Reflection on Freewrite

Strength

• Easy to brainstorm and generate ideas about the topic
• Interesting things come up when you are not thinking straight
• Very fast process; train active thinking skills
• Can relate from one idea to another idea and to another idea
• Train your writing skills

Weakness

• Can easily get off topic
• Students can just repeated write, “I don’t know what to write, what to write…”
• Sometimes the time constraint prevents the legibility of your writing and thus unable to go over what you thought of at the time

Poem: Division by Zero

Isn’t zero mysterious?
You are allowed to multiply by zero,
But not divide by zero.

Say we have 3 * 0 = 0,
The rule of multiplication indicates,
We should get 0 / 0 = 3.

But we also have 7 * 0 = 0,
And we get 0 / 0 = 7.
Does that mean 3 = 7?

Continuing this pattern we will get,
1 = 2 = 3 = 4 = 5 = 6 = 7 = 8 = 9 = many more. Huh?
Oh, how wondrous zero can do to math!

Freewrite on Divide and Zero

Divide

• Sharing of same amount amongst people
• Cut something in proportion to each other
• Separation of an object into pieces
• Mathematical operation
• Sorting into categories
• Opposition to multiplication
• Division

Zero

• Nothing
• Neither positive nor negative
• Indication of none; non-existence
• Often compared with infinitely as extremes
• Degree zero is when water becomes ice; when rain becomes snow
• Represented by a symbol, a circle 0; unity
• A number can have infinite number of 0 in front and it doesn't change the values
• Not in possession; do not have
• Zero, zero, zero; something you don't want to get in your tests and quizzes
• Help demonstrate tens, hundreds, and etc.
  

Group Teaching Reflection

I think the main problem of our presentation was that we didn’t test out the lesson plan prior to teaching. Our group was not really in coherence. Also, since we were not able to follow the lesson plan directly, we forgot about incorporating WIN strategies into our presentation. In addition, there was some misunderstanding within the group. I was thinking of graphing together on the white board and my partner was thinking of letting the students graph on their own. Overall, I think our presentation is okay, but requires some more work on improving explanation and the content.

Group Teaching Summary

In general, people agreed that our group has great attitude towards teaching. They also liked the participation we had in our presentation. Some concerns are the contents and the explanation of translation. We didn’t explicitly explain the idea behind translation and that may have confused some people. Also, we kind of just make an assumption about the students being able to relate translation of a graph by graphing. Another concern is that there was no graph paper provided. Some people suggested that having graph paper would have helped their understanding.

Micro-Teaching: Transformation of a Function

Bridge: Function Transform? Is a function a transformer!?

Learning Objective: SWBAT translate a graph vertically and horizontally

Teaching Objective: To prompt the students to observe the relationships and patterns between given graphs

Pre-Test: Does anyone know how to translate a graph?

Participatory:

• What are some questions regards to the different graphs? (What-If-Not)
• Graph y = 2x and y = 2x + 1, y = 2x - 1, y = 2(x - 1), y = 2(x + 1), y = 2(x + 1) – 2
• Ask the students if they notice patterns
• Explain how the graph transforms if students can’t find the pattern

Post-Test: Give a graph y = f(x), then give another graph on the same grid but moved both horizontally and vertically. Ask students to find the equation of the graph that has been moved.

Summary: Generalization of function; what is the equation of the function f(x) if we translate it to the right by 2? And down by 5? And so on.

Citizenship Education in the Context of Mathematics

It was interesting to read about how mathematics ties in with citizenship and the society. Simmt suggests a few strategies in mathematics that have the potential to help shape our society. One of these strategies relates to our class discussion, the art of problem posing. Instead of focusing on a fixed problem, problem posing allows the students to think critically about the issues that may arise from the fixed problem. I agree that posing problems creates active participation of the students and let the students be critical about any given problems. However, posing problems also have a down side. Posing problems can get really messy as real world problems can arise from problem posing. If someone were to be critical and to problem pose, he or she may find loop holes in our society and may take advantages of the situation instead. How can we ensure the students to be critical and to be ‘good’? This is certainly an issue we still need to ponder about: how can we ensure the people to utilize mathematics for the good of the society and not for disrupting it?

“What-If-Not” Strategies

How can we incorporate these ideas in microteaching?
Our microteaching is going to be covering the transformation of a graph. At the beginning, we will be asking the students to come up with some questions regard to the different graphs we put on the board. For example, the students may reply, “the graph moved right by 2.” This is a Level I process as described by the book. Then we may response with, “What if the graph was not moved right by 2?” This is a Level II question. We can then prompt the students to come up with different cases when the graphs are not moved right by 2. Some Level III questions that may arise are, “the graph moved left by 2” and “the graph moved right by 5”. Not only that, we can further relate the original problem to, “what if the graph moved up or down instead?” Then finally, we can bring this into our main topic of function translation of vertically and horizontally.

What are the strengths and weaknesses of the “What-If-Not”?
Strengths:

• WIN strategies help to generate new ideas about the problem that we would not think of otherwise in the first place
• It intrigues new thoughts and more understanding of the problem
• It is also motivating in letting the students think more about the problem other than just solving it for the solution

Weaknesses:

• WIN strategies are too time consuming and it is a long process; it can go on and on without stopping (the cycling techniques in the WIN strategies)
• The mass amount of questions let the students down as they are bombard with somewhat unrelated and extra problems
• It is easy to get off topic with the WIN strategies; the students may focus on the wrong aspect of the questions
  

10 Questions Regards to Art of Problem Posing

1. How does common sense limit problem posing?
2. How do we use general questions efficiently in a specific setting?
3. How can we be certain that the students benefit from problem posing?
4. How can the massive amount of questions asked not be overwhelming?
5. How do we ensure the students stay on track and keep focused?
6. How do we pose a problem sensibly?
7. How do we keep the students interested?
   
8. How does past experience have to do with problem posing?
   
9. Is there a bad problem posing?
10. Is there any stupid questions in problem posing?
    

10 Year into Future

Students who love me:
- You're very caring and organized. I can follow through with the math processes with only a few problems. The lessons are fun and interesting. I especially like the free-style math projects you assigned us to do. I learned a lot about math while doing the projects. I used to hate math but now I am rather enthusiastic about math. Thanks for your teaching!

Students who hate me:
- You're too nervous from time to time. Your voice starts to waver and becomes unclear when you are nervous. I have trouble hearing you in the class, so in return, I have trouble understanding the math. Please have more confidence in yourself before teaching again. Also, I didn't like the math projects you assigned. I need a clear goal and objective when doing projects.

Comment on hopes and worries:
- I hope I don't get too nervous when the students ask me questions that I can't recall or know the answers to.
- I want to let the students be creative in the class and I hope to motivate themselves in learning math on their own.