MENON

Ingo Witzke, Horst Struve, Kathleen Clark, Gero Stoffels
ÜBERPRO – A SEMINAR CONSTRUCTED TO CONFRONT THE TRANSITION
PROBLEM FROM SCHOOL TO UNIVERSITY MATHEMATICS, BASED ON
EPISTEMOLOGICAL AND HISTORICAL IDEAS OF MATHEMATICS
76
Table 1. Age and semester at university for ÜberPro seminar participants
(February 2015).
Participant
Semester Participant
Age (in
Age (in Semester at
number (gender:
at number (gender:
years)
years) university
M(ale)/F(emale))
university M(ale)/F(emale))
1 (F) 23 7 11 (F) 22 7
2 (F) 19 3 12 (F) 22 7
3 (M) 23 7 13 (F) 21 3
4 (F) 23 7 14 (M) 26 13
5 (F) 22 5 15 (M) 26 5
6 (M) 20 3 16 (F) 20 3
7 (F) 21 3 17 (M) 25 7
8 (F) 25 10 18 (M) 22 7
9 (M) 26 3 19 (F) 22 5
10 (F) 20 3 20 (M) 24 8
The three-day seminar was organized in four parts:
1) Raise attention to the importance of beliefs about and philosophies of
mathematics.
2) Historical case study: Geometry from Euclid to Hilbert. (In particular,
which questions led to the modern understanding of mathematics?)
3) Exploration of Hilbert’s approach (Or, what characterizes modern
formalistic mathematics?)
4) Summary discussion and reflection.
We employed several instructional techniques during the intensive seminar.
During the 18 hours of instruction students engaged in small group work,
which included engaging in active learning tasks and short discussions, and
whole class discussions, which included individual students and small groups
sharing their work. The self-activating sequences were enriched by short
instructional lectures of the participating mathematics educators (i.e. the first,
second, and fourth authors). Moreover, seminar participants worked with a
variety of materials, including reading original historical sources, excerpts from
research literature, and school textbooks; using hands-on materials to model
concepts from projective and hyperbolic geometry; and investigating concepts
using dynamic geometry software. We provide further context and description
for a number of the seminar activities within the elaboration of the four parts of
the seminar that follows.
1) Raise attention to the importance of beliefs about and philosophies of
mathematics.
In the first part of the seminar we wanted to make students aware of the
idea of different belief systems and natures of mathematics. Here we began
with individual reflections and work with authentic material such as transcripts
MENON: Journal Of Educational Research [ISSN: 1792-8494]
http://www.edu.uowm.gr/site/menon
2 nd THEMATIC ISSUE
05/2016