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?