Student's understanding and misconception of the concept of variable in preliminary algebra

Understanding the concept of variable is a foundation for comprehension of many concepts of algebra. Abstract nature and multiple applications of variables are perceived as difficult by students. The goal of current research - which was a descriptive survey - was to identify misconceptions about the concept of variable in preliminary algebra. In this study, 185 female 10 years old students in two educational districts of Tehran were selected based on convenience sampling method. Measurement tools for this study were a written exam and a semi-structured interview. The reliability of the test was calculated using Cronbach’s Alpha (α = 0.811).The results showed that many students have a limited understanding of the concept of variable. Students’ performance in understanding the variable as a general number was weaker than the other application of variable as a specific unknown and its application in functional relationship. Moreover, they had various misconceptions such as considering variable as a label or abbreviation of the name of objects, considering a variable as a specific number, determining the amount of variable according to its sign, processing the non-homonymous units as homonymous ones, and supposing variable as positive number. They also believed that different variables cannot hold the same value.