Columbus Regional Mathematics Collaborative - Language Proficiency in Mathematics and Enumeration

This is a short video summary of two research articles by a current Columbus State University mathematics education graduate student, Jami Welch, in the EdS program. The CRMC hopes you enjoy!

Shortened Written Description by Jami:
Battista (1999/2022) investigated how fifth-grade students build a conceptual understanding of volume through hands-on constructions and reasoning strategies. The focus is on spatial structuring—the ability to mentally organize and represent objects in arrays. In the classroom, the teacher prompted students to predict how many cubes would fit inside different boxes, then test those predictions using actual cubes (Battista, 1999/2022). The findings highlighted the importance of making predictions before using manipulatives, as this encourages strategic thinking and reflective communication (Battista, 1999/2022). The study emphasized that students benefit from acting like scientists—making conjectures, testing ideas, and navigating confusion as part of the learning process. Repeated and varied opportunities to construct and refine mathematical reasoning are critical for deep understanding (Battista, 1999/2022).

Another study explores the connection between language proficiency and algebraic thinking, emphasizing metalinguistic awareness—the ability to reflect on and analyze spoken or written language (MacGregor & Price, 1999/2022). Unlike prior research that often included confounding variables such as socioeconomic status, this study isolates metalinguistic skills. The authors identify two key components of metalinguistic awareness relevant to algebra learning: symbol awareness and syntax awareness (MacGregor & Price, 1999/2022). Success in algebra is linked not just to reading ability but to the capacity to understand the structure of language, which mirrors the structure of algebraic expressions. The study assessed 1,500 students using both language and algebra tests. After revising an initial test that was too easy, the researchers found strong correlations between language proficiency and algebra performance across all grade levels (MacGregor & Price, 1999/2022). The findings suggest a need for further research on whether algebra instruction should be delayed until students have developed sufficient metalinguistic awareness and how instruction can better support students in navigating symbolic challenges (MacGregor & Price, 1999/2022).

Battista, M. T. (2022). Fifth graders’ enumeration of cubes in 3D arrays: Conceptual progress in an inquiry-based classroom. In J. Sowder & B. Schappelle (Eds.), Lessons learned from research (pp. 75–83). National Council of Teachers of Mathematics. (Reprinted from “Fifth graders’ enumeration of cubes in 3D arrays: Conceptual progress in an inquiry- based classroom,” 1999, Journal for Research in Mathematics Education, 30(5), 417–448, https://doi.org/10.2307/749772)

MacGregor, M., & Price, E. (2022). An exploration of aspects of language proficiency and algebra learning. In J. Sowder & B. Schappelle (Eds.), Lessons learned from research (pp. 109–113). National Council of Teachers of Mathematics. (Reprinted from “An exploration of aspects of language proficiency and algebra learning,” 1999, Journal for Research in Mathematics Education, 30(3), 449–467, https://doi.org/10.2307/749773)