The instructor of the course was professor Ed
Dubinsky from Georgia State University, Atlanta, USA. His framework
of combining research and teaching had interested many of the participants
in advance, and he could be hired rather inexpensively since he was on
his way to Umeå, Sweden, to a Workshop on Research of Mathematics
Education (Taina Malvela, Martti Pesonen and Sisko Repo accompanied him
and participated the Workshop).
"I learned that ISETL is an effective tool in learning mathematics and it is usable in high school as well. I know that students learn mathematics better when they have to work with the problems and it makes learning much more fun too! It is significant that a teacher is familiar with the computer program which he is using in his teaching, otherwise nothing is going to work!"
"It was interesting first get to know about the theory and the paradigm on which the teaching was based later. One good point which I still remember was that we should make students be interested in mathematics itself with new methods and not offer a substitute which might be easier to understand and maybe at first more interesting."
"The idea of learning mostly in groups was definitely a new one to me, at least in mathematics. But it didn't sound too far out, in fact, it made sense in many ways. Thinking about the way mathematics is being taught in my university (it's a pity I do not have any knowledge of other universities), and the way that I think that the usual mathematics students are, that means quiet and not very social, I truly believe that this would make learning much easier in many ways."
"The purpose of this course is to provide a background for using innovative pedagogical strategies in the context of a theoretical framework for research in learning and teaching that is applied to curriculum development.
The first day of the course will be devoted to discussion of a paradigm for doing research and curriculum development which consists of theoretical analysis, design and implement of instructional treatments based on that analysis and the collection and analysis of data. The APOS theory will be discussed in detail and applications to particular topics in post-secondary mathematics will be described. Specific pedagogical strategies to be considered include active learning, cooperative learning, and the use of computers. The day will end with an overview of three courses: abstract algebra, calculus, and discrete mathematics, in which these ideas have been applied to a greater or lesser extent.
The second day will take place mainly in a computer laboratory and will model portions of a course in abstract algebra. The participants will be assigned to cooperative groups and they will work in these groups on computer tasks similar to the ones assigned to students when this course is taught. As the participants work through these tasks, formal and informal discussions will take place to reflect on the activities and their affect on student learning.
The third day of the course will be similar to the second day, but for a course in calculus.
The fourth day of the course will be devoted to reflections on the experiences of the previous three days and a discussion of ongoing research activities related to these ideas.
During the evenings, informal discussions will take place among those participants who will be mentoring other participants in projects based on this course."
The student evaluations (link to the reports) were largely positive, only one student did disagree to a large extent. The overall research and development framework, the APOS-step-interpretation of learning mathematical concepts as a relevant model of "measuring" the depth of understanding, and the cooperative learning were well understood and accepted (student Report 1 can serve as an overview of the framework).
The main reason for complaints was the grass-root-level approach to
computer actitivies which took almost half of the time. Especially some
undergraduates
had much difficulties with the programming and even with the mathematics!
However, the activities were arranged intentionally so, because
the computer activities are an essential component of the teaching method
and one cannot come to understand and appreciate this within a short space
of time.
On the whole, the course was a success. In fact, there were so many participants that the computer activities could not have been properly carried out in our small computer labs, but the new "portable" lap-top lab worked fine and provided a comfortable environment for working.
It is likely that the course has had a very positive and encouraging
effect on the pedagogical atmosphere and dawning educational research activities
in the faculty.
We are now using Ed Dubinsky's methods and ideas in the currently ongoing
Algebra course. See the Algebra
course's homepage for more details (in Finnish).