Developmental Growth Trajectories of Students' Fraction Arithmetic Skills from Fourth through Sixth Grades

• In Event: Poster Session 10
  In Poster Session: PS 10 Topic - Education, Schooling

Abstract

Fraction proficiency is critical for success in algebra, STEM professions, and performing everyday skills (e.g., cooking, home repairs, and personal finances) (Booth & Newton, 2012; NMAP, 2008; Siegler et al., 2012). Based on common core benchmarks (e.g. CCSSO, 2010) students typically receive their fraction instruction between 4th and 6th grades. Unfortunately, many students make little or no progress during this critical period (Resnick et al., 2017) and are thus unprepared for algebra. Fraction arithmetic appears to be especially difficult for struggling students (e.g., Siegler & Pyke, 2013; Newton et al., 2014).

To better understand students’ fraction arithmetic difficulties, we documented student growth of these skills between 4th and 6th grades. Participants included 536 students of diverse ethnicities, socioeconomic backgrounds, and ability levels. Fraction addition and subtraction word problems involving common denominators were administered five times over the study period.

Latent class growth analysis (LCGA) was used to explore whether students displayed distinct fraction arithmetic growth trajectories during the intermediate grades. A three class linear model (Consistently Accurate, High Growth, and Low Growth) was ultimately selected based on model fit and interpretability. Individuals in Class 1 (Consistently Accurate), displayed high fraction arithmetic accuracy in the fall of 4th grade (M = .772), followed by small yet significant growth resulting in near perfect accuracy in the winter of 6th grade (M = .966). Students in Class 2 (High Growth) demonstrated initial low levels of fraction arithmetic accuracy (M = .026) but large growth across subsequent time points, yielding high levels of accuracy in the winter of 6th grade (M = .927). In contrast, student in Class 3 (M = .927) exhibited low levels of fraction arithmetic accuracy across the five assessment time points. Although individuals in Class 3 displayed significant growth from the fall of 4th grade (M = .133) to the winter of 6th grade (M = .318), they still displayed poor fraction arithmetic accuracy on the final assessment, answering the majority of questions incorrectly (i.e. mean accuracy > .5).

Preliminary analysis of student responses indicated two main types of errors: (1) whole number bias errors where students added/subtracted across the denominators
(e.g., 3/4 - 1/4 = 2/0) and (2) other errors, reflecting a mix of inappropriate procedures (e.g., generating multidigit whole numbers, multiplying instead of adding, and guessing).

Overall, results indicate that among students who initially struggle in fraction arithmetic (i.e. Class 2 and Class 3), the majority respond to classroom fraction instruction; however, a sizable portion of students do not. These low growth students are particularly concerning given these skills are expected to be well mastered by the 6th grade (CCSSO, 2010). Preliminary error analyses suggest difficulties with fraction arithmetic are linked to whole number bias and use of conceptually inappropriate procedures. Together, these findings suggest struggling students possess fundamental difficulties that should be addressed by instruction grounded in core fraction and number concepts to promote the growth and development in this area.

Authors

• Kelly-Ann Gesuelli, University of Delaware
  Presenting Author

• Nancy C Jordan, University of Delaware
  Non-Presenting Author