Interpreting literal symbols in algebra under the effects of the natural number bias

ABSTRACT

In this study, we investigated how secondary students interpret algebraic expressions that contain literal symbols to stand for variables. We hypothesized that the natural number bias (i.e., the tendency to over-rely on knowledge and experiences based on natural numbers) would affect students to think that the literal symbols stand for natural numbers only rather than for any rational or real number (integrity effect); and that the arithmetical values of the algebraic expressions are of the same sign as the expressions’ phenomenal sign (phenomenal sign effect). The participants (138 8th and 9th graders) were asked to evaluate 48 statements about numbers that can or cannot be assigned to six algebraic expressions that contained literal symbols (e.g., a, -d-4). The results supported the main hypothesis of the study with respect to the integrity as well as the phenomenal sign effect and also indicated that the former was stronger than the latter. Additionally, the most salient characteristics of the form of each expression, such as its sign, appeared to affect students’ responses regarding the arithmetical values they may represent. Theoretical and educational implications are discussed.

KEYWORDS:

• Literal symbols
• variables
• algebraic symbols
• natural number bias
• negative sign

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Konstantinos P. Christou

Konstantinos P. Christou is an Assistant Professorin the School of Early Childhood Education at the Aristotle University of Thessaloniki, Greece. His first degree is in Mathematics, and he holds a master’s degree in Mathematics Education, and a Ph.D. in Basic and Applied Cognitive Science (University ofAthens, Greece). His main research area is the learning and teaching of mathematics from very early ages till adult living. He is particularly interested in studying the development of the concepts and the understanding of algebraic concepts such as the concept of variable.

Despoina Ioanna Kyrvei

Despoina Ioanna Kyrvei is currently working as a Mathematics teacher with children with learning disabilities in Greek public High Schools. Her first degree is in Mathematics and she also has a master'sdegree in Mathematics Education. Her research interests lie in teaching and learning Mathematics in various educational environments.

Xenia Vamvakoussi

Xenia Vamvakoussi is an Associate Professor in the Department of Early Childhood Education at the University of Ioannina, Greece. She holds a Mathematics degree, a master’s degree in Mathematics Education, and a Ph.D. in Basic and Applied Cognitive science (University of Athens, Greece). Her research is in the area of mathematics learning and teaching focusing on number concepts and multiplicative reasoning in a broad age range, from pre-primary children to educated adults, including mathematics educators.