A Case Study Examining Links between Fractional Knowledge and Linear Equation Writing of Seventh-Grade Students and Whether to Introduce Linear Equations in an Earlier Grade

As a part of the larger study, a case study of two seventh grade students, Peter and Willa, was conducted. To examine links between their fractional knowledge and algebraic reasoning, the students were interviewed twice, once for their fractional knowledge and once for their algebraic knowledge in writing linear equations that required explicit use of unknowns. Peter and Willa’s fractional knowledge influenced the linear equations they wrote to represent quantitative situations. In particular, the findings showed that a reversible iterative fraction scheme is important to understand reciprocal relationships between two quantities in writing a basic linear equation of the form ax=b. Also, considering fractions as multipliers on unknowns is important to write linear equations. Implications for the possibility of introducing linear equations in an earlier grade and how to support the introduction are suggested.