Reflection on Microteaching

I think I learned more from this lesson than any other so far because it was by far the worst lesson I have ever done. It is amazing how much more learning one can have from mistakes than from doing things right. I thought the feedback from other teacher candidates was very useful and somewhat uplifting as I thought our group lesson was much worse than they did. Here are the things that went wrong:
1. technology - too much of it for a short time like this, did not work (used 10 minutes of class time to get going), lost slides, students did not know how to use graphing calculators (which we did not budget time for) and so on.
2. never once rehearsed, real problem with group flow
3. Esther did the slides for my part so I had no idea what I was doing till I saw the problem just briefly before the lesson and then while presenting. I assumed because the problem is so simple I could just do it. But because I was thinking about how to teach where the information is coming from, whether it was going to appear or not (as we did loose some material), stressing about the timing, and all these things that come with being a new teacher, I did not focus on the problem itself and, therefore, made math related errors, which are the core of the lesson.
I lost focus and was just thinking this is the same as riding a bike I can just do it, but if I tried to eat the ice cream and talk on the phone while riding a bike then it's not the same bike ride... tip for next time: drop the ice cream and the cell phone and ride the bike.
I lesson example, if we can stop worrying about other lesson related things we should have notes (no matter how simple the material is) to refer to in case we loose focus like I did. Also, a good rehearsal would reduce a lot of the other anxieties that I had about timing, technology and general flow.
4. I anticipated a question that Matthew asked but knew would not have the time to explain thoroughly because I was dealing with other group related things before class and did not have the time to think what the best answer would be. Should have said: more specifically how we are going to show the shift of the fn even if we did not have the time to demonstrate rather than just say that we'll talk about it. next class. That kind of answer would give students partial answer and give them something to look forward to in the next class.
5. I knew the intro was the only sure thing before the lesson but the rest I knew would have to be tight for time. Obviously this is a huge lesson: rehearse till we're ready and know will work.
6. Lots of group issues - but mainly timeline of when things were done - it was all last minute. So, when I think of my good lessons I've had I had them "mocked" (in front of friends, family) well before the day of the lesson. That was not the case here.
For next time, if we work with anyone to produce a lesson whether that be an SA or teacher candidate we will have to make sure to work on a well established time line, and allow members to jump in whenever they are ready, but keep going with the program so that we are ready on time.




 

	WHAT	HOW LONG	MATERIALS
BRIDGE	*Review Quadratic Formula by introducing the fun song from the web: http://www.youtube.com/watch?v=CnJT1ojHT28&feature=related *Tell students being able to graph basic quadratic functions without using a graphing calculator is important (why?) and the Quadratic formula will be a useful method to remember in graphing a quadratic function	1 minute
LEARNING OBJECTIVES	*to learn how to graph a quadratic function of a standard form, y=a(x-p)2+q, by hand
TEACHING OBJECTIVES	*to teach effective ways of graphing a quadratic function: using domain, range, vertex, x/y-intercepts using a shortcut (a, b, and c relations iny=ax2+bx+c)
PRETEST	*Test if the students can rewrite the general quadratic equation in standard form by using the method of completing the square	2 minutes
PARTICIPATORY LEARNING	*Observe changes in graphs by altering a, b, and c in y=ax2+bx+c: - discuss the role of a, b, and c (use the following simulation to demonstrate the role of ‘a’ http://phet.colorado.edu/sims/equation-grapher/equation-grapher_en.html) *Do a specific example by sketching a quadratic function of standard form by finding:      1. vertex      2. maximum and minimum      3. x & y-intercepts - analyze the domain and range *Compare the graph on paper with the one on the graphing calculator screen	1 minute 4 minutes	graphing calculators
POST-TEST	*Give students an example to work on their own and let them check their graphs with the graphing calculator *Each of us will go to a group of 5-6 students and help them if questions/difficulties arise	5 minutes	graphing paper, graphing calculators
SUMMARY & WRAP-UP	*If the students grasp the main idea, then we can introduce the shortcut method. (a, b, and c relations in y=ax2+bx+c )     1. x-coordinate of vertex = -b/2a     2. y-coordinate of vertex = c-b^2/(4a)         (or by plugging in the x-coordinate to the          given function)     3. y-intercept = (0, c)     4. x-intercept = (x, 0), where x can be found by          using the quadratic formula *For some quadratic functions with complicated numbers, we might not be able to draw by hand; however, it is important to understand the process and the basic shape of the graph.	1-2 minutes

