Fraction errors in a digital mathematics environment: Latent class and transition analysis

Abstract

Student struggles with fractions are well documented, and due to fractions’ importance to later mathematics achievement, identification of the errors students make when solving fraction problems is an area of interest for both researchers and teachers. Within this study, we examine data on student fraction problem errors in pre- and post-quizzes in a digital mathematics environment. Students (n = 1,431) were grouped by prevalence of error types using latent class analysis. Three different classes of error profiles were identified in the pre-quiz data. A latent transition analysis was then used to determine if class membership and class structure changed from pre- to post-quiz. In both pre- and post-quiz, there was a class of students who appeared to be guessing and a class of students who performed well. One class structure was consistent with the idea that early fraction learners rely heavily on whole number principles. Identification of co-occurrence of and changes to fraction errors has implications for curricular design and pedagogical decisions, especially in light of movements toward personalized learning systems.

Fraction arithmetic development: An examination of students’ patterns of growth and errors across the intermediate grades.

“…We calculated the frequency and proportion of error types for each student across grade levels for all eight fraction arithmetic word problems. Proportion of errors represent the number of times a student makes a certain type of error among the total number of errors made on the assessment and were used to control for the differences in the total number of errors displayed (Karamarkovich & Rutherford, 2019). Students’ errors on the fraction arithmetic assessments were hand scored by the primary researcher using the previously described coding scheme.…”

Applying Fractional Strategies on Number Line among Primary School Students

“…On the other hand, making a move to study the subsequent topics of mathematics, upon completing whole numbers, compels a strong foundation not only in whole numbers but also the previous concepts namely the basic mathematical operations. In fact, while working with fractions, students rely heavily on the principles of whole numbers (Karamarkovich & Rutherford, 2019). All concepts learned and mastered as prior knowledge need to be integrated and connected to the new concepts.…”

Analysis of Elementary School Students' Difficulties in Fraction Addition

“…Fractions are important in elementary school students learning mathematics and everyday life (Braithwaite et al, 2017;Siegler et al, 2011). The importance of fractions in elementary school mathematics education is a prerequisite for students' success with subsequent material, including algebra (Fennell & Karp, 2016;Flores et al, 2020;Karamarkovich & Rutherford, 2019). Meanwhile, fractions in everyday life are often used to divide food into equal sizes or understand the quantity of packages that are divided into multiple parts (Muharram et al, 2019).…”