A PERMA-Informed Approach to Vocationally Contextualised Mathematics Teaching: A Mixed-Methods Action Research Study in Further Education

Abstract

This mixed-methods action-research paper develops a PERMA-informed interpretation of vocationally contextualised mathematics teaching for GCSE resit learners in Further Education (FE). Seventeen learners completed matched pre- and post-intervention questionnaires comprising 15 five-point Likert items grouped into behavioural engagement, perceived relevance, and emotional engagement/confidence. A five-week intervention embedded GCSE mathematics within vocational and real-world contexts. Quantitative re-analysis used paired-samples t-tests, Shapiro–Wilk diagnostics, exact Wilcoxon signed-rank sensitivity tests, 95% confidence intervals, Cohen’s , small-sample-corrected Hedges’ , rank-biserial correlations, bootstrap confidence intervals, Holm multiplicity adjustment and Cronbach’s alpha. Qualitative responses were analysed thematically and mapped cautiously onto PERMA. Behavioural engagement increased from  to 3.67 (mean change=1.08, 95% CI [0.95, 1.21], , , =4.24). Perceived relevance increased from  to 3.78 (change=1.08, 95% CI [0.93, 1.24], , , =3.60). Emotional engagement/confidence increased from  to 3.49 (change=0.69, 95% CI [0.32, 1.07], , , =0.95); the exact Wilcoxon test corroborated this change. Qualitative themes also shifted positively: relevance 4/17→15/17, motivation/engagement 3/17→14/17, confidence/reduced anxiety 5/17→12/17, and understanding 6/17→13/17. The study does not claim that PERMA itself was experimentally tested; rather, PERMA provides an integrative lens linking positive emotion, engagement, relationships, meaning and accomplishment to vocational mathematics pedagogy.

Keywords: PERMA; positive education; vocational contextualisation; GCSE mathematics resit; Further Education; student engagement; mathematics confidence; action research; mixed methods

DOI: 10.7176/JEP/17-10-05

Publication date: October 30th 2026