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Recognising students’ uncertain mathematics responses as interactions snagged at the boundary STEM thematic group presentation - ISCAR 2014 Megan Anakin Solving a Missing Number Problem Mathematics Education Research Methodology √ X • Error analysis and misconceptions • Pathology and deficit models • Reinforces transmission teaching and reproduction learning (Anakin & Linsell, 2014) Theoretical Framework • Appreciation of mathematical structure (Mason, Stephens, & Watson, 2009) • Students’ acts of communication are viewed as legitimate attempts to participate in mathematical activity (Davydov, 1990, Anakin, 2013) • Researching mathematical knowledge as fluency (Anakin, Linsell, & Ingram, 2014) Aim To investigate the mathematical structure expressed by primary students as they solve 7+3=□+2 What is the missing number? Explain why you say that. Methods • Micro-analysis of video recordings (Drew & Heritage, 1992; McNeill, 1992; Roth 2001; Siegler, 1997) • Mapping technique (Grune & Jacobs, 2008; Anakin, 2013) • Inductive analysis (Caspi & Sfard, 2012; Thomas 2006) • CHAT (Engeström, 1987; Roth & Lee, 2007) Results Problem 7+3=□+2 Explanations 7 + 3 = 10 and 8 + 2 = 10 7 + 3 = 10 Answers 10 8 12 Ambivalent Other Numbers 7 + 3 = 10 + 2 = 12 Ambiguous 7 + 3 = 10 and 10 + 2 = 12 Results No shared object No possibility of boundary crossing Results Shared object Potential for boundary crossing Results Shared object Boundary crossing event Discussion Students’ answers and explanations: • reflect how they express the mathematical structure of the problem and it differs from a mathematician’s approach • provide tools for conversations about learning • suggest future teaching directions (e.g., increase algebra-like language) Implications In and Beyond Mathematics Classrooms • A focus on what students know and can do (fluency) • Allows students and teachers to recognise the tools present in their acts of communication about mathematics • Antecedents of teachable moments can be recognised and developed into deliberate acts of teaching Solving a Missing Number Problem Social situation of development (Vygotsky) Thank you [email protected]