Number tricks as a didactical tool for teaching elementary algebra

MSc thesis defence by Asger Brix

Censor: prof. Morten Misfeldt, AAU.

Examiner/supervisor: prof. Carl Winsløw, IND.


The master thesis examines the adidactical potentials of using number tricks as frame for teaching elementary algebra to low level math students at Danish STX. A diagnostic test was made and implemented, and from this was dened target knowledge. Using the theory of didactical situations, two lessons were designed to specically induce the target mathematical knowledge through adidactical situations.

The lessons were analyzed using the theory of didactical situations, and it was concluded, that high adidactical potentials exist when using number tricks as a frame for teaching elementary algebra. It was also concluded, that the test students in low level math classes in Danish STX exhibited both didactical and epistemological obstacles with elementary algebra leading to misconceptions such as sqrt(a+b)=sqrt(a)+sqrt(b).

Through the analysis, it was concluded, that in cases, where the devolution leading to the adidactical phase was successful, the misconceptions were successfully dealt with, while in cases where the devolution was lacking, the misconceptions were not dealt with at all. Instances of broken didactical contract, Jourdain effect and Topaze effect were observed. Post-lesson diagnostics revealed, that progress had been made for the students both regarding the specic misconceptions and the overall abilities to handle algebraic expressions.