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An investigation into the capacities of pre-service post-primary mathematics teachers to effectively teach problem-solving.

Owens, Emma orcid logoORCID: 0000-0002-8720-4596 (2023) An investigation into the capacities of pre-service post-primary mathematics teachers to effectively teach problem-solving. PhD thesis, Dublin City University.

Problem-solving has always been a part of mathematics, but the formal study of problem-solving has a short history. There is widespread agreement that the development of students’ problem-solving capabilities is a main goal of mathematics instruction with emphasis on problem-solving in curricula nationally and internationally. In Ireland, problem-solving is specifically mentioned in post-primary curricula. However, according to the PISA and TIMSS results, it appears that students in Ireland have a lower performance in translating real-world situations into mathematical representations than in applying procedures. Since teachers play a key role in students’ problem-solving, the aim of this research was to investigate and develop the capacities of pre-service post-primary mathematics teachers (PSMTs) to effectively teach mathematical problem-solving. These capacities involve: knowledge of problems, knowledge of problem-solving, knowledge of problem-posing, and affective factors and beliefs. This research focuses on designing a university module to investigate and develop these capacities in PSMTs in Ireland. Based on these capacities, specific instruments were developed for the intervention, namely: mathematical task classification instruments and rubric, mathematical problem generation and reformulation instruments, implementation of taught strategies rubric, and open-ended affective questions. These instruments were implemented alongside pre-existing instruments: the Indiana Mathematics Belief scale (Kloosterman & Stage, 1992), a mathematical problem-solving proficiency rubric (Oregon, 2010), and ‘Think Aloud’ interviews. This intervention was developed and implemented with four cohorts of PSMTs over four years. Our findings include that PSMTs: demonstrate adequate ability to communicate reasoning and use representations while problem-solving but have difficulty in reflecting on their solution; have difficulty in posing mathematical problems; and text based tasks are often misclassified as mathematical problems. In relation to the affective domain, the beliefs stated by the PSMTs about problem-solving, in some instances, contradicted the affective factors expressed while problem-solving. These findings have led to refinements of the module mentioned above, and to suggestions for further developments.
Item Type:Thesis (PhD)
Date of Award:November 2023
Supervisor(s):Nolan, Brien and Breen, Sinéad
Uncontrolled Keywords:Mathematics teacher education
Subjects:Social Sciences > Education
Social Sciences > Teaching
DCU Faculties and Centres:DCU Faculties and Schools > Faculty of Science and Health > School of Mathematical Sciences
Use License:This item is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 License. View License
ID Code:28899
Deposited On:07 Nov 2023 11:34 by Prof Brien Nolan . Last Modified 07 Nov 2023 11:35

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