Reflection on Battleground Schools: Mathematics Education

Reform movements in mathematics education have constantly emerged over the past 100 years in North America. In the early 1900s, the progressivist views of the mathematics education changed the way mathematics had been taught in class. According to John Dewey, mathematics is more than just getting correct answers. Rather, it is about thinking deeply as part of inquiry learning, which makes students question why they use particular procedures and how they get answers to the  problems. However, the New Math curriculum was introduced in 1960s, but it failed eventually since new math topics were not ideal for K-12 students as many teachers and parents did not understand why new topics including university mathematics were taught. Then, NCTM standards were introduced in 1990s. Indeed, if there is any better way to help students learn better, I believe that new education movement should be developed. As a future math teacher, I understand that I should be a progressivist. Not just delivering math lessons, I should make sure that I motivate students to wonder about learning, which they could link to real life situations. Moreover, I should be able to adjust/ implement instructional strategies/ pedagogy to cope with the new curriculum. Although I have to follow curriculum, instead of having to cover many topics in a given time, it will be better if I can help students understand less materials more in depth. 

Reflection on Microteaching Experience

Through microteaching in class today, I clearly realized my strengths and weaknesses. At first when I made a lesson plan, I was worried I wouldn't be able to finish my presentation on time, because it seemed impossible to me to explain all the important steps/tips of making Kimchi. However, I finished teaching within the time limit, which I believed would be hard, so I was good at managing my time. Since it was hard for me to make Kimchi with actual ingredients in class, I used pictures of ingredients instead. I think that I was able to introduce interesting activities to engage my group members in learning such as filling in the blanks or putting pictures/sentence strips in order. I think that students learn better when they have something visible or tangible that promotes creative thinking. Moreover, I think that I had a good opening that I was able to get the attention of my group members when I got started with pictures of different types of Kimchi, which only two of them could guess.

However, I still need to work more on time management, which I believe would be the hardest when I start my practicum. Although I stayed within my time limit when I was presenting, I spoke fast and couldn’t answer all questions to keep track of my time. Instead of speaking fast, I should have reduced some of the activities I created, so I would have had more time to spend answering the questions. I think that teaching is not just about introducing as many ideas/activities as possible. Rather, it involves helping students become aware of the importance/purpose of the activities they do in class in order to motivate and encourage them to understand better. Also, I think that closing would have been better if I brought new ideas/questions at the end of the activities for students to think about. Over all, I enjoyed learning from others as well as teaching others.

Lesson Plan: Individual Micro Teaching

Lesson Plan: Individual Micro Teaching
Topic	How to make Kimchi
Objectives	Know how to make Kimchi, a traditional Korean fermented cabbage. Understand Kimchi making is not hard. Know roles of fermentation in Kimchi and healthy benefits of Kimchi.
Materials	PowerPoint Presentation Pictures of ingredients (Each bundle for myself & 4 students) Pictures of directions Sentence strips on directions
Opening (1 min)	(1 min) Show photos of different types of Kimchi.             Ask students what photos represent.             Explain healthy benefits of Kimchi.             (Vitamin A, B, C, and Lactobacillus bacteria)
Body (8 min)	(3 min) Show pictures of ingredients.              Explain directions along with pictures of ingredients.
	<Activities>
	(2 min) Fill in the Blanks. (Answer with appropriate pictures of ingredients)
	(1 min) Put the pictures of directions in order.
Assessment	(2 min) Put sentence strips on directions in order.
Closing (1 min)	(1 min) Explain roles of fermentation in Kimchi.

Estimated Volume of the Giant Soup Can

         First, I measured the height of the bike in the photo from the bottom of the wheel to the handlebars. It has a height of about 5.5cm. Then, I measured the diameter of the water tank in the picture. It has a diameter of about 10.5cm. Then, I measured the height of an actual bike that looks the same size. Then, I found that it has a height of about 104cm if I measure it from the bottom of the wheel to the handlebars. Also, I measured the actual Campbells Soup can (540mL) in the refrigerator. It has a height of about 10.5cm and diameter of about 5.5cm.

         Using a ratio, I found the estimated diameter of the water tank.
diameter of the water tank in the photo : height of the bike in the photo = estimated diameter of the water tank : height of the actual bike of a similar size
-> 10.5cm : 5.5cm = x : 104cm -> x = 198.545cm = estimated diameter of the water tank

         Since the tank was in exactly the same proportions as a soup can, I found the estimated height of the water tank using a ratio as follows.
estimated diameter of the water tank : estimated height of the water tank = diameter of the actual soup can : height of the actual soup can
-> 198.545cm : y = 8.5cm : 11.5cm -> y = 268.620cm = estimated height of the water tank

         Therefore, the estimated volume of the water tank = area of the base * height = (estimated radius of the water tank)^2* π*estimated height of the water tank = (198.545/2)^2* π*268.620 = 8316606.156 cm^3 = 8316606.156 mL = 8316.606 L = 8.317 m^3 = 2197 gal

Two Imaginary Letters from My Future Students

Dear Ms. Jeon,

Hi. How have you been doing so far? You always supported me. When I first immigrated to Canada, I felt very frustrated because everything was new to me. However, my favourite class was math subject because you were my teacher. There was one time I couldn’t finish all the exam problems because I couldn’t understand word problems. However, you explained them step by step through drawings, so I was able to understand better and get better grades on my next test. I knew you had extra time with not only me but other students like me who were behind in class. Still, I felt very special. Moreover, I liked how you taught in class because you were loud enough for me to hear even from the back of the class. Also, I really liked your math problems, because I found them beneficial! Indeed, values from the graphs you have shown us in class were very helpful in understanding facts about social issues. Thank you. Bye.

