Learning fractions with and without educational technology: What matters for high-achieving and low-achieving students?

Reinhold, Frank; Hoch, Stefan; Werner, Bernhard; Richter-Gebert, Jürgen; Reiss, Kristina

doi:10.1016/j.learninstruc.2019.101264

Cited by 82 publications

(98 citation statements)

References 57 publications

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“…The schools were of type Hauptschule, which is the lowest school track of secondary school in the German school system. Students in this school track demonstrate below average performance at the end of primary school (i.e., grade 4) in mathematics, language, and science, and show typically low performance in secondary school mathematics (Götz et al, 2013;Sälzer et al, 2013;Reinhold et al, 2020). Thus, we expected to find patterns of NNB in the present sample of low-achieving students.…”

Section: Samplementioning

confidence: 76%

“…Continuous diagrams, on the other hand, do not allow for counting (Jeong et al, 2007;Boyer et al, 2008;Boyer and Levine, 2015)-because there are no countable pieces-and may force students to rely more strongly on fraction magnitude. Visual representations may be presented in dynamic formats, for example, on touchscreen devices (Reinhold et al, 2020; see also Boyer et al, 2008), which allows students to respond with gestures (i.e., drag and drop, see section Magnitude Estimation Task). Compared to paper-pencil assessment, touchscreen devices may prevent students from using procedural part-whole strategies (e.g., calculating the angle of the segment in a circle diagram, or adding auxiliary lines to the representation) that do not rely on fraction magnitude processing (Reinhold, 2019).…”

Section: Assessing Fraction Magnitude Processingmentioning

confidence: 99%

“…Thus, we expected to find patterns of NNB in the present sample of low-achieving students. The data was collected within the research project ALICE:fractions (Hoch et al, 2018a;Reinhold et al, 2020), 8 weeks after students received the first introduction to fraction magnitudes in school. Note that according to their curriculum, students had been formally introduced to fractions at the beginning of grade six only.…”

Section: Samplementioning

confidence: 99%

“…It is also not very clear how instruction can best support students in reaching higher levels in fraction magnitude processing, although multiple recommendations on enhancing students' understanding of fractions exist (e.g., Behr et al, 1983;Butler et al, 2003;Prediger, 2008;Obersteiner et al, 2019a;Reinhold et al, 2020). Further research with longitudinal and/or experimental designs is necessary to identify potential causal effects of instruction on transitions between the suggested levels of fraction magnitude processing.…”

Section: Natural Number Bias and Fraction Magnitudementioning

confidence: 99%

“…While our study aimed at assessing fraction magnitude processing, we suggest that our digital assessment tool can be utilized as an effective tool for supporting students' development of fraction magnitude, when adequate feedback is implemented (Reinhold et al, 2020).…”

Section: Assessing Fraction Magnitude With Continuous Diagrams On Toumentioning

confidence: 99%

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The Interplay Between the Natural Number Bias and Fraction Magnitude Processing in Low-Achieving Students

et al. 2020

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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 ["Natural Number Bias" (NNB)]. Yet, the relation between these two difficulties is not well-understood. 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. 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. 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. 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). 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. 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. 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. The results of this study suggest that the occurrence of the natural number bias and the ability to process fraction magnitude are closely related. The continuous representations used in our digital assessment tools appeared to be suitable for assessing both the natural number bias and fraction magnitude processing.

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Section: Samplementioning

confidence: 76%