Improving Students’ Mathematical Understanding by Engaging with the Mathematical Structure

Richards, Fiona (2024) Improving Students’ Mathematical Understanding by Engaging with the Mathematical Structure. Doctoral thesis, University of Wales Trinity Saint David.

Text Richards_F_PhD_Thesis.pdf - Accepted Version Available under License CC-BY-NC-ND Creative Commons Attribution Non-commercial No Derivatives. Download (13MB)

Abstract

This study investigates whether teaching using the underlying structure of mathematical concepts improves students’ understanding. This case focused on fractional magnitudes. For this study, instantiations are defined as mathematical concepts considered from the viewpoint of the learner. Mathematical structure consists of the instantiations alongside their properties. The pragmatic approach explores the research aims using qualitative and quantitative methods. A series of interventions was designed with Year 7 students. The interventions focussed on teaching students about fractional magnitudes; an area of mathematics vital for much of the secondary mathematics syllabus. The approach was cyclical, with three interventions. The design for each intervention was informed by the specific mathematical ideas that the students had misunderstood in the previous intervention. Although students’ understanding of fractional amounts had improved at the end of the first intervention, the post-test and interview indicated a persistence of incorrect responses, which were automatic and accompanied by mantras. The second intervention included tasks to try to address these intuitive responses. The third intervention focussed on intuitive responses and language around fraction magnitude. The first intervention investigated the mathematical thoughts and understanding of students. The second and third interventions allowed for in-depth investigation of specific incorrect intuitions and perceptions of mathematical structure from the viewpoint of these learners. This cyclical approach exposed specific incorrect intuitive responses that appeared to be persistent. The study demonstrates a process of designing teaching episodes interpreting both the mathematical structure and the student errors through the students’ viewpoints. The results indicate ways that teachers can address intuitions in their classroom. The findings suggest that the use of mantras, helpful in teaching early mathematics, may be a basis for intuitive errors that persist. Exploration of a possible link between a learner’s general mathematical difficulties and dependence on intuition could be an area for future research.

Item Type:	Thesis (Doctoral)
Subjects:	L Education > LB Theory and practice of education > LB1603 Secondary Education. High schools
Divisions:	Theses and Dissertations > Doctoral Theses
Depositing User:	Victoria Hankinson
Date Deposited:	21 Aug 2025 14:02
Last Modified:	21 Aug 2025 14:02
URI:	https://repository.uwtsd.ac.uk/id/eprint/3885

Administrator Actions (login required)

Edit Item - Repository Staff Only