Microteaching Reflection

From self reflection as well as comments from our peers, there was much that could be worked on with our microteaching. Mostly with regards to time constraints, our lesson plan wasn't fully expressed in the microteaching. Firstly, we already had a limited time for the microteaching, add on the fact that setup took a while and the end result was a lack of a post test and summary for the lesson. Upon thinking about it, the setup that took up much of our time produced minimal educational purposes for the class. But saying that, it did engage the class right away and it let to the topic of the lesson. I was also proud of our multimedia approach as well as allowing the students to participate in multiple activities. I thought our group did well presenting the actual transformation part of topic, which included participation from the class. So although it didn't materialize as what we had hoped, the lesson was still a pretty good lesson. For the future more emphasis will be put on the time constraints and make sure any set-up done will be very beneficial especially if it takes away from presentation time.

Microteaching Lesson Plan

Bridge: Hopefully we can lead in from Sara’s group who discuss translations. Transformations are everywhere: small child -> stretched child, smiley face -> stretched to oval face, motorcycle to transformer

Learning Objectives: SWBAT graph y=af(x); y=1/f(x); y=-af(x); y=f(-ax)

Teaching Objectives: TWBAT have a group work together to ensure that all concepts are understood

Pre-test: Sara’s group activity. Show some pictures of graphs, ask about what kinds of transformations

Participatory Activity:
Materials: peg board, graph paper
1.) graph 1; given transformation instructions, what will the graph look like afterwards?
2.) graph 1b; given the transformation, what was the transformation instructions?
3.) graph 1 and 1b by using TI-Nsprie, let student see how their answers are.

Post-test:
have each group set up a graph using the peg boards, and a set of instructions; pass graph to R and instructions L. following those instructions, transform the given graph.

Summary: review of the transformation rules and translation rules.

Reflection on Citizen Education in the Context of School Mathematics

The article brings up a few points that I’ve never thought of before that I find intriguing. First of all the idea of Mathematics being very much integrated into our society but yet seemingly so invisible. It seems that although Math is very much in economics, weather predictions, employment rates and even sports stats, the subject still isn’t something that appeals to the masses. Like I’ve mentioned before through interviews with Math teachers, a lot of people are very much capable of being good, working citizens by knowing up to say grade 7 Math, that is simple arithmetic and a bit of fractions. For the most part other than economics and a bit of probability in prediction of weather, the list mentioned above does not require too much Math. The more intriguing part of the article is more of the process of learning Math, than the actual Math itself. Math is a lot of problem solving and translating that to students is very important in become a functioning citizen. Learning to investigate problems and explain the process of solving it is more vital to the education of the students rather than the answers itself. This I agree with a lot, especially since in our society, there are many ways to solve problems that come up without one proper answer and it is important for people to investigate and explain why they think there’s a certain way of solving that problem. So that’s where high school math I think applies more to citizenship. Not in functioning in society with what math they learned in high school, but the process of thinking through and explaining the way to solve a problem. High school math offers a wider range of questions that students can think through and in the long run will help them in the way they go about solving problems and tasks when they become working citizens of society.

Throwing a Football "Microteaching" Reflection

My "microteaching" on how to throw a football finally happened. I was very grateful that I was able to do it infront of the entire class, so it actually became a "macroteaching". From what I felt and from what I gathered from comments from my classmates was that it went well. I felt great doing it, just thought I stumbled on a few words here and there. But I, along with a few people in the class thought I was very enthusiastic and engaging, which I'm proud of. From the comments, the class seemed to enjoy it and liked the hands on experience with holding the ball but thought it would have been much better if they actually got to throw the ball. Of course I would have loved to have taken them outside so they actually get to throw the ball or at least have more space to get the motion down. Like many future lesson plans though, I would touch it up a bit more and try to get a better sense of timing down. The class was great in that they were very receptive and participating so I had no problems with that. One thing I did take out of it and from thinking about other presentations is keeping my arms less animated. In this lesson I fidgeted with the ball a bit and I realize I do talk with my hand a lot so hopefully it's something I can fix. But overall I was satisfied at how it went.

