Reflection on 2nd Microteaching Lesson

First of all, I'd really wish that each of our lesson plans were recorded. This way, we can for ourselves clearly see how our teaching went and most importantly we can share with the teaching techniques different groups came up with. For our group, the basic structure of a lesson was presented pretty well. An excellent introduction was done by Rong, and the proof was carried through with a good flow. However, there are three things to look after. The diction in mathematics needs to be carefully considered and chosen. Some students may not understand some of words we are used in the university level and some vocabulary needs to be introduced at times. The connections among presenters were poorly bridged. This left some of students uncertain of what we were trying to teach. The game designed was not deliberative and engaging. What may seem to be easy for us now may not suit the level of students we aim for. It is important to be able to put ourselves into their shoes. Nevertheless, the lesson was carried through with a somewhat simple rhythm and I really liked the part that nearly the end that Rong brought students back to his very first “hook” and went through the real life problem with them.

Reflection on Citizenship Education in the Context of School Mathematics

A mellow resonance rises from the introduction of the interconnection of mathematics and citizenship education. However, much of the argument in an attempt to the indication of the relationship is unsound,inconsistent , and disagreed. In this journal, mathematics is investigated and distinguished in layers of perspectives. Mathematics, to personal belief, is a language system in forms of numbers and symbols, which can be utilized to describe and simplify phenomena of several different aspects. As used in calculating processes, numbers are dealt with generically and the inevitable outcome of correct and logical procedure is the "right answer" of a problem or an exercise. In exploring the implication of mathematics, mathematics is then applied and structured to illustrate and convey the models, which contain no definite "truth." The interpretation of mathematics may not alter the essence of mathematics. Furthermore, even though the very essence of mathematics advocates the development of logical and critical thinking, philosophical concept at its intuitive level coincides exact description of correlative purposes and contributions. Consequently, citizenship education can progress and proceed irregardless of the presence of mathematics and this simply results in collapses of the ground of arguments. Nevertheless, Mathematics, as well as social construction, is of complex synthesis and needs deliberative analyses to attend proper representation.

Reflection on Reading II

Students like to ask questions. They are keen to find out what they want to know. However, the minds and perceptions of students are narrowed and limited by several reasons in pursuing in their studying. A simple example is that as students try to come up with so-called good questions, they neglect the possibilities of what are considered as stupid questions may lead them into an investigation to an enlightening result. The "what-if-not" strategy then is here to help students free their tied-up minds. The idea is to develop the critical thinking ability in students that they can produce a more thorough and comprehensive perspective of a subject matter. Students can then have the whole image of what they are learning and to further develop it, find the connection among different subject matters and create a board spectrum of view where knowledge are intertwined altogether. To implement this strategy into our teaching, teachers have to, before the students, obtain the thorough views of subject matter, know all the question levels where they can lead the students on step by step to explore more into the subject and expand the minds of these students. I think its definitely important to let students know that there are no stupid questions and they need to learn to "leave them(questions) in" so that they can come back and examine them later once they have connected the topic to another and come to realize that these questions can in fact help them to a boarder realization of knowledge which may appear in an unconscious level sometimes. Then, teachers can help students to think more and more and later students can think and explore independently in their interested fields. I think couple limitations of this strategy are that it is abused by students who are too smart to realize this is to help them progress in their studying rather than using to backfire teachers, and sometimes by teachers who think that life is easy just by questioning their students and do not care whether these questions are "acceptable" or over-whelming to students. Too many questionings and sometimes too many "meaningless" questions really depress students with their interests in studying and can result in a fixed minded students after all.

My Frequently Asked Questions

1. (p.14) It has appeared to me so many times as to try to understand some explainations from the text or of the teachers that the saying "it is obvious to see..." or "because you can tell..." always precedes the understanding of some students. I was not a very smart student to begin with, to be honest, and I am sure that the "because you can tell..." or the "it is obvious to see..." often confuse and frustrate some students, including myself, even more when, at times, they really do not understand why they can or why it is obvious to carry onto the next step.

2. (p.15)Pythagoras Theorem: What is it, really, other than "accepting" it as a given whether related or insightful activities are arised for students to participate? Other than the explaination that it is an essential element that makes up a right angle triangle, what other purpose does it serve? What other ways can I explain to my students other than its generic purpose? What

3. (p.20)Very so often that it is through questioning, especially with seemingly meaningless questions, that a situition is cleared, even though at times some meaningless questions really are meaningless.

4. (P.25) If the starting point is about propositions, how are teachers able to make it intersting and engaging for students in the first place?

5. (p. 25) It is sometimes fun to ask the questions the other way around and some insightful concepts may surface.

6. (P. 26) Due to the construction of how problems are asked, students can be more engaged and interested in exploring the problems. Traps! Teachers set traps in a way for students to step in and then learn the mathematical concepts inside usually before they realize the fact.

7. (p. 26) Relations from one subject matter to another and patterns to create concepts of a subject matter remind me of this question: Is Mathematics an invention or a discovery?

8. (p.27) Do we have to have answers to all problems? So far, we cannot prove that there are no answers for some problems. Can, on the inverse, we prove there are answers to all problems?

9. (P. 27) It is the curiosity that encourages and drives people to pursue the investigation of certain subject matters. In English, the pattern of past tense is set but there are some verbs make exception to that pattern, but why? The solution may usually be obvious once the history of those verbs are given. Is it the case for some of the Mathematical investigations? Is it enough just to know the history?