Reflection on Thinking Mathematically (ch2&3)

Most of us who have studied mathematics at upper division levels can relate to these two chapters because years three and four math seem to be more challenging and we were getting ‘stuck’ more so than in junior years. Hence, we grouped and used various approaches to solve problems and probably used a lot of these Mason’s elements but never really defined them as such. These courses for me were the most fulfilling. Therefore, I can relate to Mason where he talks about how to stay positive in that situation because the hard thinking that you do to find an answer is quite rewarding in the end.

It is great to point out to these problem solving essentials in such a way so that we can help students organize their thoughts when working on their problems.  Otherwise, we may overlook them as we do not find their problems always challenging enough to come up with a slower step by step process like this one.

I found it surprising that the attack phase was the least crucial one but I can see why. If the question is not understood properly the attack is going to result in solving the wrong question. And the review phase is also very important because the students can make sure they understand the material well by expanding it to a wider context.

“Dividing for More than Zero”

Numbers divide and diminish

But never to finish in only a zero,

Because a number is more than just a zero.

It can be not just an accounting of debits or credits,

It can also be an accounting of food, friends and family.

Do we divide numbers or do we divide people?

When we divide numbers we shouldn’t divide people.

Unlike numbers, when people are divided

It can feel like less than zero.

So we divide numbers for people not of people.

We divide food, we divide shelter, we divide opportunity.

We divide hope

And in these numbers we divide, we become more than zero

We divide.

Time Writing

Divide
is a word that can be used in Math as well as in many other areas of life. It can mean divide two numbers, or divide a group of people into smaller groups. So, it can be used in social context where kids divide themselves into various groups like cool, not so cool, smart, etc. In our society we are divided as well in ethnic, economic, and other groups. We can be divided in groups based on our religious beliefs and lifestyles.

Zero
I think of the value zero in the social context. In my mother tongue, there is a really mean way to say that someone is not worth anything it is said the person is a 'total zero'. This means all of his attributes as a individual add to zero. There are some political figures that they often describe like this.
In the context of Math, zero is an important number in many of its areas.

Reflection on Simmt Article

I enjoyed this article because it explains some of the reasons why we study math and how we, as a society, benefit from it whether it is pure or applied. It states that mathematics helps those in power influence public opinion but at the same time it helps general folks in developing skills necessary to assess those opinions and allow them for active participation in democracy. I, also, agree that there is a particular way of thinking when we learn mathematics and that can be used in many aspects of life. In our teaching practice, we should be aware of the varying approaches to solving problems. Discussion about these different methods can be as meaningful as the theoretical discoveries themselves. We tend to think more critically and find reasons for our beliefs and convictions just the way we look for proofs in mathematical theories. We find practical use for these theories in everyday life, business, science, medicine, economics, etc. As our theories evolve and we produce more discoveries we induce further growth from which we benefit as individuals and as a society.

Reflection on the letters

From this exercise I looked at both my potential strengths and weaknesses as a teacher. The strengths were based on my past tutoring experience. I was told that I can break difficult concepts down to more comprehensible elements. So I hope to keep up with that. On the other hand, my weaknesses are based on my different educational background. I feel that my high school experience in Europe was more beneficial to me than Canadian high school would have been had I gone to school here. Therefore, I have to be careful not to put down the very system that I am going to be part of and further diminish students' perception of public school education.