Melody McCormick

Despite the construct of challenge being recognized as an essential element of mathematics instruction, concerns have been raised about whether such approaches benefit students with diverse academic needs. In this article, we focus on the beliefs and instructional practices of teachers teaching students in the first three years of school (5 to 8 years of age). These teachers participated in professional learning focused on challenging mathematical tasks differentiated through their open-ended design and the use of enabling and extending prompts. The instructional practices are explained using the Theory of Didactical Situations. Questionnaire data from pre-intervention (n = 148) and post-intervention (n = 100) groups of teachers indicated that teachers in the post-intervention group held more negative beliefs than those in the pre-intervention group about the capability of instructional approaches involving a priori grouping of students by performance levels. Interviews with ten teachers from the post-intervention group revealed and characterized the ways teachers employed open-ended tasks with enabling and extending prompts to engage all learners. Findings reveal that teachers knowing their students as individual learners accompanied by knowledge of a range of teaching practices to differentiate instruction are central to engaging all learners.

Teacher reluctance to teach mathematics through challenging tasks is frequently linked to beliefs that such approaches are not appropriate for students perceived as less mathematically capable. One potential means of shifting such beliefs is inviting teachers to reflect on students that surprise them when working on such tasks. Early years’ primary teachers (n = 160) participated in a professional learning initiative that supported them to implement up to ten sequences of challenging tasks in their classrooms across the school year. When asked to describe a student who surprised them when working on the sequences, approximately half (47%) of teachers described students previously assumed to be less mathematically capable being successful in their mathematical learning. Most remaining teachers (36%) commented on the depth of student mathematical thinking and positive learning dispositions demonstrated, without making any explicit reference to preconceptions of student capability. By contrast, a notable number of teachers (15%) instead described their surprise at how students labelled as mathematically capable struggled with working on tasks that were more open-ended, had multiple solutions, and required them to explain their reasoning. Our findings suggest that teaching with sequences of challenging tasks has the potential to disrupt rigid teacher preconceptions as to whom might be considered a mathematically capable student.

Australian schools, like schools elsewhere, have been through a period of closure. The closure creates both threats and opportunities for teachers and students. In the context of a project exploring approaches to teaching in early years, we outline some considerations and offer advice to teachers and educators on strategies for welcoming students back to school.