Forschungsbericht 2008 - Pädagogische Hochschule - Schwäbisch ...

Learning The Concepts Of Limit And Calculus Through
Interdisciplinarity – A Historical And Empirical Study
Institut für Mathematik und Informatik – Mathematik
Leitung: Tine Golež (St. Stanislav Institute for Education, Slowenien),
Prof. Dr. Astrid Beckmann (PH Schwäbisch Gmünd)
Kontakt: astrid.beckmann@ph-gmuend.de,
tine.golez@guest.arnes.si
Schlagwörter: Concept of limit, concept of calculus, interdisciplinarity
Kurzinhalt:
Background: The European project ScienceMath emerged from a deep conviction of
the ScienceMath group initiators that the teaching of mathematics could be enhanced
by physics experiments and other real life ‘hands on’ experiences. The project´s aim
is to invent, produce and shape some incontext teaching sequences, which will be
detailed, explored and researched further so that their use and effectiveness will be
confirmed.
Research questions: How can the use of a motion sensor device which enables us to
measure and plot real time graphs of a moving body, influence the effectiveness of
teaching the calculus also from the perspective of historical developments of calculus
concept?
Method of investigation: The approach to teaching calculus based on real time
kinematics graphs will be proposed as an alternative to the classical (abstract)
teaching of the calculus. The research questions and hypotheses will address the
efficiency of the proposed interdisciplinary physics and mathematics teaching
approach.
The phases will be: preliminary design phase, the teaching experiments (implementation
of proposed sequences) and data analysis phase.
A pilot experiment will be a precursor for further finalization of the instructional
design. Our proposed teaching sequences will be based on the use of a motion
sensor device, a computer guided measurement system for kinematics. The teaching
sequences will be theoretically and practically elaborated.
The teaching experiments will be based on the design of concrete teaching instructions.
The proposed sequences will be used by (math and physics) teachers. A
thorough reflection of the theme, proposed experiments and learning achievements
will be carried out at the end of the sequences. We expect to design further and new
experiments and sequences on the basis of teaching experiences. Experiments will
be carried out at different schools to test the applicability of the sequences in diverse
school environments. Learning achievements will be measured by tests prepared in
advance and by open discussion with teachers and students. The methodology of
these practical experiments in learning will be compared with historical developments
of calculus ideas, which evolved through history from intuitive to abstract, as we
believe, a successful teaching of a calculus should be for every individual.
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