Systematic variation of function representations

Rukiye Dogan defends her MSc-thesis in mathematics.

Censor:

prof. Claus Michelsen, SDU.

Supervisor:

prof. Carl Winsløw, IND.

Abstract: 

One of the central elements in the curriculum for secondary level students in Denmark is the concept of function and the conversion between different representation forms. The thesis focuses on that specific topic for this reason. In order to understand the underlying factors of how students acquire an understanding of mathematics, Sfard’s terminology of process and object perception was used, as were Tall’s theory of proceptual thinking. Combined with these two, the thesis also draws upon Duval's four different types of semiotic systems, called registers, which are connected to conversions. The thesis uses a two step approach to the problem: 1) data collection through a diagnostics test aimed to uncover which types of conversions are the most challenging for high school students and 2) making a teaching design which aimed to remedy some of the difficulties found in the diagnostics test.

The diagnostic test was given to 79 math students at a Danish high school and the findings showed that most students found it difficult to make the conversion from one representation to another. It also found that even though many students mastered a specific type of conversion, it was not a given that they would master the opposite conversion. An example of this is that conversion from graph to table caused more problems than the conversion from table to graph. One of the areas that stood out the most was the conversions where verbal language was involved. This seemed to be a particularly challenging area for the students. One of the reasons for this could be that many of the students at the school, where the diagnostics test was administered, are bilingual, thus suggesting that there could be a connection between language skills and the ability to make verbal conversions. The teaching design was not tested due to the corona crisis, which means that only the thoughts behind the design and the aim with the design will be processed in this thesis.