17. maj 2024

# Undersøgelsesbaseret undervisning i Pascals trekant

Undersøgelsesbaseret undervisning i Pascals trekant

IND’s studenterserie nr. 117, 2024, bachelor - matematik.

Milla Mandrup Fogt

Vejleder: Carl Winsløw

Abstract

This thesis aims to investigate whether Pascal’s triangle and the binomial coefficient can be introduced in Danish high schools through inquiry-based learning. The literature review in the thesis highlights that exercises in high school combinatorics are often repetitive and can be reduced to identifying keywords and applying them to formulas. It is considered beneficial for students to work with combinatorics without instructions. The literature review and the Theory of Didactic Situations have been the inspiration for the designed material. An a priori analysis of the adidactical potential of the material is carried out to serve as a basis for the a posteriori analysis. In the a priori analysis, the material is analysed in relation to the model of students’ combinatorial thinking by Lockwood (2012). The material has been tested on 28 students in a Danish upper secondary school in Copenhagen. Based on the a posteriori analysis, the designed material about the construction of Pascal’s triangle and [the binomial coefficients] is established to contain great opportunities for students to construct their own combinatorial arguments. This made it possible to institutionalize Pascal’s triangle and [the binomial coefficients] directly in the extension of the students’ adidactical actions. The students used sets of outcomes in the form of drawing routes to optimize their hypotheses and construct enumerative arguments for the numbers in Pascal’s triangle. The exercises about identities for [the binomial coefficients] are seen to have less adidactic potential. This is due, among other things, to the dominant Topaz effect during this part of the lecture. To improve the material proposals for changes have been made, such as different words for the definitions in the exercise. In a shorter sequence after the inquiry-based learning, the students showed that they could use their acquired knowledge in a different context.