Lieven Verschaffel

Lieven Verschaffel
KU Leuven | ku leuven

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576
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Publications

Publications (576)
Article
Research Findings: Shared-picture book reading can stimulate children’s mathematical development. Evidence of learning-supportive characteristics in picture books is limited in this domain. A first step is systematically analyzing the occurrence of domain-specific features in publicly available picture books. We analyzed the occurrence of general b...
Article
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The success or failure of education systems in promoting the problem-solving skills of students depends on attitudinal, political, and pedagogical variables. Among these variables, the design of mathematics textbooks is thought to partially explain why students from high-achieving countries show better problem-solving ability in international asses...
Article
Full-text available
Several studies have shown that children do not only erroneously use additive reasoning in proportional word problems, but also erroneously use proportional reasoning in additive word problems. Traditionally, these errors were contributed to a lack of calculation and discrimination skills. Recent research evidence puts forward an additional explana...
Article
Full-text available
Research on rational numbers suggests that adults experience more difficulties in understanding the numerical magnitude of rational than natural numbers. Within rational numbers, the numerical magnitude of fractions has been found to be more difficult to understand than that of decimals. Using a number line estimation (NLE) task, the current study...
Article
The present study longitudinally investigated proportional reasoning abilities in early elementary school before the start of its instruction. Three aims were put forward: (a) distinguishing the different developmental states in young children’s understanding of missing-value proportional situations, (b) investigating how children transition throug...
Article
We investigated elementary school children's use of direct subtraction (DS) and subtraction by addition (SBA) when mentally solving multi-digit subtractions. Fourth- to sixth-grade children of varying mathematical achievement levels were offered subtractions in one choice condition (choice between DS or SBA) and two no-choice conditions (mandatory...
Article
El propósito del estudio fue examinar si los niños preescolares se enfocan espontáneamente en estructuras matemáticas –patrones y clasificación– y si dicho enfoque se asocia con sus habilidades para trabajar patrones. La metodología fue cuantitativa de tipo descriptivo y comparativo. Participaron en el estudio 60 preescolares que fueron evaluados a...
Article
Recent literature suggests proportional reasoning develops at an earlier age than traditionally assumed. It also indicates that in tasks where both additive and multiplicative reasoning are appropriate, some children have a preference for additive relations, while others have a preference for multiplicative relations. In this study we investigated...
Article
Full-text available
Ellis et al. (2021, this issue; in the following abbreviated as EEA) conducted a conceptual replication and extension of a recent meta-analysis relating number line estimation to broader mathematical competence (Schneider et al., 2018; in the following: SEA). EEA pooled and analyzed data from seven new studies and compared the results to SEA’s find...
Article
This study presents a patterning intervention for 5-year-olds, who were in their third year of preschool in Flanders (Belgium), with two key elements: A focus on the structure of patterns, and the inclusion of growing patterns (e.g., ABAABAAAB) in addition to repeating patterns (e.g., ABABAB). We evaluated the impact of this intervention on pattern...
Article
This longitudinal cross-lagged panel study investigated the development of the structure of young children’s spontaneous number focusing tendencies and their longitudinal associations with numerical abilities and mathematics achievement over the course of a 3-year period, that is, in the second and third year of kindergarten and in first grade of p...
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Research distinguishes three types of arithmetic: exact arithmetic, computational estimation and approximate arithmetic. Little is, however, known about the interrelationship among these three arithmetic skills and the general cognitive and early numeracy skills that underlie these arithmetic skills. The current study investigates this interrelatio...
Article
The current study examined upper elementary school children’s frequent, efficient and adaptive use of direct subtraction ( DS ) and subtraction by addition ( SBA ) when mentally solving multi-digit subtractions, replicating and expanding previous research by Torbeyns et al. (2018). First, children were offered subtractions in two choice conditions...
Article
Computational estimation is seen as an important mathematical competence. Little is known, however, about the mathematical skills that are predictive of early computational estimation development. The current study longitudinally followed a group of about 350 children at four time points: second (K2, 4-year-olds) and third grades of kindergarten (K...
