In April 2016 Manchester eScholar was replaced by the University of Manchester’s new Research Information Management System, Pure. In the autumn the University’s research outputs will be available to search and browse via a new Research Portal. Until then the University’s full publication record can be accessed via a temporary portal and the old eScholar content is available to search and browse via this archive.

Related resources

Search for item elsewhere

University researcher(s)

Academic department(s)

Evaluating the teaching and learning of fractions through modelling in Brunei: Measurement and Semiotic analyses

Haji Harun, Hajah Zurina

[Thesis]. Manchester, UK: The University of Manchester; 2011.

Access to files

FULL-TEXT.PDF (pdf)

Abstract

This thesis is submitted to the University of Manchester for the degree of Doctor of Philosophy (PhD). This study developed an experimental small group teaching method in the Realistic Mathematics Education tradition for teaching fractions using models and contexts to year 7 children in Brunei (N=89) whose effectiveness was evaluated using a treatment-control design: the E1 group was given the experimental lessons, the E2 group who was given “normal” lessons taught by the experimenter, and a whole class (E3) group which acted as the control group. The experimental teaching was video recorded and subject to semiotic analysis, aiming to describe the objectifications that realized ‘learning of fractions’ by the groups.The research addresses two research questions:1. How effective was the experimental teaching in helping learners make sense of fractions, with respect to equivalence of fractions and flexibility of unitizing?2. What were the semiotic learning and teaching processes in the experimental group of the RME-like lessons? This study used a mixed method approach with a quasi-experimental design (QED) for the quantitative side, and a semiotic analysis for the qualitative side. Quantitatively, the experimental teachings proved to be relatively effective with an effect size of 0.6 from the pre- to the delayed post-teaching test, compared to the E2 and the control groups.The basic findings pertaining to the semiotic analyses were:a. The mediation of the production of fractions in terms of length, from the production of fractions in terms of the number of parts which led to equivalence of fractions;b. The use of language and gesture help to objectify the equivalence of fractions and the flexibility of unitizing–in some case it involved gesturing to the self;c. The role of the Hour-Foot clock (HFC) as a model in a realistic context; andd. The complexity of the required chains of objectifications reflects the difficulties of the topic.