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### An apology of a mathematics educator

IoannaMamona-Downs

Department of Mathematics

University of Patras

Greece

We should search for ways to bring students to abstraction (T. Eisenberg)

Mathematicians can expect from educators:

- Explain to students the need for abstraction.
- Facilitate transition from school to university.
- Find and examine different textbooks to test readability vis-à-vis rigor .
- Trace the students’ development of skills that run through different mathematical theories.

An apology of a mathematics educator IoannaMamona-Downs

Educators can expect from mathematicians:

- Accept the role of educator in improving university mathematics instruction.
- Acknowledge different types of students

- The known dichotomy: semantic/syntactic

- Fast and deliberate thinkers.

- Teach in a way that encourages alternative argumentation (other avenues to answer questions outside the theory are available).

An apology of a mathematics educator IoannaMamona-Downs

Undergraduate Courses

- First year Real Analysis course

- Difficult for students to understand and to pass exams.

- More than one lecturers share the teaching.

- Resistance in having a common exam paper.

- A repeat course of Real Analysis for students who failed the first time.
- An elective course in problem solving in the undergraduate program.

- Attracts some of the very best students

An apology of a mathematics educator IoannaMamona-Downs

Postgraduate Courses

A Master program in Mathematics Education at a mathematics department :

An opportunity for mathematicians to have a hand on prospective teachers development.

- Problem Solving and Proof

- How does this differ from the undergraduate course?

- Elementary Mathematics from an Advanced Point of View.

-Deeper analysis for some topics so that teachers are aware of the ‘jumps’ occurring whilst transition from school to university.

- Cognitive and Social dimensions of Mathematics education

- A reading course: comparing and making essays on various educational frameworks.

An apology of a mathematics educator IoannaMamona-Downs

Issues of Collaboration

- An active role for educators:

- Pursue regular communication with lecturers

- Mathematicians ask advice on a particular didactical point, leading to conducting fieldwork.

- The above might help to regulate the direction and style of the ‘discipline’ at tertiary level.

- Document the results of this cooperation in a way that both educators and mathematicians can digest.

An apology of a mathematics educator IoannaMamona-Downs

What qualifies a good lecturer?

“ I have observed, not only with other people but also with myself… that sources of insight can be clogged by automatisms. One finally masters an activity so perfectly that the question of how and why [students don’t understand them] is not asked anymore, cannot be asked anymore and is not even understood anymore as a meaningful and relevant question”.

Freudenthal (1983), p. 469.

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