Math Art Project Reflection

 I found it interesting to be able to connect Math with Art. Typically when you think of Math you don’t think of Art or vice versa. I liked being able to apply mathematical ideas to art. For example in our project for the extension, I was able to use another artwork and apply the concepts of circle packing and arranging circles without overlapping. While working on this assignment, I learned that you can use Math in so many forms and it is used everywhere. For example not only is circle packing used in Math and Art but, also in other subject areas like Chemistry. I think encouraging students to apply math concepts beyond the classroom is a great way to keep students engage and interested in what they are learning. It also allows them to critically think of different connections that can be made to math. I also think using math art in a classroom will be useful because it gives students a hands-on experience to learn abstract math concepts. The project also allows students the freedom to bring their interests from outside the classroom and find ways to incorporate them and apply them to math. 

Math Art Project

Here is the link to our math art project: 

https://docs.google.com/presentation/d/1RxSqZqU9R9eCmB62hOtF8ftWUS0f0H02X0lU01uhtd8/edit?usp=sharing 

Dishes Problem

 

This is a picture of how I tried to solve the puzzle and the solution I came up with. I think it does make a difference to use problems from diverse cultures. It provides an opportunity to encourage students to be curious and excited to learn about math. I think it also provides a diverse learning environment where students are able to share their different points of view. I think the imagery in word problems matters when it comes to the enjoyment of solving them. This is because it allows students to feel connected to the content and to be interested in what they are learning. I also think it’s a great way to present word problems to those that don’t particularly enjoy math. 

Locker Problem

Before the group discussion, this was my solution for solving the locker problem. I tried to simplify the problem by using 10 students and 10 lockers and look for any patterns. I noticed that 1, 4, and 9 were the only ones closed and they were perfect squares. However, after our discussion, I realized I didn't consider factors and skipped over that part. I'm glad we were able to have the in-class discussion because it allowed me to think of different perspectives. 

Letters From Future Students

Dear Miss Dhaliwal

I’m not sure if you remember me but I was in your math 9 class 10 years ago, and I just wanted to let you know that I loved your class. I felt that the lectures and projects you had were very engaging and interesting. I think that was great because I never felt learning about math was boring or forced. In a lot of my other classes I would zone out however, in your class I wanted to pay attention and learn more. I found that I could actually understand the material and solve the practice problems. Another thing that I loved about your class was allowing students to work in groups to solve problems. I found that sharing my ideas and thought process with another student was helpful. It allowed me to learn from others and collaborated with other students. In my opinion, it built a sense of community where I felt safe asking questions and for help. I also found as someone who wasn’t great at math that I could approach you for help or ask you questions because of your patience and attitude towards students. I hope that you continued to use and improved the techniques you used in the classroom 10 years ago as they were very helpful for me. 

Thanks, Student 1 

Dear Miss Dhaliwal,

I was a student in your math 8 class 10 years ago and I wanted you to know that my experience in your class was awful. I found that your instructions were unclear and the way you explained concepts didn’t make sense. I couldn’t relate to the way you taught and at times I couldn’t pay attention in your class. I also felt I didn’t have any support when I was confused or had questions. I felt that you didn’t teach in a way that encompassed my learning style so I became disengaged and was no longer interested in what you were teaching. I also thought you were unapproachable so I was afraid to ask you for help or ask any questions. I didn’t like working in small groups because I thought other students were judging my math skills and I didn’t feel included. I hope over the 10 years, you have improved and made

adjustments to your teaching because when you taught me I learned nothing.

Thanks, Student 2 

Reflection:

As I take a look at these letters one of my biggest hopes is to create a welcoming and safe environment where students feel comfortable. My hope is to have a class where all the students feel like they have a voice and aren’t afraid to ask questions when they are confused. I hope working in smaller groups with others students can help them build upon each other’s knowledge but, I also don’t want anyone to feel isolated in their groups. Perhaps one solution could be to have each student pick a partner and then assign them into groups. This way they have at least one person in the group they are comfortable with. I also worry that as I teach I may not explain something clearly or in a way that everyone can understand. I would like to teach in a manner that makes learning math fun and interesting. I hope I can come up with some creative ideas and projects to do that. I also hope that students would provide me feedback on what worked for them and what didn’t work for them in the class. I think this feedback will be helpful for me to make adjustments and improve my teaching style. 

