Poster #35 - Performance Profiles in Fraction Arithmetic

• In Event: 1-169 - Poster Session 04
  In Poster Session: PS 04 Section - Cognitive Processes

Integrative Statement

Fractions are an important topic in mathematical development. Knowledge of fractions predicts success in algebra and affects children’s overall math achievement years later (Booth & Newton, 2012; Siegler et al., 2012). Unfortunately, fractions, and fraction arithmetic in particular, are challenging to learn; many children never master them (Lortie-Forgues, Tian, & Siegler, 2015). Prior research on fraction arithmetic has examined differences between higher- and lower-performing children in order to identify predictors of success in learning (e.g., Siegler & Pyke, 2013). However, little is known about the individual differences in children’s performance, especially within the population of less successful learners.

In the present study, latent profile analysis (LPA) was used to analyze patterns of accuracy across different types of fraction arithmetic problems in two datasets of U.S. children—one from a previous study of sixth and eighth graders (Siegler & Pyke, 2013; N = 120) and one from a new study of seventh and eighth graders (N = 394). Problems varied in arithmetic operation (addition, subtraction, multiplication, division) and denominator equality (equal or unequal).

The analyses revealed four profiles with analogous characteristics in both datasets: (1) High Performers, characterized by high accuracy on all problem types, (2) Multiplication Accurate, characterized by high accuracy on multiplication problems, (3) Addition/Subtraction Accurate, characterized by high accuracy on addition and subtraction problems, and (4) Common Problems Accurate, characterized by high accuracy on problem types that are more common in mathematics textbooks (Braithwaite & Siegler, 2018), specifically, equal denominator addition and subtraction and unequal denominator multiplication problems.

Error analysis revealed that distinct patterns of strategy use underlie each profile’s characteristic accuracy pattern. Children who fit the Multiplication Accurate and Addition/Subtraction Accurate profiles demonstrated strategy perseveration, consistently applying only one strategy—multiplication or addition/subtraction, respectively—across problem types. Children who fit the Common Problems Accurate profile were less consistent with their strategy use, but tended to use the addition/subtraction strategy more on equal denominator problems and the multiplication strategy more on unequal denominator problems. Although High Performers committed errors infrequently, a more common strategy error was applying the addition/subtraction strategy to equal denominator multiplication problems, a type of problem that is rare in mathematics textbooks.

The findings indicate that children encounter different difficulties with fraction arithmetic: While some children display inconsistent strategy use, other children overuse a single strategy. According to a recent theory of fraction arithmetic learning, inconsistency in strategy choices and over-generalization of strategies are generally key sources of children’s difficulties (Braithwaite, Pyke, & Siegler, 2017). The present findings extend the theory by suggesting that each of these factors is critical for different children. The findings also suggest that fraction arithmetic instruction and interventions could be made more effective by adapting them to address individual children’s needs.

Authors

• Elena Leib, University of California, Berkeley
  Presenting Author

• David Braithwaite, Florida State University
  Non-Presenting Author

• Robert Siegler, Professor
  Non-Presenting Author

• Jake McMullen, University of Turku
  Non-Presenting Author