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

• Published in: Mathematical thinking and learning Vol. 26; no. 4; pp. 331 - 344
• Main Authors: Christou, Konstantinos P., Kyrvei, Despoina Ioanna, Vamvakoussi, Xenia
• Format: Journal Article
• Language: English
• Published: Philadelphia Routledge 01.10.2024; Taylor & Francis Ltd
• Subjects: Algebra; algebraic symbols; Bias; Integrity; Literal symbols; natural number bias; negative sign; Number theory; Real numbers; Students; Symbols; variables
• ISSN: 1098-6065; 1532-7833
• DOI: 10.1080/10986065.2022.2128276

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.