# One dimensional regression in high school

**MSc thesis defence by Jeanette Kjøbæk.**

Censor: prof. Morten Misfeldt, AAU.

Examiner/supervisor: prof. Carl Winsløw, IND.

**Abstract.**

The 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 mathematical 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 of the mathematical community and the possibilities to work more theoretically with one-dimensional regression in high school is investigated.

Initially, the external didactic transposition was analyzed. This was done by analyzing and presenting the theory of regression of 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 the 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 focuses 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 sums were found to be challenging. The determination of the best class of functions was found to function in practice.