The relation between metastrategic knowledge,strategy use and task performance: Findings and reflections from a numerosity judgement task     

Koen Luwel  Joke Torbeyns  Lieven Verschaffel 《European Journal of Psychology of Education - EJPE》2003,18(4):425-447

In the research literature several positions concerning the role played by metacognition in adaptive strategy choice can be distinguished. While many authors adhere so-called metacognitive models of strategy choice and strategy change, others have questioned the extent to which metacognitive factors are associated with strategy choice and task performance and have proposed alternative theoretical frameworks wherein strategy choices are described in terms of associative models. In the present article we report data coming from a larger research project on the development of children’s numerosity judgement strategies and skills. The experimental task involved judging numerosities of colored blocks presented in a rectangular grid. Participants were 59 second grade and 50 sixth grade children, whose strategic performance data — obtained by means of a systematic analysis of their response-time patterns — were compared with interview data collected at the end of the experiment. The major result of this comparison is that not only the children from the oldest age group, but also the children from the youngest age group showed clear evidence of metacognitive awareness and understanding of different aspects of their strategic performance.  相似文献   

The development of computational estimation in the transition from informal to formal mathematics education     

Sekeris  Elke  Empsen  Michaël  Verschaffel  Lieven  Luwel  Koen 《European Journal of Psychology of Education - EJPE》2021,36(3):845-864

European Journal of Psychology of Education - The transition from informal to formal mathematics is an important episode in children’s mathematical development. The current study investigated...  相似文献   

The attainment of doctoral degrees at Flemish Universities: a survival analysis     

M. S. Visser  M. Luwel  H. F. Moed 《Higher Education》2007,54(5):741-757

This paper examines the propensity to attain a Ph.D. degree at the five largest universities in Flanders, the Dutch speaking part of Belgium. It provides insight into the rate at which junior scholars appointed at the universities involved attained their Ph.D.-degree, and the duration of the doctoral training period. Cox’s regression model was applied to statistically analyse the influence of a number of ‘demographic’ and ‘merit’ variables, and variables related to funding source and type of appointment of the junior scholarly staff. Large differences in Ph.D. durations and attainment rates were found across funding sources, research disciplines and types of appointments. The policy background and implications are discussed briefly.  相似文献   

Strategic aspects of children’s numerosity judgement     

Koen Luwel  Lieven Verschaffel  Patrick Onghena  Erik De Corte 《European Journal of Psychology of Education - EJPE》2001,16(2):233-255

A previous study (Luwel, Verschaffel, Onghena, & De Corte, 2000) revealed that 2^nd and 6^th graders use at least 3 different kinds of strategies for determining different numerosities of blocks presented in square grids: (a) an addition strategy by means of which (groups of) blocks are counted (and added), (b) a subtraction strategy in which the number of empty squares is subtracted from the total number of blocks in the grid (i.e. the anchor), and (c) an estimation strategy, whereby the number of blocks is determined in a quick but imprecise way. Although 6^th as well as 2^nd graders used the clever subtraction strategy, the majority of 2^nd graders had serious trouble with the correct determination of the anchor, resulting in huge numerosity judgement errors. Since this finding seriously complicated the testing of a number of hypotheses in that study, we replicated the above study but presented the children information about the grid size. This manipulation led to a substantial increase in the proportion of appropriate subtraction strategy users and made it possible to investigate the effect of several subject and task variables on the frequency, accuracy, and adaptiveness with which the different strategies were applied. Results are discussed in terms of the conceptual framework of Lemaire and Siegler (1995) regarding strategic change.  相似文献   

Children’s use of number line estimation strategies     

Dominique Peeters  Tine Degrande  Mirjam Ebersbach  Lieven Verschaffel  Koen Luwel 《European Journal of Psychology of Education - EJPE》2016,31(2):117-134

