11/13/2023 0 Comments Are fractions natural numbers![]() Another issue is that the tasks that have been used to assess fraction magnitude often allow the use of alternative strategies (e.g., number line estimation task) that may not solely require processing of fraction magnitude, or they actually require processing the magnitudes of two fractions instead of one fraction (e.g., fraction comparison task). ![]() Moreover, most previous studies have used whole-sample analyses to study students’ difficulties, while research about individual students’ profiles is scarce (but see Rinne et al., 2017 Gómez and Dartnell, 2019 González-Forte et al., 2019). While both difficulties have been discussed in the literature, there is still little evidence about the relation between the two. Two major difficulties seem to be that students (1) are not sufficiently able to understand and process fraction magnitudes, and (2) rely on natural number principles when reasoning about rational numbers, causing Natural Number Bias (see Ni and Zhou, 2005 and see section “The Natural Number Bias as a Source of Individual Errors in Solving Fraction Problems”). Plenty of research has shown that many students struggle with learning of rational numbers, particularly of fractions (e.g., Behr et al., 1983 Siegler et al., 2011 Lortie-Forgues et al., 2015). The continuous representations used in our digital assessment tools appeared to be suitable for assessing both the natural number bias and fraction magnitude processing. The results of this study suggest that the occurrence of the natural number bias and the ability to process fraction magnitude are closely related. Students in the No Bias cluster were significantly slower to solve both fraction comparison and fraction magnitude estimation tasks than students in the other clusters. Linear mixed models on the percent absolute error in the magnitude estimation task revealed significantly lower percent absolute error for students in the No Bias cluster compared to students in the other two clusters. Only students in the No Bias cluster but not students in the other clusters demonstrated a distance effect in symbolic fraction comparison, suggesting fraction magnitude processing. A cluster analysis on the comparison task revealed three distinct clusters: a Typical Bias cluster (better performance on symbolic fraction comparison items congruent to natural number-based reasoning), a Reverse Bias cluster (better performance on items incongruent to natural number-based reasoning), and a No Bias cluster (similar performance on congruent and incongruent items). We analyze data of 234 low-achieving 6th-grade students from Germany who completed a symbolic fraction comparison task, and a fraction magnitude estimation task with continuous circle and tape diagrams. In the present study, we investigate individual students’ profiles of the occurrence of the NNB and their ability to process fraction magnitude, using a dynamic assessment that utilizes continuous diagrams on touchscreen devices. Moreover, while most studies of the NNB relied on analyses of whole samples, there is empirical evidence that the occurrence of the NNB differs between student subgroups. Yet, the relation between these two difficulties is not well-understood. ![]() Research has identified two core difficulties many students have with fractions: first, they often struggle with processing fraction magnitudes, and second, they rely on natural number concepts in fraction problems. ![]() 3Centre for International Student Assessment, Technical University of Munich, Munich, Germany.2Institute for Mathematics Education, University of Education, Freiburg, Germany.1Heinz Nixdorf-Chair of Mathematics Education, TUM School of Education, Technical University of Munich, Munich, Germany.Frank Reinhold 1* Andreas Obersteiner 2 Stefan Hoch 1 Sarah Isabelle Hofer 3 Kristina Reiss 1,3 ![]()
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