Response to Lockhart's Lament

I found the article, Lockhart’s Lament, very interesting as it was the first time I’ve heard math described in this manner. One thing in the article that I agree with is many math classes are taught by memorizing facts and formulas. The math classes I had also encouraged this way of learning as well. I think it’s important to focus less on this method of recall and shift the focus to the bigger picture. Looking back at my math classes, most of them were taught by giving students problems and having them practice the problems over and over until they understood the concepts. I think due to this, students aren’t able to build on their problem-solving skills or form deeper connections with what they are learning. This may be the reason why many students are unsure of how to approach a problem they haven’t seen before or haven’t had to memorize. I also relate to the part in the article where it discusses learning and memorizing facts such as 5 x 7 = 7 x 5 and how it shouldn’t be the way math is taught. I agree with this because when I was tutoring a student and I explained this rule they didn’t understand it at all. However, when I used counters and conceptualized the rule by making five groups of seven and seven groups of five, the student was better able to learn and understand the concept. One thing in the article that I disagreed with was the part about how there is no need to make math interesting and relevant to students' lives as math is already interesting. I would disagree with this because from my experiences as a student, I found when the teacher would make the topic relevant to daily life I was able to understand more and remember it easily. I think making math interesting and relevant, allows students to pay attention in class and be engaged with the lectures. Overall, I enjoyed this article and the unique perspective on learning and teaching math in a classroom.

My Favourite and Least Favourite Math Teacher

Looking back at my previous math teachers, one quality that stands out the most is when the teachers were enthusiastic and created a fun classroom environment. I think this is important because it allows learning about something as boring as math to be interesting. It also encouraged students to learn more and be more curious about math. For example, one of my high school math teachers would always come up with creative math games and projects to keep us engaged in the material. I believe another important quality that my previous teachers had was they were caring and patient. I remember not understanding one of the units in my math class, so I went to ask for help after school and my teacher was more than happy to help. He took the time to make sure I really understood the topic. In fact, he realized I didn’t understand the way he taught the topic in class so instead, he explained it in a couple different ways to ensure I understood. I think that this experience was a great teaching moment because it showed me that not all students learn and think in the same manner. I appreciated this teacher taking time out to show me that there are multiple ways to learn something. Another one of my math favourite teachers took the time and showed a personal interest in each one of her students. For example, one time I didn’t do well on one of my math tests and she noticed this. She approached me after school and asked me what happened as this test wasn’t some of my best work. I had told her that I had another test that day so I didn’t study as much for the math test. She then replied with I know you can do better so in a couple days come in and rewrite the test. Now, reflecting back on this experience it showed that this teacher cared and wanted the best for me. She knew what I was capable of and did her best to help me achieve it.

My least favourite math teacher was from a high school math class that only consisted of the teacher lecturing and assigning textbook questions for homework. I remember his classes were the hardest to learn anything because they were very boring and the easiest to zone out of. I also think his lack of enthusiasm for the topic made it hard to learn and be interested in what he had to say. He also came across as unapproachable so I was afraid to ask questions or ask for help. I would then usually end up learning everything he taught on my own. Another one of my least favourite teachers was from my university classes and it was because this teacher was very disorganized. He always seemed unprepared and scattered for class and that made it difficult to understand and learn from him. He also didn’t provide feedback on the assignments on time so his expectations were unclear. The lack of feedback and communication made it hard to grasp what I needed to know and the topics I needed to improve on.

I think the biggest takeaway from these reflections on my previous experiences is the way teachers act and behave plays a major role in learning in a classroom. A teacher that is engaging, patient and caring provides the opportunity to inspire and motivate their students to want to learn rather than making them learn.

Response to Skemp Article

One thing I found interesting while reading was the part where Skemp discusses, instrumental understanding and how sometimes it is described as “rules without reason”. This particular part of the article reminded me of when I first started working at a tutoring company. I was explaining multi-digit multiplication to a student. I first showed the student an example of one question where I went over all steps and one of the steps was to place a zero under the one’s place. My employer had overheard this and asked the student do you know why the zero goes there and the student had said no. I then realized my mistake that I shouldn’t have just given the student the steps on how to answer these questions. Instead, I should explain the reasoning and why things were done the way they were to help the student have a clear understanding of the concept. Another thing that made me “stop” while reading this piece was the part about the area of the field where two different units were used and students answered the question without really understanding it. I found it interesting that the article mentioned this because this also reminded me of my experience while tutoring. A lot of times students would look at similar questions and instead of reading what the question was asking, they would be quick to use the same method to solve all questions resulting in getting a few of the questions wrong. Another thing that made me “stop” while reading this piece was when Skemp uses the example of having fixed routes to get around town versus creating a cognitive map of the town. I found this interesting because it was a  simple and unique way to demonstrate instrumental and relational understanding. I agree with the article on how by creating this mind map of the town, one is able to form these different connections and paths that they wouldn’t be able to if they only had a fixed route. 

I think Skemp raises many good points on learning for both instrumental mathematics and relational mathematics. I think relational mathematics is beneficial to use in a classroom because it allows to students to form connections and it allows for long-term learning. I think once relational understanding is established students will remember it for longer and may perhaps use this knowledge to build on other things they’re taught. I also think that instrumental mathematics has a place in the classroom as well. At times when first introducing a topic, it can be easier to explain the concept without providing the why behind it. The article mentioned that relational understanding in math may take longer. I think that perhaps at times there may not be enough time to focus on the relational understanding. This is where instrumental understanding comes along as it is easier to use during a short amount of time. I think that both relational and instrumental understanding should be used in a class. This is because at times it may be beneficial to use relational mathematics and for other topics, instrumental mathematics may be more beneficial.