Fraction Sense: An Analysis of Preservice Mathematics Teachers’ Cognitive Obstacles

Abstract

Research on cognitive obstacles related to fraction sense in preservice mathematics teachers is significant, because their success depends on their skills. The acquisition of fraction sense is a complicated problem requiring a strategy to solve it. This study presents cognitive obstacles with fraction sense tests in preservice who will teach in secondary schools. It focuses on the following categories of cognitive obstacles: epistemological (language representation, tendency to generalise and rely on intuition) and didactic (less meaningful learning, and strategy). This paper takes a qualitative descriptive approach to examine 20 preservice mathematics teachers. The preservice teachers who encountered cognitive obstacles related to fraction sense testing were then grouped based on the similarity of their answers, and seven of them were selected to be interviewed. The research findings showed that five preservice teachers had overlapping obstacles: language representation and tendency to generalise; tendency to generalise and less meaningful learning; language representation, tendency to rely on intuition and trial and error strategy in; language representation and trial and error; and language representation and tendency to rely on intuition.

The Development of an Instrument on Negative Fractions to Measure the Cognitive Obstacle Based on Mental Mechanism Stages

“…In this research, an instrument to measure cognitive obstacles to negative fractions learning material has been developed. At the same time, previous studies revealed only a cognitive obstacle to positive fractions learning material [9], [26], [16]. Other researches showed the cognitive obstacle to negative integers [1], [27].…”

“…The pre-service teachers in question had already finished the course of Mathematical Foundation and School Mathematics Development Studies 1. Both classes instill an understanding of numbers so that the candidates have sufficient cognitive knowledge to solve fraction problems [16]. The candidates were selected based on various abilities they already have.…”

“…The different signs between positive and negative will lead to a contradictory concept [13], [14], [15]. The contradictory concept leads to cognitive obstacles [1], [16].…”

Prospective teachers' perceptions of didactic obstacles in the online mathematics learning

“…The results of previous studies have revealed didactic obstacles in online learning based on teacher and student perceptions. There has not been much research on didactic obstacles to prospective teachers (Akkaya et al, 2021;Murniasih et al, 2020). This study aims to describe the didactic obstacles in terms of prospective teachers' perceptions regarding online learning.…”

“…Implementing online learning causes didactic obstacles in learning (Van & Thi, 2021). Didactic obstacles are part of cognitive obstacles (Brousseau, 1997;Murniasih et al, 2020). Didactic obstacles are caused by school teacher teaching (Nurjanah & Juliana, 2020;Mustika et al, 2018).…”