Previous theoretical research has revealed conceptual similarities among a number of mathematical learning theories and theories regarding language acquisition. This intersection of ideas led to a novel framework defining four stages of mathematical learning: Receiving, Replicating, Negotiating Meaning, and Producing. Through qualitative research…

This study begins by connecting semantic elaboration with conceptual understanding and syntactic elaboration with procedural understanding in the context of fractions. Through case studies and discourse analysis, the work and communication of students in fourth through sixth grade is analyzed to determine the extent of their semantic and syntactic…