Abstract
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.
Highlights
A major challenge facing teachers at all levels of education is the ability to address the diverse needs of individual students in the mathematics classroom [1,2,3]
Not conceived with prior knowledge of the Theory of Didactical Situations (TDS) as proposed by Brousseau [45], we find it useful to reflect upon the EMC3 approach in the light of such theory
They were asked to indicate the degree to which they considered each of eight different approaches useful for teaching mathematics by responding to the prompt: “The following teaching approaches are useful for catering to students of different performance levels in the mathematics classroom”
Summary
Traditional approaches to student diversity include tracking classes or within-class groupings according to prior achievement. In both these approaches, students are usually given different tasks that vary in cognitive demand and sometimes, in content, which can exacerbate existing achievement gaps [4]. A more equitable and desirable approach currently advocated by most educational systems, involves whole-class instruction that is adaptive to individual student needs [5]. Within-class differentiated instruction might involve adaptations to content, teaching strategies, learner outcomes, or learning time [6]. Another important consideration is task design [2]
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