SPECIAL COURSE ON DIDACTICAL MATHEMATICS
 
A Framework for Research and Curriculum Development in Post-Secondary Mathematics
July 30 - August 3, 1998
University of Joensuu
 

A Short Informal Evaluation of the Course

1. Some Background Facts
The evaluator is a person with a long-term professional experience of teaching. But this career concerns teaching a lot of religion (theology), psychology and education. As mathematician he is quite new with studies in some recent years at the University of Joensuu.

2. Language problems
A student of the course on didactical mathematics must think in four languages. The mother tongue of the student is Finnish, the course is in English, the mathematics is the language of numbers or logical concepts and the computer language is the fourth one.

It was easy to follow the speech of the teachers of the course. They could communicate at very high level with the participants. The mathematical topics were understandable. But naturally the topics were typical to elementary studies of mathematics. It was a little bit difficult to the evaluator to learn elementary programming skills on computer. The language of the machine should be more fluent within your memory. It was lucky that Mikko Vesisenaho, another member of our Atlanta group was a very skillful person on computer. However, the Atlanta group had repeatedly difficulties with the machine because the program could not run fluently. The evaluator was the stronger partner in pure mathematics. That is why the Atlanta group could use different skills of the group very effectively. It was a splendid idea to develop so called mixed workshop groups.

Remark. It is possible to learn something if you master three languages from four and you have in your group a specialist in every language you need.

3. New ideas to mathematics instruction
First time in five years the evaluator could hear something about developmental theories of such students who are studying mathematics. It was a pleasure and joy to participate in the course! The evaluator is an expert on the known and famous theory of Jean Piaget. But he has never seen this kind evolutional model of Piagetian theory concerning the human development in the area of mathematics.

The fact is that mathematics is the most difficult way of thinking in the Finnish school practice in high school. Now after the course it is somehow possible to begin analyzing where the difficulties hide. It is possible if you have a good theory about the theme How a human can learn mathematics? The APOS theory or the RUMEC project is a promising beginning.

It is also a wonder how little the Finnish university research focuses on the intellectual or motivational difficulties of the students. It is not enough to do only statistics if someone gives up his studies.

4. After the course
After the course the evaluator has read papers available on the course. To the honor of prof. Ed Dubinsky and dr. Asuman Oktaç should be mentioned that they didn’t mind teaching also such students who don’t know elementary issues. That is very good. Without the article of dr. Martti Pesonen and fine guidance of Martti Pesonen and Tanja Terho the short course could not have been so successful.