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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

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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