U.S. grade 4–6 students’ rational-number substitutions for odd-sum unknown addend tasks

ABSTRACT

Research findings have established common student misconceptions for literal symbolic representations of variables but lack corresponding findings of when or how these misconceptions arise. This article reports findings from an exploratory study of U.S. grade 4–6 students’ conception(s) for various representations of unknown addends commonly found in U.S. elementary mathematics textbooks. Thirty-six U.S. grade 4–6 students participated in two semistructured task-based interviews designed to explore their conception(s) of conventional and nonconventional representations of unknown addends as revealed by their number substitutions across task types and core mathematical tasks. Results showed that participants initially demonstrated a bias toward positive integers, upon further questioning a bias toward non-negative integers, potential conflict factors related to rational-number substitutions, and did not demonstrate common difficulties with literal symbols exhibited by students in algebra and higher-level mathematics courses.

KEYWORDS:

• Algebraic thinking
• grades 4–6
• mathematical representations
• number sense
• operation sense

Notes

¹ No consent forms were received for sixth graders at site A, resulting in six sixth-grade participants. Due to a video camera malfunctioned during one sixth grader’s interview, the number of students included in the results section is 35.

² In conventional algebraic terms, a response for that the y’s can only be 6 or that in the equation the x and y have to be different values would indicate that the participant is distinguishing between the unknown addends.