'Can you show me what it is not? Representations of ‘non-examples’ as a tool for developing pre-service primary mathematics teachers pedagogical content knowledge and intra-mathematical connections

Conceptual variation continues to be an essential aspect of mathematics teaching and learning (Drury, 2018) with the use of standard and non-standard examples helping to deepen conceptual knowledge. However, this paper explores often-forgotten non-examples (Tsamir et al., 2015) which allow learners to identify features (Ali, 1981), characteristics (Taylor et al., 2016) or critical attributes (Zodik & Zaslavsky, 2008) of concepts reducing the probability of misclassification, overgeneralization and undergeneralization (Ali, 1981). Pre-service teachers’ experiences of mathematics education, as well as their own content and pedagogical knowledge, often originates in their own mathematical learning experiences (Simmons and Back, 2014). Furthermore, Ulusoy (2021) suggests that subject knowledge of concept definitions and representations directly impacts pedagogical choices and effectiveness. Opportunities to explore mathematical concepts may influence efficacy in making pedagogical choices (Johnson et al., 2022) and yet there remains little exploration of how pre-service teachers utilise ‘non-examples’ in their pedagogy. This paper addresses the gap in the literature, utilising Tsamir et al.’s (2008) exploration of non-examples as a teaching intervention with a cohort of undergraduate pre-service teachers. Trainee teachers' subject knowledge and confidence in utilising non-examples in their pedagogic practice is explored in the form of quantitative and qualitative data.