10. (P. 31) Is this relevant? Are these questions for deeper investigation in Mathematical studyings or Are they for developing problem sovling skills?Though generalizing problems with HOT list of questions makes it easy for students and teachers to attack problems, will they limit our mind?

ten years after..

mr. paul

I really enjoy your lesson because you are able to make us do well in tests and I do not even know how that happens. Your stories are always awesome and your expressions are really entertaining. I like that you encourage us to speak of our minds and let us know that making a mistake is abosolutely okay. Jerry told me that you are really cool because he can speak to you like friends and can smoke together after class. I especially enjoy your puzzles most. It allows me to work on somethig fun while taking a break from doing homework. Even though your homework is hard, I can always get help from you personally or by going to the discussion board at your blog. I really appreciate your way of teaching and I am glad to have you as one of math teachers. Oh! I like your smile. When I saw you the first time I thought you were a really angry teacher, but everything changes onece you start smiling.

-I wish to introduce math to students in a subtle manner and welcome them to a free learning environment. I want my studetns, based on my personal experience, to be not afraid of making mistakes and so they can enjoy more learning math.


Mr. Chen

I am writng to you just to let you know that I wish that I can get something different from your lecture. I think your homework problems are too hard and it does not really help with my improving test scores. I think you spend too much time in class telling stories and even though I know it is not entirely irrelevent to your math teaching, I still wish that you can focus more on teaching us how to work on problems so I do not have to spend more time working on my homework when I get home. And, you know, as a teacher, you really are not supposed to smoke with your students. I think this is a bad influence to your students and It makes you look bad as a teacher.

- My only concern is that different students may react differently to my teaching. As teachers are sometimes role models to students, what I do may not always be adequate and appropriate to some students. I wish can learn more to improve myself over years and hopefully during the practicum, I get to know what is the students' envision of a math teacher.

Reflection on Battleground Schools and Video About Math Teaching

This article briefly describes how Mathematics falsely appears to people as hard, and inhuman. In twentieth century, Mathematics has gone through three major movements, John Dewey, New Math and NCTM. These changes are more subject to political purposes rather than its generic concept. Up until today, the battle between conservatives and progressive continue to enact and the fighting over which method is better in educating students or in producing more elite members has not come to an consensus due to the involvement of politics.

This article ties closely to the discussion about instrumental and rational understanding. the feeling of arguing over which conception is better and the thought of not to come to a consensus seems to never-ending because the intention has been misled by and from the political point of view. This pretty much explains the reason that in some countries that children were told to proceed excessively in Mathematical studying and think that by succeeding in mathematics, a better education is achieved, which ultimately contributes political pleasure and purposes, rather than personal educational development. Nevertheless, I find that John's idea towards math coincides with mine. As discussed in instrumental and relational understanding, there is actually a fine line between these two understanding before bringing both methods to an extreme. a balance with adequate adoption of these understandings may benefit more in math education and create more elite members. However, because of political intention about the national superiority, math ends up facilitating between two ends.

The concept of teaching mathematics is beneficial as to equip students with understanding and thinking skills. However, it is the discouraging presentations and the curriculum that drop bombs on students and parents. Students with bad experience naturally turn their face away from learning mathematics. In order to catch their attention and cultivate their interests in learning math, teachers need to present in a way so that they can engage with their students. This reminds me of the class discussion with Dr. Lucus over the topic: Is Mathematics an invention or discovery?. One of my thinking is that Mathematics is a language which can describe our daily living experience into the alphabets created by mathematicians. In the video, the teacher cunningly lures out his students pure interest in the language he uses. With simple back-and-forth routine, in fact the basic sequential concept in math. Along with the skillful introduction of mathematical language linked closely to spoken language combined with the visual illustration, the teacher also engages his teaching with several hands-on activities. There are different types of students where they learn better reading, listening and doing. Knowing this can be beneficial for students while adequately adopted and as "knowing is half a battle," the real challenge is to be able to equip these into classroom teaching. And, it is amazingly intellectual that the teacher actually combine all three learnings into his lecture. His teaching provides an inspirational perspective for teachers to think about how they intend for their own teachings.

Pesonal Reflection On The Interview

Through the interview with teachers and students, I found the results to be very helpful and inspirational. It helps me know more thoroughly how a teacher really is. The knowledge, other than what is being prepared right now, such as being confident, the ability to demand respect, and holding onto the principles and being flexible towards adjustment takes years of experience, with maybe some blunt mistakes, to come. Also, it was an excellent experience to obtain the understanding of a more professional perspective. There were so many brilliant ideas that young teachers can adopt to make their classes more fun and interesting. I also like Mr. Ahn and Dr. Yamamoto's comments on the challenges young teachers usually confront and how teachers can overcome the challenges to become better teachers. It cleared up several doubts and confusions I had. The answers from the students also rose up many interesting issues that not only young teacher, but I think, all teachers should participate to deliberate. As a math teacher, being able to understand what students think and help them with their difficulties is what makes student feel that their teachers care, and such feeling encourages and motivates students to participate more in the subject matter. One of my instructors once told me that the best method to understand students is to ask them directly. They can feel that they are also important. A successful communication between students and teachers makes a more successful teaching career.