Algebraic Equations: Can Middle-School Students Meaningfully Translate from Words to Mathematical Symbols?

Using symbolic algebra to represent and solve linear equations is one of the expectations within the Algebra content standard for the 6–8-grade band in the National Council of Teachers of Mathematics (NCTM) Principles and Standards for School Mathematics (2000). Students' understanding of these concepts, even before a formal algebra course, prepares them for future success. Students need a balance of conceptual (comprehension) and procedural (vocabulary) skills as they begin to develop algebraic understanding. This study investigated the extent to which middle school students showed facility with translating English language into mathematical symbols or vice versa using conceptual or procedural indicators as measures of comprehension and vocabulary. Students ( N = 668) in 25 middle-school teachers' classrooms were assessed on three algebra tasks. In addition, ( n = 60) random incorrect responses were examined to identify patterns in their responses that emerged. As a confirmatory procedure, five ( n = 5) students were interviewed in a cognitive lab as they solved certain tasks. Only 58 (9%) of the students answered all three items correctly showing that students were not procedurally or conceptually ready even at the seventh and eight grade level to translate from the written word to mathematical equations.