The Impact of Mental Computation on Children's Mathematical Communication, Problem Solving, Reasoning, and Algebraic Thinking

Moving from arithmetic to algebraic thinking at early grades is foundational in the study of number patterns and number relationships. This qualitative study investigates mental computational activity in a third grade classroom's and its relationship to algebraic thinking and reasoning. The data sources include classroom observations, field notes, students' verbal and written communications, and interviews. The study occurs in two phases; phase one includes establishing roles, rules, and expectations regarding how to talk about mathematical ideas; and phase two involves creating a classroom community that encourages participation, active listening, students' voices, and multiple perspectives. The findings of the study suggest that students' verbal communication enhances their problem-solving, reasoning, and communication. In addition, the findings suggest that creating learning opportunities for all students to do sophisticated mathematics requires competent and caring teachers who know their students' backgrounds, who understand the subject, and have strong pedagogical knowledge.