What If Not Problem Posing

The What-If-Not Method is something that it seems has been used a lot before in our math studies, but making it more conscious to ourselves can definitely improve our abilities to becoming thought provoking teachers. The method firstly allows the teacher to make sure they posses a good knowledge of the subject and also prepares the teacher for possible questions arising from students’ curiosity. By posing these questions beforehand, a teacher will be able to be more prepared in class discussions rather than possibly being blindsided by a student’s question. But more importantly the teacher allows the student to not only understand the taught subject, but deepen the student’s understanding of it. From the example given in the book, a student not only learn about Pythagoras’ theorem of right angled triangles, but it also makes the student think of why only right angles? It broadens the students’ understanding of that subject and doesn’t just focus on one aspect of it, like just memorizing the theorem. This way when given geometrical problems, the student will also be more aware that if it’s not a right angled triangle, then the Pythagorean Theorem does not apply and they have to find another way to find its sides.
At the same time it seems like the WIN Method they discussed in the book do take it too far in questioning. It’s great that the student is challenged and engaged when they’re learning topics, but sometimes the questions go beyond the topic and sometimes becomes irrelevant to the learned topic. With regards to the Pythagorean Theorem, once we get into the cycling phase, it starts talking about a2 + b2 < c, and it seem to become more number theory rather than the theorem students are taught to relate to triangles.
But putting it to practical use, such as introducing sines and cosines for teaching, it is a great way to make the students think about the ratios of the triangle’s side lengths when it’s not a right angled triangle. In this manner they can be more cautious as to when to use sin and cos.

Comments on "The Art of Problem Posing"

I wasn't too sure exactly what types of questions we're supposed to post on to here. Whether it would be questions I had or questions I found intruiging within in the book. So while I wait to hear the answer to that I'm just going to post a few things that stood out to me:

1) I've known that Math isn't everyone's favourite subject but it's until reading this book that I realized it might be because of the objectivity of the answers. It was either right or wrong and I guess a lot of people would be scared off by that

2) That leads me to my next point of the book encouraging to break from the "right way" syndrome. That is to move away from merely looking for the right answers but look more for how problems are being answered.

3) It was interesting to see when the posted question of pythagorean triples appeared that all I thought of was answers for them and indeed we should enourage students from simply looking for the answers but to question it in different levels.

4) With the geometry problem, it was amazing how the book stated that sometimes learning a topic to whatever degree does sometimes narrow our understanding of something and how concentrated we are on finding the answers that sometimes it seems we have blinders on and are just looking straight at finding the answers.

5) I do question how as high school teachers we do try to change our students' way of looking at problems. Since all their life, they're looking for only the answer in order to get a good grade, how do we get them to ask more of the questions posed in the book.

6) At the same time there are some questions where it does seem to distract the students from moving forward. There are some questions that might confuse the student because it is far beyond what is being taught at their grade level. Though it is good to question it, the student might be stuck on finding the answer and prevent him/her from moving forward.

10 Year reflection

So I have this math teacher that's just so much fun! He's really energetic and outgoing and keeps the class always interesting. He's really approachable and really seems like he gives the time to answer your question. The best part about his classes is that we get to talk to learn at our own pace and we get to constantly talk to our friends in class. He encourages EVERYONE to share and talk in class, I used to be really scared of sounding stupid infront of the class but I started to see how everyone is encouraging in class and so I was able to speak up without a worry of sounding stupid. We really learn a lot in our class and it doesn't even seem like we're studying a lot. Mr. Chan has really made the classroom such an interactive place but still such a great way to exchange our ideas in class. It's great that I get to share my ideas to my classmates when I know the topic and it's great that my classmates get to share with me when I don't get the topics. Mr. Chan has really broadened my understanding of math and I was really surprised at how much I knew when it came to our finals. I used to hate math, but now I really like it!

-Laura
P.S. He's also good looking!


Dear. Ms. Principal,

I have a complaint against Mr. Chan, my math teacher. He doesn't seem to be teaching us anything. It seems like we're always just talking in class and I'm not learning a thing. He's always cracking jokes and they're not even funny. It seems like he doesn't know a lot about math and that's why he's making us do all this group work. I can't believe he makes us talk so much in front of the class too! And his tests are so easy and so narrow in terms of what we learned. All he gives are word problems that are pretty much the same question. I'd like to be transferred to another class, one that teaches faster and one that learns more.

-Chris
P.S. He's good looking though.


I can see from my hopes that I want to be a teacher that is more intereactive with the class and move away from the traditional classroom way of teaching. I hope to be always outgoing and energetic. But I am worried that I might joke around too much and might not make the curriculum challenging enough though and at the same time might not teach the students exactly what I want to teach.