Exploring the association between self-efficacy and future utility beliefs in mathematics: A practical tutorial on correspondence analysis

It has long been understood that there exists a strong association between a student’s belief in the future utility of mathematics and their self-efficacy in mathematics. This study re-examines this association by studying these variables based on data collected from a sample of 21,444 ninth-grade students who participated in the 2009 High School Longitudinal Study (HSLS09). The nature of the association between future utility beliefs of students in mathematics and self-efficacy of students in mathematics is explored visually using the simple correspondence analysis technique. The main feature that will be utilised from this technique is a two-dimensional graphical display, referred to as a correspondence plot. By studying the HSLS09 data, the first two axes of such a plot summarised nearly 99% of the statistically significant association that exists between a student’s beliefs in the future utility of mathematics and their mathematics self-efficacy. It is shown visually that students who strongly believe in the future importance of studying mathematics also perform strongly in the subject, while those who do not believe that there is any future utility from studying mathematics do not perform well at it. This study, therefore, suggests that mathematics ability is associated with a student’s perception of its future importance.