reflection on timed writting exercise

It is a good exercise if one can think of ideas quickly, but for myself, it is not my favourite.
I usually get frustrated with it because i can't come up with ideas, i feel pressured.

Strength:
-a good way to get students actively thinking about the topic
-we can get ideas from many people
-teacher get to know what those people who are little bit shy are thinking
-get the work done quickly
-we can get some dynamic ideas

Weakness:
-time pressure
-thoughts could be really wild
-frustration can come in if can't think of anything in short period of time

division and zero

Division:
-opposite arithematic operation from multiplication
-hard
-inverse
-scary
-flip
-division of 0 => yuck

Zero:
-zero could be good and bad, "no" problem or "no" clue. it could be no mistakes or 0/100
-middle of the number line, maybe that's why it's good and bad. It could go either way
-not positive nor negative
-nothingness/emptieness
-division of 0 => yuck
-freezing point

Division by Zero poem

Division by zero

What did i just wrote

teacher says no no no

division rules doesn't hold

the answer on calculator doesn't show

it does not make sense at all

thus i do what i was told

that is,

don't talk about it at all

second micro-teaching self-reflection

Due to lack of experience and time working together, I think the lesson wasn't fluent enough. It's a unique experience to do a team teaching, next time for sure though, i will need to communicate with Sara a bit more. One thing i am happy about the lesson is that we clearly indicate what we want to do for the lesson and i think our examples lead to our ultimate goal quite nicely. However, if we used powerpoint instead of the white board, it would be more clear because there're some confusions of the graphs. Also, it could be more interesting if we add some real life examples to engage the students.

second micro-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.

second micro-teaching lesson plan

Transformation of a Function

Bridge: Does a function transforms? if so, does that mean function is 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

It is important for us as educators to realize the importance of mathematical education in our society. First of all, the basic mathematics (numeracy, basic addition and subtraction operations etc.) plays an important role in our daily lives. Whether we want to or not, we are all assigned to numbers: age, height, weight, and many other attributes. So the first step I believe to develop a mathematical citizen is to teach quantitative literacy. Furthermore, “we must educate our youth, our citizens, so that they begin to understand and critique the formatting power of mathematics in society.” There are many different ways to prepare the students for citizenship; one of them is through problem posing. By encouraging students to create problems within the given problem will help them to understand the mathematical concepts behind it. Not only that, we should encourage students and explain their rationale and the mathematical concepts clearly to others. This improves their communication skills as well as helping them to listen to other opinions from colleagues. After all, math is a fundamental aspect of the society in my opinion. Thus, every citizen should have an equal chance of being mathematically educated from their school experiences.

The What-If-Not strategy

How can I incorporate the What-If-Not strategy in the micro-teaching?
Our micro-teaching topic is going to be on graph transformation. We will start by graphing some simple graphs, and ask students if they recognize the pattern or relationships between the graphs. For instance, y = 2x+2 is moved vertically upward by two units from y = 2x. From here, I can ask “what if the graph is not moved upward?” Let students explore how equations would change if the graph is moved downward or sideways and then ask students to make some conjectures about the transformation. Finally, I can ask “how would the equation change if the graph moved both vertically and horizontally?” as the “problem posing” part.

What are the strengths and weaknesses about the What-If-Not strategy?
I think the strengths of this approach are:
1. It allows students to think creatively.
2. It might lead to some unexpected and interesting questions that one may not think of.
3. It helps both “strong” and “weak” students by getting students involved in thinking about the problem not just doing the problem.

Here are some weaknesses of this approach:
1. It is very time-consuming; I personally don’t think it will work well in a regular class setting.
2. It could end up like an endless loop, as we create more and more problems.
3. It could lead to some totally unrelated topic.
4. We could scare people away from math with series of math questions.

To be honest, I think this approach works well with students who are interested in Math but not so much for those who are already bored with math and yet we throw even more questions at them. I think it works best for those graduate students or mathematicians who are looking for more ideas.

10Questions/Comments for the book "The Art of Problem Posing"

1.Do you think we should just ask for more questions from students instead of solving the question?

2.I was fascinated because how many possible patterns we can find from a table of values.

3.Is it always good to pose a problem?

4.When is the time that exact answers are not necessary? and why?

5.How do we avoid posing a bad problem?

6.What's your defination of a bad problem?

7.Since when do you think posing problems is important?

8.Did your teachers used the strategies that you suggest when you were in school?

9.What was your motivation of writting this book?

10.You said that we impose a context on the situation, how can i avoid that?

letters of good and bad

Dear Mr.Hsueh

I was your student ten years ago, the year that you had your first full time job. Your attitude towards students taught me that we should treat every individual equally and fairly. You were always caring about students, not just the academics but also their lives. You brought new ways of teaching to the school system. Instead of notes taking, we were doing some fun activities and group discussion was encouraged. The broad math knowledge you had was incredible. You were the one that I was really looked up to. I am glad that I had you as my math teacher and I will always remember you.

Sincerely,

Alphonse

I hope that my style of teaching will help students to learn better.

I want to help them both academics and some personal issues if appropriate.

Dear Mr.Hsueh

I was your student ten years ago, the year that you had your first full time job. I guess you were not well trained, as you made tons of mistakes in class. I was very confused to what you were saying, teaching. The teaching style you had was horrible; we had class discussions but usually you lost the students because students started chatting on their own issues rather than concentrating on math topics. I hope your skills of class-management improved through some experience. I can’t let you to destroy the kids of the next generations. Good luck!

Best regards,

Betty

I hope that my class-management will not be described as above.