Prepared by Malgorzata Dubiel
Department of Mathematics and Statistics, Simon Fraser University
The first "Changing the Culture: Towards a Closer Mathematical Community" conference, organized by the Pacific Institute for the Mathematical Sciences, was held at Simon Fraser University at Harbour Centre in Vancouver, February 20th and 21st, 1998. Following the path started in December 1995 by the BC Miniforum on Education in Mathematics, 99 mathematicians and mathematics educators from schools, universities and colleges from B.C. and Alberta meet for two days to attend lectures, panel talks, and discussion groups, aimed at changing the culture of school mathematics in order to allow students to experience what "doing" mathematics means.
The opening talk, Post-impressionism and Math Education, was given by Peter Taylor, Queens University. In a memorable lecture, Peter linked the crisis faced by mathematics education today to the one faced by painting 100 years ago. Showing coloured slides of famous paintings, he discussed the struggles of Cezanne, Van Gogh, Gauguin, Matisse and Picasso, living to the audience to discover how the lesson learned from them can be applied to teaching mathematics. Not being afraid of new, innovative ideas and trying to look for beautiful, rich concepts in mathematics and discussing them with students like one would a beautiful painting are some of many inspiring ideas one could take away from this talk.
Peter Taylor's draft grade 12 calculus text book which exemplifies these ideas was available at the conference.
The afternoon of the first day featured the first panel discussion: "What is happening in the math classroom?", chaired by Susan Pirie, Education, UBC. Malcolm Sneddon, Ministry of Education, Skills and Training, described the new Applied Mathematics curriculum being introduced in BC. Tom O'Shea, Education Faculty, SFU, talked about the results of the Third International Mathematics Survey, and what can they tell us about the mathematics classroom today. David Ryeburn, Mathematics and Statistics, SFU, talked about high school students performance in calculus courses at SFU.
The day concluded with the second plenary address of the conference: The Olympiad Spirit --- Encouraging students in Mathematics through Competitions, given by Bruce Shawyer, Memorial University of Newfoundland. Bruce described how the format of mathematics olympiads and structure of the reward system embodies the olympiad spirit, and how this spirit can also be found in other mathematics competitions for high school students in Newfoundland. He followed with suggestions on how to capitalize on the olympiad framework and the relative advantages and disadvantages of single student competitions and cooperative team competitions. He shared with the audience some good competition problems, and, by involving participants in a competition-like situation, demonstrated that humans are competitive animals.
The second day started with the panel discussion: "DOING mathematics with students", chaired by Malgorzata Dubiel, Mathematics and Statistics, SFU. George Bluman, Mathematics, UBC, reported on the work done at UBC, in cooperation with SFU and UVic, on developing a calculus challenge exam for high school students. He also talked about the UBC Mathematics Department's extensive Euclid workshop program in BC schools which in 1996/97 involved about 15 faculty and 40 undergrads giving 68 workshops throughout the province, and a new 4th year course titled "Mathematics Demonstration", which arose from this experience. Nathalie Sinclair, Simon Fraser University and Island Pacific School, described how she uses Java applets in exploring mathematics with her students. Pamela Hagen, Westwood Elementary, reported on "Math Unplugged" - a whole day mathematics conference she organized at her school.
The presentations were followed by extensive discussion period.
An integral part of the conference were Small Group discussions. Conference participants were assigned to one of the four discussion groups for the duration of the conference. During two discussion periods in the first day and one more the second day, the groups talked about changing the culture: in how we teach, what we teach, what we ought to teach, who we are, what we should keep of the "old" ways and what we should discard. How to come to terms with mathematics today - what it is, what is needed, how much one can ever really know.
The group leaders reported on their discussions to the entire conference during the wrap-up on Saturday.
Below are reports from three of the groups:
Group 1 (red): Leaders: Katherine Heinrich and Leo Boissy
Report submitted by Katherine Heinrich
This was an excellent group with broad representation (elementary and secondary schools, government, college and university) - all who identified themselves as mathematicians. So we had a lot in common.
Although there were themes for each of the three times the working group met our discussion did not always comply precisely with the topic. The best way to present the report is therefore divided into the several topics that we moved back and forth between during the two days.
