Abstract
In this research, we set two main goals: to provide empirical data that point to the knowledge of fractions among fifth-grade primary school pupils on a national scale; and to determine the level of knowledge about fractions among university students, including future primary school teachers. We used two tests—the national-wide test T5 for the fifth-graders (a research sample of approximately 45,000 pupils), and the modified fraction test based on Sfard’s theory of reification, for the university students (162 students). At the end of the study, we focused on a content analysis of the university students’ solutions. We identified persistent difficulties with concepts of fractions not only by fifth graders but also by future primary school teachers.
Highlights
The processing of fractions is part of our everyday life and is used in situations such as the estimation of rebates, following recipes, or reading maps
We present evaluations of tasks with fractions that appeared in Testing 5 (T5) in 2015 and 2019
Fractions have a significant place in mathematics
Summary
The processing of fractions is part of our everyday life and is used in situations such as the estimation of rebates, following recipes, or reading maps. Fractions involve a qualitative leap for students learning mathematics. Fractions belong to one of the most problematic thematic units in the teaching of mathematics. This was proven by many Slovak, Czech, and foreign studies [3–6]. Pupils learn the rules for counting fractions relatively quickly, only to forget them after a while. We often find that, even though students control the rules for counting fractions, they remain clueless in a task that involves unusual situations. This means that knowledge is stored only as memory traces, regardless of the previously created knowledge structure
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