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1

IS THERE A GAP OR CONGRUENCY EFFECT? A CROSS-SECTIONAL STUDY IN STUDENTS’ FRACTION COMPARISON

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González-Forte J. M., Fernández C., Van Dooren W.
Studia Psychologica
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2020
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vol. 62
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issue 2
109 – 122
EN
Many studies have addressed the natural number bias in fraction comparison, focusing on the role of congruency. However, the congruency effect has been observed to operate in the opposite direction, suggesting that a deeper explanation must underlie students’ different reasoning. We extend previous research by examining students’ reasoning and by studying the effect of a gap condition in students’ answers. A cross-sectional study was conducted on 438 students from the 5th to 10th grade. The results showed that the gap effect could explain differences between congruent and incongruent items. Moreover, students’ use of gap thinking decreased towards the end of Secondary Education.
2

ROLE OF THE INHIBITION OF NATURAL NUMBER BASED REASONING AND STRATEGY SWITCH COST IN A FRACTION COMPARISON TASK

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Van Hoof J., Ceulemans E., Van Dooren W.
Studia Psychologica
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2021
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vol. 63
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issue 1
64 – 76
EN
Previous research amply showed the importance of a good fraction understanding but also people’s lack of fraction understanding. It is therefore important to investigate the cognitive processes that underlie reasoning with fractions. The present study investigated the role of inhibition and switch costs in fraction comparison tasks. Participants solved a fraction comparison task that alternated between 4 items congruent and 4 items incongruent with natural number reasoning. This allowed to not only investigating congruency switch effects, but also inhibition, given that inhibition was experimentally increased by the prolonged exposure to incongruent trials. Based on data of seventh graders, the present study showed that inhibition does not only play a role in learners’ general mathematics achievement, but also in specific areas of mathematics, such as fractions. Moreover, a switch cost was found in the lower accuracy rates and higher reaction times needed to correctly solve switch items compared to non-switch items.
3

RELATION BETWEEN LEARNERS’ SPONTANEOUS FOCUSING ON QUANTITATIVE RELATIONS AND THEIR RATIONAL NUMBER KNOWLEDGE

88%
Van Hoof J., Degrande T., McMullen J., Hannula-Sormunen M., Lehtinen E., Verschaffel L., Van Dooren W.
Studia Psychologica
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2016
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vol. 58
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issue 2
156 – 170
EN
Many difficulties learners have with rational number tasks can be attributed to the “natural number bias”, i.e. the tendency to inappropriately use natural number properties in rational numbers tasks (Van Hoof, 2015). McMullen and colleagues found a relevant source of individual differences in the learning of those aspects of rational numbers that are susceptible to the natural number bias, namely Spontaneous Focusing On quantitative Relations (SFOR) (McMullen, 2014). While McMullen and colleagues showed that SFOR relates to rational number knowledge as a whole, we studied its relation with several aspects of the natural number bias. Additionally, we 1) included test items addressing operations with rational numbers and 2) controlled for general mathematics achievement and age. The results showed that SFOR related strongly to rational number knowledge, even after taking into account several control variables. The results are discussed for each of the three aspects of the natural number bias separately.
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