Hello. My talk has the title:
The Affects of Culture on Mathematics--Is there really a difference between the mathematics in the US and the one here in Germany?
I would like to break this talk into four sections:
· the first one is a little bit of my background
· my experience teaching and learning in American and German schools
· my experience teaching and learning in American and German universities
· the results of these differences.
Please feel free to stop me at anytime during my presentation to ask questions or if you do not understand something.
My name is Georgine Alicia Kalil and I am American. I have been living in Germany since 1999 and have been in Berlin since 2005. I studied mathematics in the US in a small liberal arts school in Upstate New York. Even though I was one of about 25 women who were studying this subject (out of about 50), I found it very hard to fit into this world. I often found that I was speaking another language and had to fight with all of my might to be able to understand the mathematical language, a language that I so wanted to speak and express myself in. After graduating I gave up the hope of doing my doctorate in this subject and became a teacher instead, so I would be able to encourage other girls and young women to continue on in this subject.
I left the United States directly after my studies and began to teach English as a Foreign Language, which enabled me to move around and experience living and working in other cultures. Since about 2002 I have been doing research in the area of mathematics and gender.
My project focuses on the difference which culture plays on the concept of what mathematics is, how it is thought of in society and how it is presented in the media and in learning environments. Different cultures and different times produce different mathematics. As we already know, mainly white males created the mathematics, which we know today, and study today, about 100 years ago. This mathematics was suitable for the time and culture, in which it was created, but is not suitable for our society right now.
My project focuses on the mathematics of two countries, the United States and Germany, the two countries that have influenced my life the most thus far. Even though these two countries are fairly similar to each other, I would like to prove that the mathematics are different. I draw a lot from my personal experiences in each of these countries. I have taught mathematics in both countries and have also studied mathematics in both countries at the university level (even though my study experience in Germany is quite limited).
I am going to be doing this research by interviewing mathematicians in both of these countries. They should be finished with at least their Masters and could possibly be a professor or working at a higher level in mathematics. I would like to find out what they think mathematics is and how they think they were able to get so far in this subject, that seems not to attract many people, be it woman or man.
In this talk today, I would like to discuss the differences that I have experienced in the world of mathematics in both of these countries. I would like to emphasize out that these ideas are something, which I have personally experienced and have not been proven scientifically. So the viewpoint is mine, a woman with Lebanese and Italian forefathers, born in 1972 into a large family in rural Upstate New York.
I have taught mathematics in both of these countries. In the US I did my student teaching in the 7 th and 8 th grades in an open school in Cambridge, MA. I also taught remedial mathematics in a community college in Baltimore. In Bonn and Cologne I taught mathematics in a Gymnasium and in a Realschule. In both of these schools, I taught again in the 7 th and 8 th grades.
In the States I tried to encourage all of my students to think independently and to seek out the method of solving that best suits their personal needs. Especially in the Open School, I treated my students as mathematicians who were able to explore and discover something new. They in turn thought of themselves as mathematicians able to make a change and able to possibly find and create something new. These feelings had been fostered in this school since its beginning. This to experience in a classroom is a wonderful thing. We worked hardly from the book and mainly from hand on experiences. I built a house with them from the ground up. The students evaluated themselves and this grade effected their final grade. Portfolios were used and worth more than tests that were written in class. The main emphasis was placed on learning the mathematics and being or becoming active learners and proceeding in this field in high school rather than on passing tests and state exams.
In my small experience in German classrooms, I haven’t experienced this feeling yet. It could be because I taught in two “normal” high schools here and in the US I had the opportunity to be a part of a teaching team in an Open School. When I asked my pupils in Bonn if they were mathematicians, they laughed and said that they hadn’t studied. They only wanted the right way to solve a problem and didn’t want to explore and answer the questions themselves. They wanted me to teach by standing at the front of the class and lecturing. They were very uncomfortable with my teaching approach, which consisted of exploring and looking for the answers, small group activities, questions, etc. and often expressed that I wasn’t teaching and didn’t have the control of the classroom situation. It does take awhile to get used to a different teaching style and method but I think this is a shame.
