Friday, October 16, 2009
Micro Teaching Reflection
The preparation for this assignment was somewhat rushed. The bridging activity was pretty good because it connected seamlessly with the weekend that just passed and the students were able to identify with the story. The lack of rehearsal was evident in the presentation was the group argued a bit with each other during transitions and other parts of the presentation. The classroom set up wasn't as optimized since some people couldn't see parts of the board while the proof was being presented. The review exercise was too 'academic' to really be a fun game and the class wasn't as engaged as we thought. But overall the presentation was still good as most of the mathematical ideas were presented in a transparent fashion that we thought was easy to understand.
Sunday, October 4, 2009
10 Questions to the Authors of 'The Art of Problem Posing'
1. Is it appropriate to abstract the statement of a problem or deliberately leave it in some 'simple' form? (For example, "show that it is impossible to write 2009 as the sum of two even numbers" versus "prove that an odd number cannot be expressed as the sum of two even numbers")
2. What do you think of "prove or disprove" type questions?
3. How does one first introduce problems that do not involve numerical answers? (For example, proving that a power series converges uniformly within its radius of convergence)
4. Should problem solving be taught as a technique or as a vehicle to reach other results/techniques?
5. What expectation should one hold regarding how many students are able to solve a given problem?
6. Is it wise to pose problems that go beyond the immediate boundaries of 'what has already been taught' to stimulate interest and to pique desire to explore?
7. How should one interpret the term 'elementary mathematics' when it comes to posing problems to secondary students?
8. Is there any difference in creating a problem designed for math competitions versus for daily use in a classroom?
9. How do we pose problems in such a way so that students do not become 'dependent' on context and heuristics?
10. How do you design a question to urge students to ask 'why'?
2. What do you think of "prove or disprove" type questions?
3. How does one first introduce problems that do not involve numerical answers? (For example, proving that a power series converges uniformly within its radius of convergence)
4. Should problem solving be taught as a technique or as a vehicle to reach other results/techniques?
5. What expectation should one hold regarding how many students are able to solve a given problem?
6. Is it wise to pose problems that go beyond the immediate boundaries of 'what has already been taught' to stimulate interest and to pique desire to explore?
7. How should one interpret the term 'elementary mathematics' when it comes to posing problems to secondary students?
8. Is there any difference in creating a problem designed for math competitions versus for daily use in a classroom?
9. How do we pose problems in such a way so that students do not become 'dependent' on context and heuristics?
10. How do you design a question to urge students to ask 'why'?
Friday, October 2, 2009
Future Students View Points
Grigori Tao
Among the numerous people who have contributed to my success at the International Mathematical Olympiad the first I wish to recognize is Mr. Stanley Xiao, my math teacher from grade 10 to 12.
Mr. Xiao was a very unique mathematics teacher. First, unlike the majority of teachers out there Mr. Xiao is a bonafide ace mathematician whose knowledge and skill level parallels many professional mathematicians. The fact that he chose to be a math teacher attests to his passion and desire to be here. He is a teacher because he wants to be, not because he has to be. In turn his passion for mathematics and his emphasis on excellence affected all in his class. Second, he is the most passionate fan of mathematics competitions. Frequently in class he would talk about various national and international level math competitions, anecdotes about past contestants, how to get there, and how he is willing to train any and all wishing to go down that path. He treats math competitions as seriously as most people do professional sports and that made the mathletes feel very good about themselves. Finally, he constantly challenged the class with difficult problem sets that were for grades that constantly motivated us to think and act like mathematicians. Without him, I would not have had the skill, inspiration, and motivation needed to do well enough on the Canadian Open Math Challenge and subsequently the Canadian Mathematical Olympiad and the USA Mathematical Olympiad to qualify for the International Mathematical Olympiad, much less returning home as a gold medalist.
Indeed, my experiences are not unique. In his 10 years of teaching 4 students that he has taught has returned home as IMO gold medalists, more than the combined total from BC from 1980 (Canada's first year at the IMO) to 2010. I have recommended that Mr. Xiao be part of the IMO training staff in the future to continue his excellent work.