The task of "change" is immense and the fear of not knowing how to go about it can immobilize us. In teaching, most of us are stuck in a "broadcast" metaphor; we don't know how to change it and fear the risk involved. But, as one participant said, "we only do what we can do".
Our view of the traditional in the classroom includes: method of delivery - lectures, content (or by this do we mean studying topics in isolation), assigning questions from the text, students sitting in straight rows and not talking.
We are recognising that students have changed and we need to adjust to their needs and constraints and focus on their learning - not issues like attendance. They worry about getting a job, some work to support their families, others live alienated from their families - even school students. What do we want of them? What is their role in what is being taught in the classroom? Not all in high school will go on to university and we should not lament that. But the "system" wants all students to be at the same place at the same time - they aren't and we lose students. Do we see a lack of persistence in students or is it that we do not have time to let them discover for themselves? Is their attitude different from what ours was? Did we really work harder?
In teaching we are searching for a more hands-on lab approach with lots of investigation; technology is forcing us to change and allowing for deeper exploration and new ways of "seeing" what we teach and learn - it is having an impact on the curriculum; there is a focus on more "applications" of what we teach (although a better term might be "relevance" - to the subject matter and to the students' learning); we think more of the human nature of mathematics (inspiration, beauty); we recognise cultural differences in learning and approach to mathematics; there is a search for motivation and making connections between the various parts of mathematics and other disciplines.
One of our challenges today is to start talking about what is really important rather than complaining about not having enough time to cover the curriculum and always asking "what do we cut?" It's time to start thinking about "letting go" of the curriculum instead of "trimming" it. If we want to decide what is important we should try answering the following questions:
* For whom should we be teaching what and what should be in their tool kit?
* If we had only 20% of the time we now have for mathematics, what would we teach?
We should be teaching students to ask questions and come to really understand the problems, to appreciate the "art" of mathematics and what it means to prove something. Have we allowed imagination and creativity to disappear? Has the feeling for math gone from what we teach? Why aren't we like other disciplines which have a core and then lots of leeway for exploration? But teachers need a good math background and a deep commitment to mathematics to make this journey and many have not had the opportunities to achieve this.
What happens next:
There is a lot of support available for teachers and students both inside and outside the classroom. Examples include: BCAMT (through technology support, conferences and Vector), Let's Talk Science (grad science students adopt science classrooms - or are adopted by them), Scientists in the Schools (a scientist visits a classroom), Yes Camps (summer science camps for kids available at UBC, SFU and UVic), Science World, UBC Euclid Workshops (teams from the university visit classrooms), SFU Evenings of Math and Science (mini-conferences on campus in the evening), courses available at the universities, ministry workshops and conferences. But, are they enough and are they what is really needed? How do we best support the elementary teacher; the non-math math teacher? How do we provide the support of a long-term relationship actually in the classroom? How is long-term change best effected? We want to build a culture where teachers are encouraged and supported to become constructive learners but to do this they need both opportunities and time. We need to interact more and find more opportunities for sharing - what worked and what didn't.
One hope lies in the collaboration we are seeing between different interest groups in mathematics; we are considering the value we each bring to the table; the shared commitment we hold. Dialogue is improving between the teachers and the ministry; more teachers are getting involved; an excitement is building; changes are quietly happening. There is optimism and there is strength in working together.
Group 2 (blue): Leaders: Pamela Hagen and Susan Milner
Report submitted by Pamela Hagen
The blue group had an excellent mix of participants from all levels of mathematics education and interest. The diversity of the group provided a good basis for discussionand as can be seen from the questions and comments from the two sessions.
Questions discussed on Friday:
1. What was the connection between the speakers on Friday pm and THEIR classroom?
2. What would we like to change? (There seemed to be agreement that teachers would like to make math more relevant. Driven by real problems.)
3. How to get more colleagues involved?
4. How to get change at highest level?
5. Things should not be driven by use of timetabling.
1. There are common constraints of time vs. curriculum demands.
2. Resources of graphing calculators and computers generated quite a bit of discussion.
3. Architecture and design of classroom space, was this an optimum environment for learning?
4. Personal time constraints, on top of classroom and marking, extra curricular school activities etc. What are the priorities for each education sector?