Reflection: I hope to speak clearly and loudly enough so that every student in my class can hear me from anywhere. I believe that as a teacher, it's important to make sure that the messages are clearly delivered to students. In addition, I hope to take extra care of the students struggling with math, so I can prove that mathematics is actually fun, not boring!

Dear Ms. Jeon,

Hi. How have you been these days? Although I was a top student in your math class, I didn’t like math much. Most of the time, you seemed to be in a hurry when you taught us, because you spoke fast. That made me feel like I was in a hurry as well, and I wished that I had more time to finish my activities. Sometimes, you hurt my feelings because you did not seem to treat everyone in the class equally. Even when you asked us to put our hands up to answer your questions, you let other students answer, but not me. I don’t know if you still remember, but there was one time I did not do my homework, and I told you I was sick. However, I could still do my homework, but I didn’t do it, because I just wanted to get your attention. After all, I was able to catch up with the class soon because I realized how much you loved me. Thank you. Bye. 

Reflection: I will always try to treat everyone in my class equally, but I am worried if some high achieving students feel differently, because they might think I help struggling students only or give them less chances to answer in the class. I will always make sure to give all the students in my class equal attention.

Math/Art Learning Project: 60 Playing Card Polyhedron

My group created Deltoidal Hexecontahedron, which is made up of 60 playing cards in total. From this construction, I can explore matematical ideas of symmetry, shapes, and counting. It is very interesting to see that every pentagonal face is symmetrical to the one on the other side. Also, there are different shapes such as pentagons, triangles, and rhombi in this work of art. It has pentagonal and rhomic openings. Since the construction has 12 identical pentagonal faces with pentagonal opening in the middle, it has 12 pentagonal openings in total. Similarly, since 5 rhombic openings overlap each other between 12 pentagonal faces, there are 12*5/2=30 rhombic openings in this 60 card construction.

The hardest part while making this polyhedron is to make 3-fold lock. It is easy to slide the first two cards together. However, it becomes tricky when third card slides into the first two cards. Although these three cards become planar later, they should be bent while being joined. Moreover, it’s important that four slits in each card are cut as accurately as possible, so three cards can be locked together. Other than that, the rest of the process is straightforward and easy to follow.

Throughout math/art project, I started to look around, so I could find any math involved in art. Then, I realized that math is art, and art is math. Nevertheless, many people simply do not notice that many works of art and architecture are made using mathematical principles. Indeed, there are many buildings with different patterns in mathematics. People should carefully examine works of art around them so that they not only see outer visible surface but also think about math and art connections. Indeed, it is always an exciting moment for teachers and students when they start to think mathematically as well as creatively.

A Puzzle from Ancient China (Dishes)

This problem shows Chinese cultures/values and how Chinese people are considerate of others since they share food with one another. Although this is a puzzle from Ancient China, it can be used with other products in other contexts as well. For example, instead of dish of food, it can be something else (clothes, books,...etc) and somewhere else. Therefore, I do not think that its cultural context really matters when introducing mathematical principles/practices to students.

David Stocker's Maththatmatters

Maththatmatters, indeed, recalls my past math textbooks containing pizza, price discount, or circle problems. At that time, my teacher seemed just busy introducing all the topics in math. I only cared about good grades. Later in my real-world, I started to realize that the math problems, which I had learned in my class, were not really meaningful/beneficial. I did not have the opportunity to think about the world while solving math problems, since those problems were hardly designed around real-life application.

However, Maththatmatters introduces interesting activities/problems related to social justice issues aimed at “global awareness and optimism” (p.14). I believe that such method is an effective and creative approach to teaching students, because connecting to math in real life would motivate students not only to learn math skills but also to be aware of social justice issues. Math is not just about getting numerical answers anymore. Math problems should require students to apply their math skills to real-life situations. Eventually, this will lead students to question themselves about the world around them and find math problems very useful in their lives.

I definitely think that these ideas from middle school math can also inspire teaching ideas for my secondary math classes, because they help me think about how I should design/introduce math problems based on real-life. Indeed, students with math anxiety can be motivated to solve math problems related to the social issue of their interest. Nevertheless, it is not easy for me to link some social justice issues and math to deepen students’ understanding of the real world. Yet, I know that the efforts I put into integrating social justice to my math class will pay off someday when students start to wonder about the world to build a better society.