22. juli 2021

# A Diagnostic Test for Danish Middle School Arithmetics

A Diagnostic Test for Danish Middle School Arithmetics [14.7 MB]

IND's studenterserie nr. 102. Specialerapport. Matematik.

Derya Diana Cosan, 2021.

Vejleder: Carl Winsløw

## Abstract

This present thesis investigates to what extent arithmetic and algebraic praxeologies are mastered by Danish fifth- and seventh-grade students. The Anthropological Theory of Didactics (ATD) and the notions of praxeologies are the main tools for the examination of this. These are used to develop praxeological reference models for arithmetic and algebra in fifth- and seventh grade. The construction of the models is based on two different textbooks for Danish fifth- and seventh-grade students respectively and a review of the official programmes for these grades. The identified types of task related to arithmetic and algebra are among other things related to fractions, decimals, solving of first-degree equations etc. These praxeological reference models illustrates what arithmetic and algebraic praxeologies Danish fifth- and seventh-grade students are supposed to learn.

For the examination of the extent to which these praxeologies related to arithmetic and algebra are mastered by the students, a diagnostic test for fifth and seventh grade respectively is developed. The tests are developed in relation to the praxeological models.

The diagnostic test is performed by 86 Danish fifth grade students and 78 seventh grade students in Nkøbing municipality.

The results from the diagnostic tests show that the students, both in fifth and seventh grade, master almost all types of task to different extents, while similarities and difference between the classes at the same grade are identified.

It is observed that some students possess some misconceptions in types of task related to arithmetic and algebra, while other students have lack of knowledge. The most prominent misconceptions among these Danish fifth- and seventh-grade students are related to fractions and calculation of these, decimals and the magnitudes of fractions and decimals. Furthermore, it is observed that the majority of the students have an operational approach to the equal sign instead of a relational approach.