Article
Full-text available
The nature of the arithmetic word problems found in maths textbooks influences the way students develop their ability to solve them, as teachers use the books in their classes quite frequently. Given that students are better able to reason through and solve authentic problems that are contextualized in situations familiar to them, and that differen...
Article
The present study aimed to analyze the direction of the associations between repeating patterning, growing patterning, and numerical ability. Participants were 410 children who were annually assessed on their repeating patterning, growing patterning, and numerical ability, at ages 4, 5, and 6 years (i.e., spring 2017, 2018, and 2019). A cross-lagge...
Chapter
In this chapter, we review a long-standing and comprehensive line of research on the use of the subtraction by addition (SBA) strategy when solving subtractions, in which our own research center has played an important role. We document this phenomenon in a variety of subdomains of the elementary arithmetic curriculum, ranging from single-digit men...
Article
Proportional reasoning is one part of mathematics that is particularly hard to apprehend for children. At the same time, research suggests that already at an early age children develop an ability to make sense of some proportional situations. Previous research has shown that language-be it language in general or language related to mathematics-play...
Article
Full-text available
Selecting a large and diverse sample of 5-6-year-old preschool children (179 boys and 174 girls; M age = 70.03 months, SD age = 3.43), we aimed to extend previous findings on variability in children's home math environment (i.e., home math activities, parental expectations, and attitudes) and its association with children's mathematical skills. We...
Article
Children’s spontaneous focusing on Arabic number symbols (SFONS) has been identified as a relevant component of their early mathematical development. This study investigated whether SFONS is a separate construct from spontaneous focusing on numerosity (SFON) and examined whether it is uniquely related to numerical abilities and mathematics achievem...
Article
Young children’s early repeating patterning abilities are important foundations for their later mathematical development. Prior studies on young children’s repeating patterning abilities have been conducted exclusively in developed countries differing in economic, societal, and educational characteristics from developing countries. In this study, w...
Article
Full-text available
The transition from informal to formal mathematics is an important episode in children’s mathematical development. The current study investigated how young children’s computational estimation performance and strategy use develops in this transitional period. The computational estimation performance of 350 children was assessed before the start of f...
Article
Children’s spontaneous focusing on Arabic number symbols (SFONS) has been identified as a relevant component of their early mathematical development. This study investigated whether SFONS is a separate construct from spontaneous focusing on numerosity (SFON) and examined whether it is uniquely related to numerical abilities and mathematics achievem...
Article
Full-text available
Children’s own spontaneous mathematical activities are crucial for their mathematical development. Mathematical thinking and learning does not only occur in explicitly mathematical situations, such as the classroom. Those children with higher tendencies to recognize and use mathematical aspects of their everyday surroundings, both within the classr...
Article
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Recently, responding with eye fixations in the number line estimation (NLE) task was introduced. To determine if this new mode of responding replicates typical mouse cursor NLE results, 33 adults completed a 0-1000 NLE task and responded with their eyes (eye condition) or the mouse (mouse condition), while their eyes were tracked. In the mouse cond...
Article
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Previous research demonstrated that some children inappropriately solve multiplicative missing-value word problems additively, while others inappropriately solve additive missing-value word problems multiplicatively. Besides lacking skills, children’s preference for additive or multiplicative relations has been shown to contribute to those errors....
Article
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 evid...
Article
Word problems are among the most difficult kinds of problems that mathematics learners encounter. Perhaps as a result, they have been the object of a tremendous amount research over the past 50 years. This opening article gives an overview of the research literature on word problem solving, by pointing to a number of major topics, questions, and de...
Chapter
In this chapter we review and discuss a relatively new line of research in the domain of early mathematical development that addresses the dispositional rather than the ability aspect of children’s early mathematical competence, namely their tendencies to attend to and focus on various mathematical elements in their environment and its relation wit...
Article
This paper provides a survey of the research on the relationship between teachers’ professional knowledge and their instructional quality in the domain of mathematics education. First, an overview is provided of the way in which mathematics professional knowledge has been conceptualized. Second, the relation between mathematics teachers’ profession...
