Variables versus numbers: Effects of symbols and algebraic knowledge on students’ problem-solving strategies

Yun-Chen CHAN, Erin OTTMAR, Hannah SMITH, Avery H. CLOSSER

Research output: Contribution to journalArticlespeer-review

Abstract

To efficiently solve mathematical expressions and equations, students need to notice the systemic structure of mathematical expressions (e.g., inverse relation between 3 and − 3 in 3 + 5–3). We examined how symbols—specifically variables versus numbers—and students’ algebraic knowledge impacted seventh graders’ problem-solving strategies and use of systemic structures within an online algebra game where students could dynamically transform expressions. We found that on simple problems, symbols did not impact students’ strategy efficiency, although students with higher vs lower algebraic knowledge were more efficient at solving these problems. On complex problems, students with higher algebraic knowledge were more efficient at solving variable vs numerical problems, whereas students with lower algebraic knowledge were less efficient at solving variable vs numerical problems. The visualizations and examination of first steps further revealed that whether students leveraged systemic structures during their problem-solving varied across problems. The findings have implications for research on cognitive processes of symbols and practices on teaching mathematics. Copyright © 2022 Published by Elsevier Inc.
Original languageEnglish
Article number102114
JournalContemporary Educational Psychology
Volume71
Early online dateSep 2022
DOIs
Publication statusPublished - Oct 2022

Citation

Chan, J. Y.-C., Ottmar, E., Smith, H., & Closser, A. H. (2022). Variables versus numbers: Effects of symbols and algebraic knowledge on students’ problem-solving strategies. Contemporary Educational Psychology, 71. Retrieved from https://doi.org/10.1016/j.cedpsych.2022.102114

Keywords

  • Variables
  • Algebra
  • Problem solving
  • Mathematical structure
  • Online learning

Fingerprint

Dive into the research topics of 'Variables versus numbers: Effects of symbols and algebraic knowledge on students’ problem-solving strategies'. Together they form a unique fingerprint.