Basic algebra in the transition from lower secondary school to high school
"Basic algebra in the transition from lower secondary school to high school" [0.77 MB]
IND's studenterserie nr. 44. Kandidatspeciale. Matematik
Caroline Sofie Poulsen, Oktober 2015
Vejleder: Carl Winsløw og Britta Eyrich Jessen
Abstract
Many students experience challenges in the transition from lower secondary school to high school in mathematics.
Especially algebra is difficult for the students in the transition.
In this thesis the problems related to algebra in the transition from lower secondary school to high school will be examined. This will be done by identifying the techniques in exercises related to algebra that are present in the two institutions and the challenges that can be associated with these techniques. Furthermore, it is discussed how those challenges can be met on the basis of the MathBridge project.
First material containing exercises from Danish 9th grade, high school, and a screening test from Silkeborg high school are analysed using the Anthropological Theory of the Didactic (ATD). Types of task and associated techniques are identified and on the basis of this an epistemological reference model (ERM) is developed. A pilot test is then constructed from the ERM with the purpose to test the overlapping techniques in the ERM in order to identify the students’ misconceptions and challenges with the techniques. The strategies from the MathBridge project are considered in relation to the found challenges.
The analysis of the exercises related to basic algebra showed that a large part of the identified techniques were present in both lower secondary school and high school. However, the increased use of IT-tools at the written examinations in mathematics in Danish 9th grade may remove the focus from the algebraic techniques.
Some of the students’ answers to exercises in the constructed pilot test indicated that some severe misconceptions were present. In particular, collecting and reducing like terms were challenging for the majority of the students. In the Mathbridge project teachers from lower secondary school and high school collaborate with the purpose of addressing the transition problems. Focus is on developing teaching sequences in algebra and modelling to be taught in lower secondary school which may prove to be beneficial for reducing the students challenges with mathematics in the transition.