Hur använder man x egentligen?

Abstract

The purpose of this thesis was to investigate whether students understanding of letter symbols in algebra has changed since Dietmar Küchemanns study in 1976, as well as to see whether teachers’ view on students understanding and their misconceptions correlate with the test results shown by the students. To be able to measure the students understanding, the same test that Küchemann used in 1976 was used on students aged 15/16 today (although on a much smaller scale), and the results were then analysed, and the students were categorised into different levels of understanding, based on the descriptions of the levels made by Küchemann in 1981. If the students are categorized into level 1 or 2, they are able to solve problems where the letter symbols are used as objects, the letters are given a value, or they aren’t used. The difference between level 1 and 2 is that the students are able to solve problems with a more complex structure. The students at level 3 are also able to solve problems where the letter symbols are used as specific unknown when the problems have a simpler structure, and finally the students at level 4 are able to also solve problems where the letter symbols are used as specific unknowns even when the questions have a more complex structure, as well as when the symbols are used as generalised numbers and variables. The results of the study showed that the students tended to make the same mistakes as they did in 1976, but the number of students on level 3 had decreased by 11 percentage points and the amount at both level 2 and 4 had increased. The teachers also seemed to have a pretty good understanding of the misconceptions that the students have, as they were able to correctly guess the most common misconceptions on most questions that they were asked about.