5. Definite agreement that math should be taught by specialists at the secondary level and that there should be professional course work in math education/education math for all teachers. (This should be mandated by BC College of Teachers.)
6. Would like to increase discussions/contacts between all levels of math education (meetings/competitions etc).
7. Sharing of resources at same level as well.
8. Expand mathematics monthly newsletter (look for funding elsewhere)
9. More use of Internet for all teachers.
10. Would like continuity at provincial political level.
11. Need stability at local level to start to effect change.
1. Why the selection of people for speakers? (responded that they were all part of the math community.)
1. Suprising commonalities.
2. Means of assessment were discussed. Exams were felt the only way to go because of the practical difficulties of time restraints, teaching and marking.
3. Need to interpret exams results carefully.
4. There was an agreed need for greater communication between all sectors of math community.
5. That this was a worthwhile gathering and was perhaps different/unique in that all sectors of math education community had been brought together for perhaps first time. Therefore as it looked like it was going to be an ongoing thing, this was considered good.
6. There was an identified need for two-way communication.
7. Again comments about requirement for math education training/coursework.
8. There was an emphasis on test material requirements, because that was means of assessment/judgement for further on.
In summary, the participants had concensus that there was a definite desire and need for greater communication between all sectors of the mathematics community and that this should be a two way communication between all levels. A point of definite agreement was that math should be taught by specialists at the secondary level and that there should be professional course work in math education/education math for all teachers. (This should be mandated by BC College of Teachers, and emphasised by universities in their education programmes.)
In addition it was agreed that this was a worthwhile gathering and was perhaps different and unique in that all sectors of math education community had been brought together for perhaps first time. As it was believed that this first conference was going to be an annual occurence the coming together of this diversity of members of the mathematics community was considered a valuable part fo mathematics discussion.
Group 3 (green): Andrew Adler and Christine Stewart
Group 4 (yellow): Leaders: Dave Lidstone and Susan Gerofsky
Report submitted by Dave Lidstone
Our discussion on the first day of the conference returned again and again to paired ideas in math education which appeared to be polar opposites. Repeatedly, we found ourselves asking whether it was necessary to see these terms as dichotomous -- whether these apparent "opposites" were really in opposition to one other.
Some of the paired ideas that arose in our discussion were:
* hard or rigorous math versus creative math
* involving students versus entertaining students
* a curriculum centred on mathematical skills versus one centred on mathematical problems
* students actively doing math versus passively receiving math
* math as skill versus math as art
After initially setting up these oppositions, the group found many ways in which the terms overlapped, where one term at least partially contained its supposed opposite.
A number of issues arose which were specifically focussed on teachers' own attitudes towards mathematics. Some were concerned that math-phobic elementary teachers might encourage enduring negative attitudes towards math in their students. It was suggested that good math teachers were those who continued to learn new mathematics themselves, and saw themselves as ongoing learners. Those who championed the idea of mathematics as a creative art suggested that creative math teaching involved taking risks and trying new things that neither teacher nor students had ever done before. On the other hand, a group member who agued for math as a set of skills said, "Math is a game. If you learn the rules, anybody can play."
The group did agree that a teacher could be a powerful role model in encouraging students to experience "being a mathematician". Another quote from the group's discussion: "Before kids can do math and take risks, they have to see the teacher doing math and enjoying math."
Our Saturday discussion focussed around the issue of how we saw the new culture. We acknowledged that the most easily identified aspect of a new culture was the rise of electronic computational technology. We addressed issues such as financial constraints, attention diverted from mathematical issues to mastering use of the tool, and how content and expectations might change. However, we found little consensus on any of these matters especially the latter.
We did, however, find consensus with the suggestion that any new expectation will not be affected with a top-down model. The tools for change will be the practitioners in classrooms. This is where resources should be directed in order to help promote expertise that can better manage changing expectations. One suggestion was to establish district mathematics committees to promote improved articulation and communication between the elementary and secondary systems.