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In this paper we explore how participation in a constructivist-oriented, classroom aligned mathematics intervention program advanced the learning and positive dispositions of Grade 1 students who were failing to thrive when learning mathematics. Intervention programs are an approach to differentiated instruction that some schools adopt, but there are questions about whether such interventions advance equity and inclusion for students. To provide insight about these issues, we draw on data from the Extending Mathematical Understanding for All study in NSW, Australia (2016-2020) to address two research aims. The first aim was to evaluate the effectiveness of the EMU intervention approach for progressing the mathematics learning of students who were failing to thrive mathematically, and for closing the performance gap with their peers. The second aim was to consider the impact of participating in EMU intervention on students' dispositions for learning mathematics. The findings confirm the potential of intensive constructivist-based intervention approaches for closing the performance gap for students who were not thriving in mathematics, and for improving the learning dispositions of these students. However, two years after the intervention, the performance gap was again apparent for many students. It is likely that a one-off intervention program is not sufficient for enabling all students to thrive mathematically, and that well-focused classroom-based differentiated instruction and further intervention support may be warranted for some students. [ABSTRACT FROM AUTHOR]

This paper identifies binary oppositions in the discourse of mathematics education and introduces a binary-epistemic model for (re)conceptualising these oppositions and the epistemic-pedagogic problems they represent. The model is attentive to the contextual relationships between pedagogically relevant binaries (e.g., traditional/progressive, student-centred/teacher-centred, discovery/transmission, constructivist/behaviourist) and epistemically relevant binaries (e.g., concrete/abstract, pure/applied, interpretivist/positivist, subjective/objective) that operate in mathematics classrooms. The premise of this paper is that ways of knowing mathematics (i.e., epistemologies) are actualised in ways of teaching mathematics (i.e., pedagogies), and vice-versa. The binary-epistemic model describes oppositional, equipositional and parapositional ways of knowing and teaching in relation to these binaries. We argue for a more a relational-contextual or parapositional approach to binary polarities that have otherwise proven divisive in mathematical discourse. In the context of the new Australian Curriculum, we illustrate epistemically differentiated ways of teaching measurement in a Year 5 mathematics classroom. [ABSTRACT FROM AUTHOR]

This paper identifies binary oppositions in the discourse of mathematics education and introduces a binary-epistemic model for (re)conceptualising these oppositions and the epistemic-pedagogic problems they represent. The model is attentive to the contextual relationships between pedagogically relevant binaries (e.g., traditional/progressive, student-centred/teacher-centred, discovery/transmission, constructivist/behaviourist) and epistemically relevant binaries (e.g., concrete/abstract, pure/applied, interpretivist/positivist, subjective/objective) that operate in mathematics classrooms. The premise of this paper is that ways of knowing mathematics (i.e., epistemologies) are actualised in ways of teaching mathematics (i.e., pedagogies), and vice-versa. The binary-epistemic model describes oppositional, equipositional and parapositional ways of knowing and teaching in relation to these binaries. We argue for a more relational-contextual or parapositional approach to binary polarities that have otherwise proven divisive in mathematical discourse. In the context of the new Australian Curriculum, we illustrate epistemically differentiated ways of teaching measurement in a Year 5 mathematics classroom. [ABSTRACT FROM AUTHOR]