Article
Young children show large individual differences in their tendency to focus spontaneously on numerical aspects (e.g., numerosities or Arabic number symbols) of their everyday environment. The origins of these individual differences are unclear. Given the role of the home numeracy environment (HNE) in children’s early mathematical development and th...
Article
Singaporean children are the best performers on international achievement tests in mathematics (i.e. the TIMSS). Their excellent results could be due at least partly to certain characteristics of the textbooks used there (Oates 2014). Therefore, these materials could be taken as a good benchmark to describe and evaluate aspects of the textbooks of...
Article
Background: Early patterning competence has recently been identified as an important precursor of mathematical development. Whereas the focus of this research has been on children's ability regarding repeating patterns, children might also differ in their spontaneous attention to patterns. Aims: The present study aimed to explore 4- to 5-year ol...
Article
El objetivo del presente estudio fue examinar la influencia del nivel socioeconómico de los niños de jardín infantil en el desarrollo de sus habilidades numéricas tempranas y su enfoque espontáneo en el número (SFON), después de controlar por variables cognitivas de dominio general, como inteligencia y memoria de trabajo, y por edad. Al iniciar el...
Article
Full-text available
This article encompasses a systematic review of the research on ICT-based learning environments for metacognitively oriented K-12 mathematics education. This review begins with a brief overview of the research on metacognition and mathematics education and on ICT and mathematics education. Based on a systematic screening of the databases Web of Sci...
Conference Paper
Recent literature suggests that children develop proportional reasoning abilities at an earlier age than traditionally assumed. It also indicates that children's preference for additive and multiplicative relations plays a role in this development. In this study we investigated four-to nine-year olds' proportional reasoning abilities in missing-val...
Article
The present study cross-sectionally investigated proportional reasoning abilities in 5-to 9-year-old children (n = 185) before they received instruction in proportional reasoning. This study addressed two important aspects of the development of proportional reasoning that remain unclear in the current literature: (1) the age range in which it devel...
Article
In this study, we aimed to address two gaps in research on early mathematical patterning, namely the lack of attention (1) to growing patterns and (2) to the association between different aspects of patterning and numerical ability. Participants were 400 four-year olds from a wide range of socioeconomic backgrounds. Children's patterning and numeri...
Article
For several decades computational estimation is seen as an important topic in primary mathematics education. While previous narrative literature reviews on computational estimation summarized the available research on computational estimation abilities in students and adults, the present systematic literature review focuses on the measurement, deve...
Article
Previous research has shown that upper primary school children frequently erroneously solve additive word problems multiplicatively, while younger children frequently erroneously solve multiplicative word problems additively. It has been suggested that children's preference for additive or multiplicative relations explains these errors, besides the...
Chapter
Activities with patterns (e.g., making a necklace with alternating blue and red pearls) are common in many preschool and kindergarten settings. These activities are assumed to play an important role in children’s mathematical development. Nevertheless, most research on early mathematical development focuses on numerical and arithmetical abilities,...
Article
Many studies have investigated the association between children’s spontaneous attention to number and their early mathematical abilities. This work has presented number in a non-symbolic format by exclusively using numerosities as their stimuli. Therefore, little is known about children’s spontaneous attention for Arabic number symbols. We aimed to...
Article
Full-text available
Mathematics-related affect comprises an individual’s attitudes, beliefs, emotions and motivations towards mathematics. These affective constructs have been widely studied in mathematics education and cognitive psychology and have been shown to be related to cognitive outcomes such as performance on a range of mathematical tasks. However, it is not...
Article
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The current study investigated developmental changes children's benchmark-based strategy use in number line estimation. Third and fifth graders solved a 0-1000 number line estimation task in one of three conditions. In the control condition only the origin and endpoint were specified, the midpoint condition included an additional benchmark at 50%,...