This study tested whether second graders use benchmark-based strategies when solving a number line estimation (NLE) task. Participants were assigned to one of three conditions based on the availability of benchmarks provided on the number line. In the bounded condition, number lines were only bounded at both sides by 0 and 200, while the midpoint condition included an additional benchmark at the midpoint and children in the quartile condition were provided with a benchmark at every quartile. First, the inclusion of a midpoint resulted in more accurate estimates around the middle of the number line in the midpoint condition compared to the bounded and, surprisingly, also the quartile condition. Furthermore, the two additional benchmarks in the quartile condition did not yield better estimations around the first and third quartile, because children frequently relied on an erroneous representation of these benchmarks, leading to systematic estimation errors. Second, verbal strategy reports revealed that children in the midpoint condition relied more frequently on the benchmark at the midpoint of the number line compared to the bounded condition, confirming the accuracy data. Finally, the frequency of use of benchmark-based strategies correlated positively with mathematics achievement and tended to correlate positively also with estimation accuracy. In sum, this study is one of the first to provide systematic evidence for children’s use of benchmark-based estimation strategies in NLE with natural numbers and its relationship with children’s NLE performance.  相似文献   

Estimation of ‘real’ numerosities in elementary school children     

Koen Luwel  Lieven Verschaffel 《European Journal of Psychology of Education - EJPE》2008,23(3):319-338

Groups of mathematically strong and weak second-, fourth- and sixth-graders were individually confronted with numerosities smaller and larger than 100 embedded in one-, two- or three-dimensional realistic contexts. While one third of these contexts were totally unstructured (e.g., an irregular piece of land jumbled up with 72 cars), another third had a clear structure (e.g., a 16x4 rectangular parking lot completely filled with 64 cars), and a last third had a “semi-structure” (e.g., the same 16x4 parking lot but with a number of cars missing). Besides analyzing the effects of different task and subject variables on pupils’ accuracy and response-time data, the study involved and analysis of their estimation strategies, with an emphasis on multiplicative strategies that profited by some of the tasks’ geometrical (semi-)structure. It was found that many children actually made use of such strategies, that using these strategies did however not always led to accurate estimations, and that their frequency and efficiency increased with age.  相似文献   

Associations of Number Line Estimation With Mathematical Competence: A Meta‐analysis          下载免费PDF全文

Michael Schneider  Simon Merz  Johannes Stricker  Bert De Smedt  Joke Torbeyns  Lieven Verschaffel  Koen Luwel 《Child development》2018,89(5):1467-1484

The number line estimation task is widely used to investigate mathematical learning and development. The present meta‐analysis statistically synthesized the extensive evidence on the correlation between number line estimation and broader mathematical competence. Averaged over 263 effect sizes with 10,576 participants with sample mean ages from 4 to 14 years, this correlation was r = .443. The correlation increased with age, mainly because it was higher for fractions than for whole numbers. The correlation remained stable across a wide range of task variants and mathematical competence measures (i.e., counting, arithmetic, school achievement). These findings demonstrate that the task is a robust tool for diagnosing and predicting broader mathematical competence and should be further investigated in developmental and experimental training studies.  相似文献   

Conceptualizing, investigating, and enhancing adaptive expertise in elementary mathematics education     

Lieven Verschaffel  Koen Luwel  Joke Torbeyns  Wim Van Dooren 《European Journal of Psychology of Education - EJPE》2009,24(3):335-359

Some years ago, Hatano differentiated between routine and adaptive expertise and made a strong plea for the development and implementation of learning environments that aim at the latter type of expertise and not just the former. In this contribution we reflect on one aspect of adaptivity, namely the adaptive use of solution strategies in elementary school arithmetic. In the first part of this article we give some conceptual and methodological reflections on the adaptivity issue. More specifically, we critically review definitions and operationalisations of strategy adaptivity that only take into account task and subject characteristics and we argue for a concept and an approach that also involve the sociocultural context. The second part comprises some educational considerations with respect to the questions why, when, for whom, and how to strive for adaptive expertise in elementary mathematics education.  相似文献   

Which skills predict computational estimation? A longitudinal study in 5- to 7-year-olds     

Sekeris  Elke  Verschaffel  Lieven  Luwel  Koen 《European Journal of Psychology of Education - EJPE》2022,37(1):19-38

European Journal of Psychology of Education - Computational estimation is seen as an important mathematical competence. Little is known, however, about the mathematical skills that are predictive...  相似文献