This study examined preservice elementary teachers' (PETs') epistemological beliefs (EB) and their views about mathematics (VM) and the impact on these parameters by their prior experience in learning mathematics. A total of 541 PETs from an American university completed EB and VM questionnaires. It was found that participants’ EB and the relationship to their VM are different compared to those of other college students or middle/high school students. Participants hold strong beliefs about “how to study” but not “what knowledge is.” Furthermore, the more participants believe that knowledge is constructed by authority and a collection of facts, the more they make efforts to improve their knowledge of mathematics. Concerning their prior mathematics experience, the more mathematics courses they have taken during secondary education, the more developed EB and VM they have, but their prior experience in college mathematics education did not have any significant correlation with their EB and VM.
The aim of this study is to investigate task design for differentiated instruction in mathematics in professional learning communities. Based on the cultural-historical activity theory, we conceptualize a professional learning community as an activity system and use the analytical construct of contradictions to give an account of structures that bring forward the teachers’ work. Eight Swedish upper secondary teachers, engaged in designing tasks for differentiated instruction in mixed-ability mathematics classrooms, are studied. The analysis outlines three contradictions, manifested as three dilemmas, and shows how the teachers, by noticing a dilemma and making it an explicit object of inquiry, came to address a diversity of issues related to differentiated instruction in mathematics. For example, the teachers addressed students’ different learning needs, problem-solving activities for a mixed-ability classroom, and design of tasks that are challenging for all students. With input from our findings on the three dilemmas, we then discuss the design of a task analysis guide as a means for facilitating the development of a professional learning community that is inquiry-oriented with a strong content focus on designing tasks for differentiated instruction in mixed-ability mathematics classrooms.
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.
There is widespread belief that addressing differentiation within classroom practice is critical for school improvement in mathematics. School mathematics leaders and consultants are faced with the challenge of interpreting the various models of differentiation that are presented throughout professional learning programs and aligning these with existing beliefs and cultures within schools. This paper reports on a self-study of a learning consultant who supported primary mathematics teachers to plan lessons for implementing differentiation in their classrooms and aims to highlight the Mathematical Knowledge for Teaching (MKT) required to lead such planning sessions. Over three weeks, a mathematics consultant assisted teaching teams across three different schools by facilitating planning meetings. The consultant recorded self-reflections after each session and the qualitative data were coded to identify the categories of MKT the consultant relied on during her interactions with teachers. Overall, the results highlight the dominance of three categories, Knowledge of content and students (KCS), Knowledge of content and teaching (KCT) and Specialised content knowledge (SCK) emphasised by the consultant, as well as the influence different contexts had in developing a shared understanding of differentiated learning in mathematics. The findings have implications for ways in which schools and facilitators develop strategies that comprehensively support teachers to plan suitable differentiated lessons for their students. Furthermore, this study highlights the need to develop greater understanding around models of planning that adequately support teachers to plan effectively for differentiating instruction in mathematics.