Chapter
This study aims to look into the effect of L2 proficiency level on composing processes of L2 student writers in L2 writing. The research to date has produced conflicting evidence concerning the relationship between L2 proficiency and composing processes. A number of L2 studies found that L2 proficiency does not influence L2 writing performance and...
Article
A growing body of research has shown that symbolic number processing relates to individual differences in mathematics. However, it remains unclear which mechanisms of symbolic number processing are crucial—accessing underlying magnitude representation of symbols (i.e., symbol‐magnitude associations), processing relative order of symbols (i.e., symb...
Article
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 10576 participants with sample mean ages from 4 to...
Article
Full-text available
Numerical competencies acquired in preschool are foundational and predictive for children's later mathematical development. It remains to be determined whether there are gender differences in these early numerical competencies which could explain the often‐reported gender differences in later mathematics and STEM‐related abilities. Using a Bayesian...
Conference Paper
More and more research suggests that proportional reasoning emerges already at a very early age in childhood. The present study aimed to investigate these abilities in four-to five-year-old children. A five-item proportional reasoning task involving discrete quantities was administered in 389 children. On average children could solve about one item...
Article
Full-text available
Recent research suggests that individual differences in mathematics achievement relate to basic number processing skills such as the ability to process numerical magnitudes. A key issue in this recent field of research is whether non-symbolic magnitude processing predicts mathematics achievement. An alternative account posits that accessing non-sym...
Article
Full-text available
We investigated the use of the subtraction by addition strategy, an important mental calculation strategy in children with different levels of mathematics achievement. In doing so we relied on Siegler’s cognitive psychological model of strategy change (Lemaire & Siegler, 1995), which defines strategy competencies in terms of four parameters (strate...
Article
Full-text available
Recent research suggests that individual differences in mathematics achievement relate to basic number processing skills such as the ability to process numerical magnitudes. A key issue in this recent field of research is whether non-symbolic magnitude processing predicts mathematics achievement. An alternative account posits that accessing non-sym...
Article
Research has shown that children have a strong tendency to exclude real world considerations when solving word problems. In this study, we investigated a novel way to try to change this tendency. We tested whether children would adapt their behavior when solving word problems in which realistic considerations are required (P-items) when these probl...
Article
Full-text available
Previous studies have indicated that the presence of atypical endpoints (e.g., 1,639 and 2,897) on a number line has a negative effect on number line estimation (NLE) performance (Booth & Newton, 2012; Hurst et al., 2014). In the present study, we investigated whether this effect could be attributed to a disruption in the ease with which benchmarks...
Article
Interactive whiteboard offers a high-potential innovative tool in mathematical educational environments, in which teachers’ modeling processes and students’ exploring activities can easily be executed. Nevertheless, these affordances are not self-evident. There is a gap between the potential claims of the tool and its actual use in the classrooms....
Article
Full-text available
This research aims at exploring an effective set to stimulate mathematics understanding and learning in an Interactive Whiteboard (IWB) environment. IWB affordances appear to be best used when mathematical tasks engage students in mathematical reasoning and when all students are involved in the discussion. The intent of this research project was to...
Chapter
Full-text available
This chapter focuses on the neuro-cognitive, cognitive and developmental analyses of whole number arithmetic (WNA) learning. It comprises five sections. The first section provides an overview of the working group discussion. Section 7.2 reviews neuro-cognitive perspectives of learning WNA but looks beyond these to explain the transcoding of numeral...
Chapter
This chapter provides an overview of the ICME 23 Study panel on special needs in research and instruction in whole number arithmetic. It starts with a general introduction by Verschaffel about the state of affairs in and the major issues and challenges for research and educational practice in the field of mathematical learning difficulties (MLD). A...
Conference Paper
Full-text available
The focus of this paper is on two definite areas: designing of powerful learning environments, and graphical representation of music. With respect to the former, technology-enhanced learning environments (TELEs) have revealed as powerful tools for fostering students’ learning (Azevedo & Cromley, 2004). In this respect, scaffolding (Collins, Brown,...
