the university level. How can we expect a student to write a proof in their real analysis class when they don’t even understand why differentiation works? I think we need to implement relational learning in every mathematics classroom starting from a young age, the younger we start truly explaining concepts to our students, the greater their understanding will be overall!    

 

Works Cited

Skemp, R. R. (1978). Relational Understanding and Instrumental Understanding.

 

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