Report of  the
SPECIAL COURSE ON DIDACTICAL MATHEMATICS (180702):
A Framework for Research and Curriculum Development
in Post-Secondary Mathematics
Joensuu, Finland, July 30 - August 3, 1998, Ed Dubinsky

Introducing professor Dubinsky (the instructor)
Course Program
Results (in Credits) (in Finnish)
Expenses (in Finnish)
Student Reports
Ed Dubinsky's reaction (with greetings)
Algebra course's homepage (in Finnish)
Excerpts of Discussions about the contents of the course
Photo Album


The Department of Mathematics of the University of Joensuu organized an intensive four-day course under the title above. The course was supported by the Faculty of Sciences as a pedagogical training course on Discipline-specified Didactics in Higher Education for young faculty members and graduate students of Mathematics or Mathematics Education. There were also 11 undergraduates on the course who already had made their subject teachers pedagogical studies.
The course gave students 1 Finnish study week (1.5 european credits) if they participated in the workshops and lectures of the course and submitted an informal written report afterwards. Some made extra work afterwards which gave them extra credits.

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).



How did students feel about the course? Here are some quotations from students' reports:
"After all e.g. the ACE-cycle corresponds closely to my personal ideal about teaching mathematics although I haven't regarded the use of computers that important. To be honest, I haven't regarded the use of computers important at all. However, after some experience of my own on ISETL my attitude to computers is more positive. I also felt that the use of computers can be useful just for practical reasons; the group has something concrete (typing code) to start with and the atmosphere in the group (as well as in the whole class) gets easily relaxed and active. However, I'm not sure if this activity necessarily implies some deeper thinking; here the choice of activities plays an important role."

"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."



Ed Dubinsky's own description about the course :
"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 course included also a one-hour presentation by an established researcher Asuman Oktac from Mexico. She talked about her experiences in distance teaching and learning of linear algebra. She also acted, together with Dubinsky, Tanja Eskelinen and Heikki Apiola, as an assistant during computer activities. Other individuals who helped considerably with the practical arrangements were Liisa Kinnunen, Taina Malvela, Sisko Repo and Pekka Smolander.

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).



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