30. juni 2015

One-dimensional regression in high school

One-dimensional regression in high school [14,9 MB]

IND's studenterserie nr. 39. Kandidatspeciale. Matematik

Jeanette Kjølbæk, Juni 2015

Vejleder: Carl Winsløw


Development of calculators and IT-tools has caused that students can
easily solve mathematical tasks without knowing intermediate calculations
and the mathematics behind the technique. Unfortunately a
consequence of this is that the mathematics theory behind these techniques
has been given a lower priority.

This is the case with teaching in one-dimensional regression in high
school, where many students learn the instrumented techniques to
make regression without knowing what to find or how to find it.
In this thesis, the theory about one-dimensional regression at the
mathematical community and the possibilities to work more theoretically
with one-dimensional regression in high school is investigated.
Initial, the external didactic transposition was analyzed. This was
done by analyze and present the theory of regression in the mathematical
community and describe how regression is included in the
curricula, written exams and textbooks. The presentation and descriptions
were based on the Anthropological Theory of Didactic (ATD).
Based on the analysis four main questions were highlighted and an
epistemological reference model (ERM) was developed.
The second part of the thesis concerns the internal didactic transposition
and focus on the design and evaluation of the teaching sequence.
The planned and the realized didactic process was analyzed using
ATD and ERM. Finally, the possibilities and obstacles to work more
theoretically with regression were presented and discussed.
The analysis of the external didactic transposition showed that one
technological-theoretical discourse of linear regression is based on
mathematics well-known to students in high school. This discourse
were applied in the design of the teaching sequence. Further it was
found that the students only are presented for a minimum of technological-
theoretical discourse and do not learn how to determinate the
best class of functions.

The technological-theoretical discourse of linear regression and the
question of best class of functions were tested in a high school class.
It turned out that the students had a sensible basis to reach the technological
discourse. The technical work to reach the theoretical level
was difficult, especially the algebraic notation and the rules of sum
were found to be challenging. The determination of the best class of
functions was found to function in practice.