Forschungsbericht 2008 - Pädagogische Hochschule - Schwäbisch ...


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)


Schlagwörter: Concept of limit, concept of calculus, interdisciplinarity


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


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


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


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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