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In this study, the authors investigate the ways in which young students demonstrate their critical mathematical thinking (CMT). Students aged 5-6 who are beginning their first formal year of education participated in the study. Data is presented from individual clinical interviews undertaken with 16 students. These interviews were analysed using the Critical Mathematical Thinking for Young Students (CMTFYS) framework to identify common patterns in the responses. The findings suggest that these young students beginning school, most often rely on providing explanations and more specifically, justifying, to demonstrate their CMT.

This paper examines the types of teacher questions that assist young students to interpret and explain their critical mathematical thinking (CMT). Focusing on students who enter their first year of formal schooling (aged 5-6 years), this paper draws on data from a one-on-one task based clinical interview conducted with 16 students. Teacher questioning data were analysed for question type (probing, factual, guiding) and further analysed against the conceptualized critical mathematical thinking framework for young students. Findings indicated that when teachers used clarifying, noting relationships, and offering opinions style probing questions, young students were supported to interpret and explain their critical mathematical thinking.

In this paper, we report on the interim findings of a study that seeks to identify the characteristics of children's Critical Mathematical Thinking CMT. Characteristics of CMT were initially generated from a synthesis of relevant research literature and then validated using a case study methodology via trials in early childhood classrooms. This paper provides a framework for CMT distilled from the literature and an illustrative case study of one student to provide tentative evidence that young children's use of CMT capabilities can be identified. The long term aim of this line of research is to explore the potential to promote CMT capabilities in a targeted manner.