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Abstract

Learning mathematics is a challenge for many learners in Further Education. It is also a requirement since Government policy stipulates that Further Education (FE) learners in England, who have achieved a General Certificate of Secondary Education (GCSE) Mathematics grade 3 or lower, are required to continue studying this subject alongside their vocational courses. As a core subject, mathematics includes numbers, shapes, patterns and statistics with progression generally from concrete to abstract form; mathematics texts include specific vocabulary such as probability trees and procedures such as calculations using decimals. Engagement with mathematics has been shown to be related to motivation, confidence and progression. This study explores how learners and teachers interact with mathematics texts in vocational and mathematics sessions to understand why many learners tend to struggle in their tasks. Aspects of Development Work Research methodology were adopted for gathering and sharing data from observations, semi-structured interviews and focus groups. Data was analysed using a Cultural Historical Activity Theory framework. The findings illustrate how learners and teachers use a range of mathematics texts in their sessions. There was a clear dual purpose in meeting the object in mathematics and vocational sessions. In the mathematics sessions, texts tended to be shared in abstract forms whilst in vocational sessions, mathematics texts were purposely directed towards production of objects. Mathematics and vocational teachers focused on helping learners to pass their assessments and their intention was also for learners to use mathematics concepts and procedures in everyday life and work contexts, for example, use of the abstract concept of Pythagoras Theorem to square corners on a building site using the 3-4-5 rule. Tensions in concepts and procedures with mathematics texts were associated with rules and division of labour leading to struggles of completing tasks. Teachers shifted between several roles as they facilitated learners with their tasks keeping to institutional rules and regulations, for example, following procedures to mark registers within a specified timeframe, and supporting learners with their calculations to use abstract concepts and place value correctly. Suggested interventions to overcome these difficulties included pedagogical learning about using mathematics texts at an institutional level to embed and develop mastery of tools in different contexts in class activities. Reciprocal teacher development opportunities may lead to more integrated learning experiences for vocational learners to build bridges between concrete structures and abstract concepts in classrooms.

Awarding Institution(s)

University of Plymouth

Supervisor

Peter Kelly, Jan Georgeson

Keywords

Activity Theory, Further Education, Vocational Learning, GCSE Mathematics, Functional Skills Mathematics, Mathematics texts

Document Type

Thesis

Publication Date

2026

Embargo Period

2026-06-05

Deposit Date

June 2026

Creative Commons License

Creative Commons Attribution-NonCommercial 4.0 International License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License

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