In the Realschule where I taught, colleagues told me to tell them exactly how to do problems and that the pupils wouldn’t be able to handle any other way. Partly these colleagues were correct. The students were not able to deal with open questions and my method of teaching. This is something that they need time to adapt to and understand. It would have taken awhile but I do think they were capable of this transition.
From my experience in schools here in Germany, I would say that they are not encouraged to think for themselves and to discover the methods that are best for themselves. Different learning styles are not supported, used or integrated. I got the impression that differences in general, be it in culture, gender, sexuality, and etc. are not actively accepted and celebrated. There is one way and that is the only correct way. All of the other ways are incorrect.
I went to a small private, liberal arts school in Upstate New York. It is located in a very small town in the middle of nowhere. I lived on campus and thus had the full campus experience. My classes were quite small and I had a lot of contact with my professors. They often had office hours and I was the type of student who made use of all of them. I was often invited to their homes for a meal or a discussion. Like I said, I studied mathematics but along with this subject I had to study many other disciplines. I chose religion, dance, music, philosophy, etc. I majored in mathematics and minored in sociology.
My mathematics courses were never over 20 people. After my second year at university, the classes were usually 6-12 people. This means we always had the chance and opportunity to ask questions and have them answered thoroughly and individually. My education and I were taken seriously. I was encouraged to express my opinion, my problems and my questions.
When I was at Hamilton, from 1990-1994, there were two female mathematics professors. Without these two role models, I would not have ended up studying mathematics and finishing it. From my class, about 50 people majored in this subject and about half were females. Why do you think this was?
From my experience here at the university level in mathematics, the classes are very full and students do not have the chance to ask questions or express worries. They are not encouraged to think for themselves but to satisfy the professor and pass the exam. Contact with the professors is very limited. Especially in mathematics, the professors are almost seen as gods, untouchable and immortal. People that the students will never be like. There is very little discussion in the classroom. The professor usually lectures and the students hurriedly write down everything that they can. Or the students do not attend the lectures because it is easier and takes less time to copy the lecture notes from the friend who attended the lecture. So this creates an isolating atmosphere for both the professor and the student. I can imagine that the professor gets frustrated because he or she wonders why the students never understand the material and the students get frustrated because they wonder why the professors cannot explain the material in an understandable way. There thus exists a big wall of knowledge and status between the student and the professor. Of course this exists in many other subjects. I just think that the nature of mathematics causes this difference to be bigger. All in all, a very frustrating and dissatisfying situation, wouldn’t you agree?
I get the feeling that the professor research is much more important than the teaching is and that there is actually no teaching here but passing on of information and facts.
All in all the age , the experience, the knowledge and the mathematical differences are much more prominent in the German university system than the American university system which I was a part of. I feel also that differences among students and pupils are more celebrated and accepted in the US than in Germany.
I think that I should at least mention the status that mathematics has in most universities and schools in both countries and cultures. Mathematics is a discipline or subject that seems to have a very special status in our societies and in our educational systems. Not everyone can get to the position of achievement in this very mystifying realm of numbers and dimensions. Only the few gifted and hardworking are able to succeed and proceed in this area. It is like they acquire access to a language that only few are privileged enough to acquire. Mathematics is so that not every one is allowed entry into its gates. This subject is then so thought upon as so concrete that people never question the reliability or functionality of this field, a field that is thought of as rigid and systematic and a part of our world like you and I. This mathematical truth is taken and looked upon as a given, a position that hasn’t been rightfully earned, that has been created maybe to raise the status of this subject and discipline. This feeling actually then isolates itself and the few people who do work in this field.
What I described before was what I have experienced in both of these countries. I do believe though, that because of the school systems, teacher trainer programmes, university systems that are available in the two countries being presented, that the learning and teaching experiences that I had in the US are more likely to happen there and tend to encourage question solving, inquiry, opinion forming, etc., which are all key and vital in doing or creating mathematics. These skills, once acquired, foster the further studying of mathematics or the further working in this area of study for all people, regardless of sex, gender, sexuality, ethnicity, religion, political background, etc. These skills give more people the possibility to choose mathematics and go deeper in this subject area. Because these skills are easier to learn and obtain in the US, it is easier or more common for people to go on in this subject area. This is something that mathematics, be it the subject, discipline or field should or must aim for.
Thank you very much.