Exploring how children’s conceptions might advance through their implicit knowledge provides a fundamental view into children’s mathematics and elucidates possible alternative definitions of “learning difference (LD)”. I present an evolving theoretical framework that depict children with LD’s knowing and learning as nascent understandings that emerge from a real-time negotiation of meaning within “small environments” of instructional intervention. These negotiations are supported, or not, by the teacher’s propensity to engage in the knowledge of children and use teaching to construct shared goals for learning. Implications of the work include new ways educators might define LDs as a complex phenomenon that reflects how children’s knowledge of mathematics advances, or not, through a shared cognition grounded in children’s unique knowing and learning.
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