Sequential exploratory design by performing correspondence analysis to investigate procedural fluency of undergraduate student

Abstract

Procedural fluency is one of the strands in mathematical proficiency that has been a concern of several researchers in the last ten years. Accordingly, this study was designed to investigate the procedural fluency of undergraduat e students conducted by sequential exploratory design on the mixed-method research. Qualitative research observed students' procedural fluency proficiency in the first phase, followed by the second phase of quantitative research conducted through k-mean clustering and correspondence analysis. K-mean clustering aims to explain students' procedural fluency with similar characteristics in terms of initial mathematical abilities. Meanwhile, the correspondence analysis seeks to observe the association structure of procedural fluency based on the students' initial mathematical abilities. This study involved 97 participants selected from undergraduate students in the Discrete Mathematics courses offered by the mathematics education department at one university in Indonesia. There are three indicators of procedural fluency that are measured, including flexibility, efficiency and accuracy. The results showed that only a few students, or around 23.71%, could dominate the three indicators and were categorized as Grade 3. The remaining 32.99% and 43.30% were the percentages of Grade 1 and Grade 2, respectively. The largest proportion were students with good initial mathematical abilities and procedural fluency in Grade 2 that reached 25.77%. The statistical results obtained were a chi-square statistic of 24.243, which was greater than the critical value. It indicates that there is a significant association between procedural fluency and students' initial mathematical abilities. Furthermore, the association structure is depicted in the correspondence plot.