For his inspiration and countless hours of helping us learn to problem solve and challenging us to be the best we can be, I thank him with the utmost sincerity.
Nora Lau
In retrospect of my high school education, it is reminescent of the worst kind of mentality of most major universities: that is, the idea that all chemistry/physics/English/biology/geography/history/...etc. students are to be trained in such a way that they ought to be future researchers in the subject area. The one teacher I had that most underline this mentality is one Mr. Stanley Xiao. In many ways, Mr. Xiao is perhaps objectively an excellent teacher. Indeed, under his tutelage four people (Grigori Tao, Ronald Barton, Jonathan Reid, Bruno Zhai) have went to the International Mathematical Olympiad and returned as medalists. Many more scored extraordinarily high on national and international level math competitions. However, despite his glorious record, his teaching style has isolated at least as many people, including myself. I have never proclaimed to be very strong at math, nor am I very interested in having much to do with mathematics past the immediate need of my field of study (commerce). Mr. Xiao didn't believe in accommodating people of my desires and continuously bombarded us with difficult assignments and tests, forcing us to spend an exorbitant amount of time on our math courses. In the end, much of what we learned was unnecessary. This of course was not restricted to just Mr. Xiao but presents a pandemic among all of academia.
Among the numerous people who have contributed to my success at the International Mathematical Olympiad the first I wish to recognize is Mr. Stanley Xiao, my math teacher from grade 10 to 12.
Mr. Xiao was a very unique mathematics teacher. First, unlike the majority of teachers out there Mr. Xiao is a bonafide ace mathematician whose knowledge and skill level parallels many professional mathematicians. The fact that he chose to be a math teacher attests to his passion and desire to be here. He is a teacher because he wants to be, not because he has to be. In turn his passion for mathematics and his emphasis on excellence affected all in his class. Second, he is the most passionate fan of mathematics competitions. Frequently in class he would talk about various national and international level math competitions, anecdotes about past contestants, how to get there, and how he is willing to train any and all wishing to go down that path. He treats math competitions as seriously as most people do professional sports and that made the mathletes feel very good about themselves. Finally, he constantly challenged the class with difficult problem sets that were for grades that constantly motivated us to think and act like mathematicians. Without him, I would not have had the skill, inspiration, and motivation needed to do well enough on the Canadian Open Math Challenge and subsequently the Canadian Mathematical Olympiad and the USA Mathematical Olympiad to qualify for the International Mathematical Olympiad, much less returning home as a gold medalist.
Indeed, my experiences are not unique. In his 10 years of teaching 4 students that he has taught has returned home as IMO gold medalists, more than the combined total from BC from 1980 (Canada's first year at the IMO) to 2010. I have recommended that Mr. Xiao be part of the IMO training staff in the future to continue his excellent work.
For his inspiration and countless hours of helping us learn to problem solve and challenging us to be the best we can be, I thank him with the utmost sincerity.
Nora Lau
In retrospect of my high school education, it is reminescent of the worst kind of mentality of most major universities: that is, the idea that all chemistry/physics/English/biology/geography/history/...etc. students are to be trained in such a way that they ought to be future researchers in the subject area. The one teacher I had that most underline this mentality is one Mr. Stanley Xiao. In many ways, Mr. Xiao is perhaps objectively an excellent teacher. Indeed, under his tutelage four people (Grigori Tao, Ronald Barton, Jonathan Reid, Bruno Zhai) have went to the International Mathematical Olympiad and returned as medalists. Many more scored extraordinarily high on national and international level math competitions. However, despite his glorious record, his teaching style has isolated at least as many people, including myself. I have never proclaimed to be very strong at math, nor am I very interested in having much to do with mathematics past the immediate need of my field of study (commerce). Mr. Xiao didn't believe in accommodating people of my desires and continuously bombarded us with difficult assignments and tests, forcing us to spend an exorbitant amount of time on our math courses. In the end, much of what we learned was unnecessary. This of course was not restricted to just Mr. Xiao but presents a pandemic among all of academia.
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