Article
Full-text available
This study aimed at analyzing the development of Ecuadorian children’s early numerical abilities during the Kindergarten year in relation to their SES, the quality of their early mathematics education, and the attended school type. 179 Ecuadorian Kindergartners (18 classrooms, 6 classrooms per school type) were offered a standards-based early numer...
Chapter
Young children’s spontaneous focusing on numerosity (SFON) predicts their later mathematical competencies. In this study we investigated the development of SFON in Ecuadorian kindergartners as well as the contribution of early numerical abilities and the quality of mathematics education to this development. The participants were 100 kindergartners...
Chapter
Children’s Spontaneous Focusing On Numerosity (SFON) predicts later mathematics performance. This association is assumed to rely on children’s self-initiated practice in number recognition during everyday activities, which would enhance their further mathematical development. Consequently, SFON in experimental tasks should be associated with SFON d...
Article
Full-text available
Students have a great deal of difficulties learning about rational number concepts, as they are confounded by misapplying reasoning about natural numbers to fractions and decimals, referred to as a natural number bias. For example, students often think that the number of digits of a decimal, or the size of the component numbers of fractions, is eno...
Article
This study analyses whether the primary school mathematics textbooks from two Spanish publishers show a varied instructional diet of addition and multiplication problems at different levels of complexity. To do so, it analyses the problems in all the primary grades by the publishers Santillana and SM according to two levels of complexity: (a) proce...
Article
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 vari...
Article
We investigated the effectiveness of the Building Blocks program for enhancing Ecuadorian kindergart-ners' early numerical abilities and spontaneous focusing on numerosity (SFON), after controlling for working memory, intelligence, age, and SES. Following a pretest-intervention-posttest design, 18 classes comprising 355 children from varied SES bac...
Conference Paper
Dieser Tagungsband dokumentiert die Ergebnisse der Jahrestagung des Arbeitskreises Grundschule in der Gesellschaft für Didaktik der Mathematik (GDM), die in diesem Jahr wieder in Bad Salzdetfurth stattfand. Vom 09. bis 11. November 2018 widmete sich der Arbeitskreis dem Thema „Inhalte im Fokus – Mathematische Strategien entwickeln“. Mathematische B...
Article
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We aimed to investigate upper elementary children's strategy use in the domain of multidigit division in two instructional settings: the Netherlands and Flanders (Belgium). A cross‐sectional sample of 119 Dutch and 122 Flemish fourth to sixth graders solved a varied set of multidigit division problems. With latent class analysis, three distinct str...
Article
Young children’s spontaneous focusing on numerosity (SFON) as measured by experimental tasks is related to their mathematics achievement. This association is hypothetically explained by children’s self-initiated practice in number recognition during everyday activities. As such, experimentally measured SFON should be associated with SFON exhibited...
Article
Recent evidence indicates that young children's spontaneous focusing on numerosity (SFON) uniquely contributes to their early numerical abilities. This study complements previous findings by validating the relation between young children's SFON and their early numerical abilities in a developing country, namely Ecuador. We analysed 355 Ecuadorian 5...
Article
While previous studies mainly focused on children’s additive and multiplicative reasoning abilities, we studied third to sixth graders’ preference for additive or multiplicative relations. This was investigated by means of schematic problems that were open to both types of relations, namely arrow schemes containing three given numbers and a fourth...
Article
Background: Previous research indicated that in several cases learners' errors on rational number tasks can be attributed to learners' tendency to (wrongly) apply natural number properties. There exists a large body of literature both on learners' struggle with understanding the rational number system and on the role of the natural number bias in...
Article
In contrast to previous studies on Spontaneous Focusing on Quantitative Relations (SFOR), the present study investigated not only the extent to which children focus on (multiplicative) quantitative relations, but also the nature of children’s quantitative focus (i.e., the types of quantitative relations that children focus on). Therefore, we offere...
Article
In this interview we asked Paul A. Kirschner about his comments and reflections regarding the idea to apply cognitive psychology-based instructional design principles to mathematics education and some related issues. With a main focus on cognitive psychology, educational psychology, educational technology and instructional design, this internationa...