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Intuitive errors in learners’ fraction understanding: A dual-process perspective on the natural number bias

Although a good rational number understanding is very important, many learners struggle to understand fractions. Recent research attributes many of these difficulties to the natural number bias - the tendency to apply natural number features in rational number tasks where this is inappropriate. Previous correlational dual process studies found evidence for the intuitive nature of the natural number bias in learners' response latencies. However, the reported correlations do not ascertain the caus...

Abstract Many students still have not developed a robust understanding of rational number concepts at the end of primary school, despite several years of instruction on the topic. The present study aims to examine the patterns, predictors, and outcomes of the development of rational number knowledge in lower secondary school. Latent transition analysis revealed that rational number development from primary to lower secondary school (N = 362) appears to follow similar patterns as in younger stude...

Refutation texts compensate for detrimental effects of misconceptions on comprehension and metacomprehension accuracy and support transfer.

Misconceptions impair not only learners’ comprehension of a text but also the accuracy with which they judge their comprehension, that is, metacomprehension accuracy. Refutation texts are beneficial to elicit conceptual-change processes and thus to overcome the detrimental impact of misconceptions on comprehension. However, it is unclear whether refutation texts and the conceptual-change processes induced by reading them benefit metacomprehension accuracy in addition to comprehension and how rob...

In this paper we focus on the development of rational number knowledge and present three research programs that illustrate the possibility of bridging research between the fields of cognitive developmental psychology and mathematics education. The first is a research program theoretically grounded in the framework theory approach to conceptual change. This program focuses on the interference of prior natural number knowledge in the development of rational number learning. The other two are the r...

Towards a mathematically more correct understanding of rational numbers: A longitudinal study with upper elementary school learners

Abstract In this study we longitudinally followed 201 upper elementary school learners in the crucial years of acquiring rational number understanding. Using latent transition analysis we investigated their conceptual change from an initial natural number based concept of a rational number towards a mathematically more correct one by characterizing the various intermediate states learners go through. Results showed that learners first develop an understanding of decimal numbers before they have ...

Graphicacy is an important skill in today’s society; however, the interpretation of graphs proofs to be more difficult than it might seem. In this study, we focus on one specific misinterpretation, the area misinterpretation of box plots, which is caused by incorrect heuristic processing of salient features of the box plot. In this study, we tried to eradicate the area misinterpretation by the use of refutational text. We tested whether participants exposed to refutational text solved items on t...

Refutational text is one of the many instructional techniques that have been proposed to be used in education as a way to achieve effective learning. The aim of refutational text is to transform misconceptions into conceptions that are in line with current scientific concepts. This is done by explicitly stating a misconception, refuting it, and providing a correct conception. It has been applied in various curricular domains, and seems to be effective in inducing cognitive conflicts in learners ...

In this chapter, we elaborate on learners’ difficulties with rational numbers. We begin with the importance of robust rational number understanding for learners’ general mathematics achievement and then move to the challenges that many learners face with respect to various aspects of rational numbers. Third, we elaborate on previous research that focused on a major source of learners’ difficulty, namely the natural number bias. Fourth, we introduce two complementary theoretical perspectives that...

This thesis is a summary of a pilot study adopting the design experiment methodology investigating alternative approaches to the teaching of probability – the classical approach (called “Laplace approach” in our study) and the axiomatic approach (called “Properties approach”) – and alternative pedagogical treatments of these approaches: with or without explicit refutations of common misconceptions by the teacher. Four short video-lessons were designed, focused on Bernoulli trials: “Laplace-expos...

Abstract Two experiments investigated the whole number bias in the representation of fraction magnitudes with adults. A fraction magnitude comparison task was used where half of the comparisons were consistent with whole number ordering and the other half were not. Distance effects were found in Experiment 1 indicating that participants were comparing the magnitude of the whole fraction rather than just the parts. However, accuracy and response time also depended on the comparisons' consistency ...

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This study examined how reported use of learning strategies and preexisting beliefs about the effectiveness of rehearsal and comprehension-oriented strategies relate to the comprehension of text on learning strategies, and how text comprehension is related to later use of strategies and the completion of learning tasks. The participants were 2,706 students from Grades 3 and 4, and 3,782 students from Grade 9 across Estonia. Students’ learning strategies and learning outcomes were assessed via a ...

Welcome to this issue focussing on literacy as well as the self (self-studies). As is befitting an international Journal, you will see investigations from researchers representing a range of cultur...