Danish upper secondary students’ apprehensions of the equal sign
Danish upper secondary students’ apprehensions of the equal sign [pdf, 3.7MB]
IND's studenterserie nr. 110, 2023. Specialerapport. Matematik.
Aurora Olden Aglen, afleveret 2021.
Vejledere: Britta Eyrich Jessen & Mikkel Willum Johansen
Abstract
This thesis aims to demonstrate Danish upper secondary students’ understanding of the equal sign motivated by its strong affiliation to school algebra. We have used the methods of didactic transposition and diagnostic test to answer the following two research questions:
RQ1: Based on external didactic transposition, how do the scholarly meanings of the equal sign come into view in knowledge to be taught in Danish upper secondary school?
RQ2: Which challenges related to the external didactic transposition of the equal sign can be detected through a diagnostic test for Danish students in upper secondary school?
We refer to the six meanings of the equal sign proposed by Prediger (2010) in the analysis; the meaning of operational, symmetric arithmetic identity, formal equivalence, conditional equation characterizing unknowns, contextual identity in formula and specification. The external transposition was the reference in constructing the diagnostic test in which we wished to find the internal didactic transposition of learned knowledge. We show that it is challenging to construct a diagnostic test of the equal sign as it is an entity treated implicitly in knowledge to be taught. The test results demonstrate challenges concerning the meanings of the equal sign, especially what regards contextual identity and formal equivalence. Moreover, we have shown how some of the challenges link to the analyzed knowledge to be taught. However, contrary to prior studies, we show that most students do not favor an operational approach alone. On the other hand, the test show difficulties in distinguishing between misconceptions of the equal sign and school algebra. We conclude that this indeed stresses the relevance of becoming more explicit with the equal sign’s many disguises.