Profound Understandings
This week for math we read two chapters on a “Profound Understanding of Fundamental Mathematics” (or PUFM). These chapters compared Chinese and US teachers’ understandings of fundamental mathematics including subtraction with redistribution, multi-digit multiplication, division with fractions, and the relationship between area and perimeter. The author argued that Chinese teachers seemed much more likely to have a PUFM than US teachers, but only gained this PUFM after having taught for years. This PUFM, the author proposed, came from intense study of the teaching materials and the field of mathematics in addition to regular conversation with fellow teachers about different ways of problem solving. These Chinese teachers teach one subject (mathematics) for three to four 45 minute lessons a day and spend the rest of the time in one-on-one conferences with students and developing their understanding of mathematics with their peers. That is just not the reality in most schools in the US, where elementary school teachers tend to teach all the subjects and have little professional development time. Keeping this in mind, what lessons can be learned from doing reading of this kind, which compare two countries that have entirely different cultures and attitudes towards education? What do we gain from this?
posted by Elissa at 7:49 PM
8 Comments:
I believe that looking at other cultures can help us understand other methods in teaching our children. For example we man not be able to fully emulate a certain cultures way of teaching but we can take little snippets and use it in our classroom. I think that it is important to try to keep our minds open to new ideas as teachers. I notice from my co op teacher that she uses about six to seven mehtods to teach literacy to one grade!
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I accidentally deleted my comment. Here it is again:
I firmly believe that part of becoming an excellent teacher, and part of being an excellent teacher is in recognizing that improving oneself (as a teacher) is an ongoing process. And I think this also holds true for the entire education system itself. I think we need to always be open to new ideas and methodologies while keeping up-to-date with parallel and opposing views and methodologies. Even if we completely disagree, an intelligent educator will always (at least) be aware of other styles and methodologies of teaching. For this reason, I believe that reading about different cultures and attitudes challenges us to be more aware and open-minded leaders and educators. However, I also believe that we should be pro-active when reading about other cultures and attitudes. We should take our new understandings and use them to improve and to continuously challenge ourselves, and the community that we are a part of.
Thus, from this kind of reading, our gains are enormous. We gain power, understanding, motivation, ideas, and energy from these readings. These readings keep us aware and consequently keep us on our feet. Through these readings, we continuously challenge ourselves to improve and we challenge all those around us to improve. As a result, we become activists for our students, our schools and what the entire education system represents.
According to my prior experience of being educated in China for almost 12 years until I came to the U.S., most Chinese teachers and students do believe that intense exercises and only intense exercises can make one proficient and skillful in solving academic questions, especially in the area of science, and thus this requires a lot of repeated exercises of one single formula or that needs the same type problem-solving thinking pattern in order to make one highly familiar with them and even to the level of conditioned reflex.
Meanwhile, Chinese math teachers attach considerable importance to development of students' ability to come up with various approaches in addressing the same problem/question. When I was in senior high school, my math teacher required us at least to present 3 ways in solving every question she assigned.
Personally, in terms of the subject of mathematics, teachers should be more professional and focused on their self-improvment than teachers in other areas. The specific nature of this subject matter demands more depth instead of superficial breadth.
I personally think about it this way, try it and if it fails try to incorporate best ideas of both and make a new one. Is just the best and what is going to benefit the class the best, that's what we gain from this.
I am not an expert on Chinese culture and attitudes towards education, but I am impressed with the little that I do know. I wish I could say the same about American culture and attitudes toward education. I am saddened by the way we value education in this country. We are more impressed with the efforts of a star quarterback than we are with those of a mathematical genius.
In American culture we tend to see intelligence as a flaw. We also tend to view mathematics as something that only intelligent people (or “nerds”) would be interested in. I remember whenever I would tell someone what math class I was taking, their response would be, “You’re taking Calculus?” Then they would look at me as if I were crazy or had been stricken with some disease. As time passed, to avoid hostile confrontations I would often lie about the classes that I was taking. I have heard many great things about the abilities of not only Chinese but all the other Asian countries when it comes to academic success. I wonder how those societies treat the smart kids of the class?
I enjoyed reading the articles on PUFM because it gave me some ideas of how to better my own teaching skills. The results obtained in this study have led me to believe that Chinese people place a greater value on education than Americans. As a result of this, the Chinese students will have greater success in their academic careers. Hopefully, these types of readings will inspire us to improve our own levels of PUFM.
I think it's important for us to learn about education in other countries for the same reasons it's important for us to read literature from outside the US, or keep up with world history and international current events. It reminds us that we are not the center of the world and gives us new things to think about.
If we only discussed education as it stands in the US we would probably go around in circles arguing about NCLB, school funding, and the same old topics that are on everybody's mind. When we step outside of our context, we get a fresh perspective on old things. We open our minds to consider other issues that might go otherwise unnoticed and forces us to recognize the possibility that there is something else out there that works. It gives us new ideas to chew on, and who's to say that we can't incorporate some of them, in some form or fashion, into what we do as educators?
At the same time it might also provide counterexamples of good education, making us even more aware of what does and doesn't work in our system. And that's valuable because I think that when you are able to look at other systems and make a critical evaluation of whether or not it would be applicable to your school/classroom/etc, you're showing a deep understanding of the exact nature of where you're coming from. If you know that something wouldn't possibly work in your school, it's hopefully because you understand just what makes your school tick and why certain strategies would or would not be productive.
Also, on a more humanistic level, learning about other cultures--besides being important for tolerance and cultural sensitivity and all that PC stuff-- always gives us a better understanding of our own culture. We define who we are partly by defining who we are not. So it's probably a good thing to see that being a student means different things across cultures in order for us to understand what it means to the students in our classrooms.
As much as it is beneficial to look at other cultures as models of instruction and education systems, we also have to be careful of what we take from them. A system that works in place A will not necessarily work in place B. There are multiple factors that affect whether one strategy/method/approach works or doesn't work, varying from student population, culture, attitudes, etc.
When we read and learn from other places, we can't just take everything word by word and try to implement it in our own classrooms. We have to be active learners, questioning what would or wouldn't work, why, and what changes could be made, adapting them to our own settings.
Talking specifically about Math, there's a great book called The Teaching Gap, by James W. Stigler and James Hiebert that compares Math classes in Japan, the US and Germany. It's interesting to see how they have very different approaches and how each works well according to the culture of the schools. Another good book that compares teaching across cultures is Preschool in Three Cultures: Japan, China and the United States by Joseph J. Tobin, David Y.H. Wu, and Dana H. Davidson. It focuses on Early Childhood classes, but it provides very good examples of different methodologies in each country.
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