Bridging psychological and educational research on rational number knowledge

Vamvakoussi, Xenia; Christou, Konstantinos P.; Vosniadou, Stella

doi:10.5964/jnc.v4i1.82

Cited by 21 publications

(15 citation statements)

References 74 publications

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“…Similarly, educational programmes are often designed to target a specific misconception (e.g. understanding rational numbers in light of a natural numbers bias; Vamvakoussi et al, 2018 ), which require considerable time and resources from the teacher. In contrast, this was the first evaluation of an intervention informed by neuroscience that aimed to improve counterintuitive reasoning through IC training embedded within age-appropriate content from the mathematics and science curricula.…”

Section: Discussionmentioning

confidence: 99%

Domain-Specific Inhibitory Control Training to Improve Children’s Learning of Counterintuitive Concepts in Mathematics and Science

et al. 2019

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Evidence from cognitive neuroscience suggests that learning counterintuitive concepts in mathematics and science requires inhibitory control (IC). This prevents interference from misleading perceptual cues and naïve theories children have built from their experiences of the world. Here, we (1) investigate associations between IC, counterintuitive reasoning, and academic achievement and (2) evaluate a classroom-based computerised intervention, called Stop & Think, designed to embed IC training within the learning domain (i.e. mathematics and science content from the school curricula). Cross-sectional analyses of data from 627 children in Years 3 and 5 (7-to 10-year-olds) demonstrated that IC, measured on a Stroop-like task, was associated with counterintuitive reasoning and mathematics and science achievement. A subsample (n = 456) participated either in Stop & Think as a whole-class activity (teacher-led, STT) or using individual computers (pupil-led, STP), or had teaching as usual (TAU). For Year 3 children (but not Year 5), Stop & Think led to better counterintuitive reasoning (i.e. near transfer) in STT (p < .001, η p 2 = .067) and STP (p < .01, η p 2 = .041) compared to TAU. Achievement data was not available for Year 3 STP or Year 5 STT. For Year 3, STT led to better science achievement (i.e. far transfer) compared to TAU (p < .05, η p 2 = .077). There was no transfer to the Stroop-like measure of IC. Overall, these findings support the idea that IC may contribute to counterintuitive reasoning and mathematics and science achievement. Further, we provide preliminary evidence of a domain-specific IC intervention with transferable benefits to academic achievement for Year 3 children.

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Section: Discussionmentioning

confidence: 99%

Domain-Specific Inhibitory Control Training to Improve Children’s Learning of Counterintuitive Concepts in Mathematics and Science

et al. 2019

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“…Studies addressing the natural number bias phenomenon have considered three main domains in which rational numbers differ from natural numbers, causing difficulties for students: density of the rational number line, conducting operations with rational numbers, and determining rational number size (Gómez and Dartnell 2018;McMullen et al 2015;Obersteiner et al 2016;Vamvakoussi et al 2018;. In addition, the diversity of symbolic notations relating to rational numbers can be considered to be a transversal difficulty across the previous domains (DeWolf and Vosniadou 2011).…”

Section: Introductionmentioning

confidence: 99%

Various ways to determine rational number size: an exploration across primary and secondary education

et al. 2019

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Understanding rational numbers is a complex task for primary and secondary school students. Previous research has shown that a possible reason is students' tendency to apply the properties of natural numbers (inappropriately) when they are working with rational numbers (a phenomenon called natural number bias). Focusing on rational number comparison tasks, recent research has shown that other incorrect strategies such as gap thinking or reverse bias can also explain these difficulties. The present study aims to investigate students' different ways of thinking when working on fraction and decimal comparison tasks. The participants were 1,262 primary and secondary school students. A TwoStep Cluster Analysis revealed six different student profiles according to their way of thinking. Results showed that while students' reasoning based on the properties of natural numbers decreased along primary and secondary school, almost disappearing at the end of secondary school, students' reasoning based on gap thinking increased along these grades. This result seems to indicate that when students overcome their reliance on natural numbers, they enter a stage of qualitatively different errors before finally reaching the stage of correct understanding.

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“…Results further support that the NNB contributes to the effect of number size on students' evaluations of the validity of multiplication and division equations, which further suggests that classroom instructors will need to address the NNB. However, addressing the NNB in instruction is a complex endeavor that requires remedial and anticipation approaches (Vamvakoussi et al, 2018;.…”

Section: Discussionmentioning

confidence: 99%

“…Students' years of experience working with natural numbers may create a strong intuition about the results that can be expected from natural-number arithmetic (e.g., multiplication makes larger) (Greer, 1994), or addition makes larger (Dixon et al, 2001). From a framework theory approach to conceptual change, students from very early on construct an initial understanding for the number concept, which, based on their experience with counting and the sequence of the number words, acquires the characteristics of the mathematical concept of natural numbers (Gelman, 2000;Smith et al, 2005;Vamvakoussi, Christou, & Vosniadou, 2018;Vosniadou, Vamvakoussi, & Skopeliti, 2008). This initial number concept, which is organized into a framework theory for number, may form students' beliefs, their interpretations and their anticipations about the properties of numbers.…”

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confidence: 99%

“…This initial number concept, which is organized into a framework theory for number, may form students' beliefs, their interpretations and their anticipations about the properties of numbers. From this perspective, the influence of the initial number concept when reasoning with more advanced numbers such as the rational and the real numbers may result in the NNB phenomenon and lead to systematic errors in rational number tasks where the properties of natural numbers do not hold (Vamvakoussi et al, 2018). Importantly, the initial number conception remains even after learners have acquired the correct mathematical knowledge about rational numbers and, in principle, are able to solve rational number tasks.…”

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confidence: 99%

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Natural number bias in arithmetic operations with missing numbers – A reaction time study

et al. 2020

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When reasoning about numbers, students are susceptible to a natural number bias (NNB): When reasoning about non-natural numbers they use properties of natural numbers that do not apply. The present study examined the NNB when students are asked to evaluate the validity of algebraic equations involving multiplication and division, with an unknown, a given operand, and a given result; numbers were either small or large natural numbers, or decimal numbers (e.g., 3 × _ = 12, 6 × _ = 498, 6.1 × _ = 17.2). Equations varied on number congruency (unknown operands were either natural or rational numbers), and operation congruency (operations were either consistent – e.g., a product is larger than its operand – or inconsistent with natural number arithmetic). In a response-time paradigm, 77 adults viewed equations and determined whether a number could be found that would make the equation true. The results showed that the NNB affects evaluations in two main ways: a) the tendency to think that missing numbers are natural numbers; and b) the tendency to associate each operation with specific size of result, i.e., that multiplication makes bigger and division makes smaller. The effect was larger for items with small numbers, which is likely because these number combinations appear in the multiplication table, which is automatized through primary education. This suggests that students may count on the strategy of direct fact retrieval from memory when possible. Overall the findings suggest that the NNB led to decreased student performance on problems requiring rational number reasoning.

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Bridging psychological and educational research on rational number knowledge

Cited by 21 publications

References 74 publications

Domain-Specific Inhibitory Control Training to Improve Children’s Learning of Counterintuitive Concepts in Mathematics and Science

Domain-Specific Inhibitory Control Training to Improve Children’s Learning of Counterintuitive Concepts in Mathematics and Science

Various ways to determine rational number size: an exploration across primary and secondary education

Natural number bias in arithmetic operations with missing numbers – A reaction time study

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