On concept images of monotonicity of Finnish secondary students – with comparison and reference to tertiary students

Abstract

This study is titled “On concept images of monotonicity of Finnish secondary students – with comparison and reference to tertiary students”. The aim is to examine: (1) What kind of aspects of monotonicity are present and, possibly, dominant in the upper secondary school students’ (advanced level) concept images? (2) What are the most typical misconceptions and deficiencies in mathematical reasoning that the participants have concerning monotonicity? (3) To what extent do the results and answers to (1) and (2) compare with the results of university students? This thesis makes use of the study of Tossavainen, Haukkanen and Pesonen (2013), who investigated, inter alia, corresponding concept images among mathematics students from two Finnish universities. The theoretical framework is mainly based on the classic paper of Tall and Vinner (1981). The test was carried out in Tampere in April 2016 by using the same questionnaire as in Tossavainen et al. (2013). For the sake of comparability, also the similar guidelines in scoring and categorization of concept images were principally followed in processing the responses of 26 students. The quantitative analysis of the data collected consists of descriptive statistics and Student’s 𝑡�-test and it was done by using SPSS. It was found out that overall, there were so many faulty responses that erroneous concept images were most common, followed by experimental approaches, while not a single response was considered as algebraic. Among tertiary students there were more of them, but evoked mainly and superficially by imposition. There were also differences between secondary and tertiary students in the scores achieved, the formers’ scores being approximately two thirds of the latters’ in monotonicity and total items. Nevertheless, in this context the differences are not surprising and most of them are not significant