Date: Thu, 4 Jun 1998 07:55:37 -0400
From: edd@zeus.cs.gsu.edu (Dr. Ed Dubinsky)
To: "Martti E. Pesonen" <Martti.Pesonen@Joensuu.Fi>
Subject: About the themes of July - Aug. course

Martti,
I have some questions about the course.

1. As I read over our previous correspondence, there seem to be two themes involved. One is new pedagogical approaches for learning and teaching post-secondary mathematics. The second is research in learning and teaching post-secondary mathematics. The first would involve using computers, cooperative learning, and active learning. It could lead to the participants choosing one or more aspects to use in their teaching as a project for the follow-up course. The second would involve the APOS theory with specific examples of past, present and future studies of learning functions, mathematical induction, certain concepts in calculus and in abstract algebra. This could lead to the particpants choosing one or more research projects for the follow-up course. Of course, the two themes are related by our overall framework for research and curriculum development in post-secondary mathematics. My question is: Which of these two themes should I emphasize, or should the course try to strike a balance between the two?

2. Will there be a computer lab to use in the course? If so, can you describe the facility, its availability and if I can have an assistant that is knowledgeable on their use. Also, do you have ISETL on the computers? How about MAPLE? If the answer is yes, will the participants be familiar with these two software systems? If not, could they work on that before hand?

An old PC-Pentium computer lab with ISETLW and MAple V release 5 is available, nine PC:s only. We expect some 20-25 participants. Is this too many people?

3. Earlier, you mentioned something about advance readings. I think this is a good idea, but I need to give it some serious thought, especially after we have decided the answers to 1 and 2. Also, you would need some time to get the books or papers. One possibility would be for me to list the items and then send you a package with > one copy of everything you don't have.
What should be our timing on this? Would it be too late for me to decide on the readings by June 30 and then start the process of getting the material to you, which might take 7-10 days?

I propose that we use the material I and Tanja have written in Finnish about the Framework. I wrote (as a project work) about the APOS and such, Tanja wrote more precisely about the cooperative learning. We could complement these with suitable in English written texts (e.g. APOS Glossary?), if you tell what topics should be included. The reading list is a nice thing to have, for further studies after the course, but for the people just starting these things and unfamiliar with pedagogical language, I fear it would make them turn away. I have seen the RUMEC-reading list, and we shall start collecting the missing material. Maybe we ask you to help in that, since we do not have so wide literature in Math Education.

Depending on your response to 1, here are some possible titles for the course.
A. The Use of New Pedagogies for Learning Post Secondary Mathematics: Computers, Cooperative Learning, and Active Learning.
B. Research in Learning Post Secondary Mathematics: Past, Present, and Future Studies, with Applications to College Teaching.
C. A Framework for Research and Curriculum Development in Post Secondary Mathematics.

I think the choice here is whether you want the outcomes of the course to be that the participants can begin to apply some new pedagogical approaches in their teaching (A), that they can begin to conduct research projects related to their teaching (B) or that they begin to develop a foundation for long term activities involving research in learning and innovative pedagogical approaches (C).

I must discuss this with others, but I have the impression that A part might not satisfy one third of the participants, four days of B would be too much for one half, and C... a reasonable introductory synthesis ... Well, let us take the C. But since not all are so much interested in using computers, one should also have balance between the "with and without computer". And that there are undergraduate and graduate students! And faculty members just starting the pedagogical training.

Martti

Date: Mon, 22 Jun 1998 13:35:56 +0300 To: edd@zeus.cs.gsu.edu (Dr. Ed Dubinsky) 
From: "Martti E. Pesonen" <Martti.Pesonen@Joensuu.Fi> 
Subject: Distributed material, Draga & Joel 
Cc: tterho@cc.joensuu.fi, sirepo@cc.joensuu.fi, Martti.Pesonen@Joensuu.Fi

Let me now explicitely write down some names:
Ph.D. Sisko Repo (has already done some)
M.Sc. Tanja Terho (already Master's thesis implementing teaching of algebra applying APOS, teaches at school next Winter)
M.Sc. Taina Malvela (doing Ph.Lic. about understanding of binary operations)
M.Sc. Silja Pesonen (doing Ph.Lic. about the Image of Mathematics of those pre-service primary school teachers that are being specialized in teaching mathematics)
Ph.D. Liisa Kinnunen (intending to investigate mathematical literacy of the first year students in her introductory mathematics course)
M.Sc. Jari Rokkila (Teaching geometry with Gabri ... but he just got a permanent job at school?!)
Ph.Lic. Pekka Smolander (something, after Ph.D. in Maths)
Possibly a couple of others.

>Your response has helped me a lot to understand things better. I will still
>include some material on research in my lectures, but I willemphasize the
>pedagogical aspects. Also, I may start with a different paper than I said
>before, or perhaps discuss two papers in the begining becore getting more
>specialized. I will think some more about that.

I have distributed in advance the following material to the audience:
=============================================
1. My description about the APOS Framework as in Asiala & al, excluding Chapters 3.3. Data and 4 and 5 (but including a short look at post-secondary mathematics education R&D, especially RUMEC system).
2. Tanja's short description of mathematical programming environment, learning theories in general, and cooperational learning in small groups (Johnsons, Practical Guide to Cooperative Learning), advice to students how to work in computer activities and a quick reference of ISETLW with examples and exercises.
3. Diskette containing ISETLW 2.0
4. APOS Glossary (in English)

>
I await your furtherresponse on my item 2.

--------------
I think I already sent you the table of the contents of Draga's two day course. To be a little bit more precise:

DRAGA VIDAKOVIC in Joensuu Summer 1997:
==================================
Monday at 12.00-16.00

1) Technology in Math teacher education
(i) Technology in Pre-service teacher education (She talked a lot about using portfolios)
(ii) Technology in In-service teacher education: Exploring Geometry with technology, an example of a professional development program

2) Using the Geometer's Sketchpad in teaching mathematics: Hands-on activities.

Tuesday at 9.00-13.00

1) Teaching Mathematical concepts with technology in a cooperative learning environment
(i) Cooperative learning in collegiate mathematics: An overview
(ii) A theoretical foundation of instructional method used in teaching mathematical concepts (APOS - the research Framework)
(iii) Teaching a definite integral with technology (ISETLW)
(iv) Teaching a concept of definite integral: Modeling the Activity-Classroom discussion-Exercise (ACE) cycle

2) Discussion

JOEL HILLEL's titles:
===============
Wednesday 17.6.
--------------
9.15-10.15 Research in Mathematics Education; Goals, Results, and Limitations (45+15 min) Joel Hillel
As an example he talked about Research in problem solving (methods like Clinical Interviews, Protocol Analysis, Task Analysis, choice of problems)

10.30-12.00 Workshop: Using technology in the classroom - implementation ans assessment (Joel Hillel) He told about problems that are met with for example graphing with software, (induced e.g. automatic handling of scaling, treatment of singularities). Also he told some unexpected effects when using Gabri for dragging vectors in linear elementary algebra. What new meta-skills are required in CAI approach?

After the seminar he talked (an hour session) more privately at the Dept of MAth to some 10 "young" faculty members. He talked most about their experience using Maple and Cabri in linear algebra.

Ed, please do not hesitate to ask for more information when needed.

Martti