Erik De Corte

The Effect of Semantic Structure on First Graders' Strategies for Solving Addition and Subtraction Word Problems.

In a longitudinal investigation, data were collected on the problem representations and solution strategies of 30 first graders who were given a series of simple addition and subtraction word problems (Verschaffel, 1984). The children were interviewed three times during the school year, and data obtained on their solution strategies and on the influence of problem structure on the strategies. The results complement those of recent related research, especially the work of Carpenter and Moser (1982, 1984). More precisely, the influence of problem structure on childrens solution strategies appears even more extensive and decisive than that described by previous researchers.

Learning to reflect and to attribute constructively as basic components of self-regulated learning.

BACKGROUND Higher education is facing a number of problems: adjusting to larger and more heterogeneous student populations, increasing the number of graduating students, and preparing for lifelong learning. Improving learning competence can make a substantial contribution to solving each of these major concerns. The growing knowledge base on self-regulated learning was taken as one of the main starting points for our study. AIMS In this article we report on reflection and attribution as basic components of self-regulated learning. We examine their trainability and their effect on academic performance. This study is part of a wider research project aimed at improving meta-cognitive knowledge as well as affective, conative and regulation skills. The experimental treatment consisted of an integrated set of instructional conditions, which were operationalized in a series of training sessions, as well as practice and transfer tasks. SAMPLE The participants in this study were 141 first year students of business economics. The experimental group and both control groups each consisted of 47 students. METHOD The effects of the learning environment were investigated using a quasiexperimental design. To control for unintended effects of the design the experimental and the first control group had the same number of teaching hours (time-on-task) and both teachers and students were not informed about the experimental design. Attribution and reflection behaviour was measured through specific assignments; study results during and after the intervention period were taken as indicators of academic performance. To test the hypotheses, t tests and effect-sizes were calculated. RESULTS After the intervention the experimental students showed a higher degree of reflective behaviour than the control students. Moreover, their attribution skills had also measurably improved. The experimental students obtained better study results than their peers in the control groups. CONCLUSIONS This intervention study, focused on the combined training of learning to reflect and to attribute constructively, provides evidence of the successful fostering both of meta-cognitive and of conative learning activities resulting in a positive impact on academic achievement.

Teaching Realistic Mathematical Modeling in the Elementary School: A Teaching Experiment with Fifth Graders.

Recent research has convincingly documented elementary school childrens tendency to neglect real-world knowledge and realistic considerations during mathematical modeling of word problems in school arithmetic. The present article describes the design and the results of an exploratory teaching experiment carried out to test the hypothesis that it is feasible to develop in pupils a disposition toward (more) realistic mathematical modeling. This goal is achieved by immersing them in a classroom culture in which word problems are conceived as exercises in mathematical modeling, with a focus on the assumptions and the appropriateness of the model underlying any proposed solution. The learning and transfer effects of an experimental class of 10and 11-year-old pupils--compared to the results in two control classes-provide support for the hypothesis that it is possible to develop in elementary school pupils a disposition toward (more) realistic mathematical modeling.

Transfer as the Productive Use of Acquired Knowledge, Skills, and Motivations:

Historically, the notion of transfer has been very controversial, conceptually as well as empirically. Therefore, there is an obvious need for further inquiry aimed at a better understanding of the processes underlying transfer. Taking into account the recent literature, this article defines transfer as the broad, productive, and supported use of acquired knowledge, skills, and motivations in new contexts and learning tasks. As an illustration, an intervention study is briefly discussed. This study shows the possibility of designing a powerful learning environment that yields transfer effects in accordance with this reconceptualized perspective on transfer.Historically, the notion of transfer has been very controversial, conceptually as well as empirically. Therefore, there is an obvious need for further inquiry aimed at a better understanding of the processes underlying transfer. Taking into account the recent literature, this article defines transfer as the broad, productive, and supported use of acquired knowledge, skills, and motivations in new contexts and learning tasks. As an illustration, an intervention study is briefly discussed. This study shows the possibility of designing a powerful learning environment that yields transfer effects in accordance with this reconceptualized perspective on transfer.

Enhancing learning and problem solving skills: orienting and self-judging, two powerful and trainable learning tools

Abstract In this study we report on orienting and self-judging as study and problem-solving activities or learning tools. We examine their trainability and their effect on academic performance. These questions are part of a research project aimed at improving metacognitive knowledge as well as affective, conative and regulation skills. A design experiment with 141 freshmen in business economics was set up. The experimental treatment consisted of an integrated set of instructional conditions which were operationalized in a series of sessions and practice and transfer tasks. The results show that after the intervention students of the experimental group had more knowledge about orienting and self-judging than the students of both control groups and they also oriented themselves better and were more prone to self-judging when starting a new course. Both metaknowledge and transfer behavior were positively related to academic performance.

Towards powerful learning environments for the acquisition of problem-solving skills

It is generally agreed that acquiring thinking and problem-solving skills is nowadays a primary objective of general education. Responding appropriately to this challenge requires an answer to the following questions: 1. what does the acquisition of problem-solving skills involve, and 2. how can those abilities be fostered through systematic instruction? This contribution describes a four-step model of skilled problem-solving processes, and gives an overview of three major categories of cognitive skills involved in competent problem solving, namely, the flexible and integrated application of domain-specific knowledge, of heuristic methods, and of metacognitive skills. Furthermore, a framework is presented for the design and elaboration of powerful teaching-learning environments in which such problem-solving skills can be acquired efficiently. Two basic ideas underlying this model are: the view of learning as a constructive process, and the idea of cognitive apprenticeship as an effective and appropriate method for learning and teaching. Finally, some recent research findings supporting the educational significance of the framework are briefly reviewed.RésuméDe nos jours, on admet généralement que l’acquisition des capacités de pensée et de résolution de problèmes constitue un objectif primordial de l’éducation. Répliquer de façon appropriée à ce défi requiert une réponse aux questions suivantes: 1. qu’implique l’acquisition de capacités à résoudre des problèmes, et 2. comment peut-on influencer l’acquisition de ces capacités par un enseignement systématique?Cette contribution propose un modèle à quatre phases de processus maîtrisés de la résolution de problèmes. Elle donne un aperçu des trois catégories principales de capacités cognitives qui interviennent dans une résolution compétente de problèmes, notamment l’application flexible et intégrée d’un domaine de connaissance spécifique, de méthodes heuristiques et de capacités métacognitives. On décrit ensuite un cadre de référence pour le développement et l’élaboration d’environnements d’apprentissage efficaces pour l’acquisition de ces habiletés. Deux idées sous-tendent ce modèle: la conception de l’apprentissage comme un processus constructif et l’idée du «cognitive apprenticeship» comme une méthode efficace et appropriée à l’apprentissage et à l’enseignement. Finalement, quelques résultats récents de recherche viennent appuyer l’importance de ce modèle de référence dans l’éducation.

Number and Arithmetic

During the last decade several major shifts have occurred in the conceptualisation of mathematics as a domain, of mathematical competence as a goal for instruction, and of the way in which this competence should be acquired through schooling. This chapter begins with a summary of the general characteristics and principles underlying the ongoing world-wide reform of mathematics education. Afterwards it documents and illustrates how these general characteristics and principles permeate a major domain of the mathematics curricula for the elementary school, called ‘Number and Arithmetic’. Five related topics within this domain are discussed, namely: number concepts and number sense, the meaning of arithmetic operations, mastery of basic arithmetic facts, mental and written computation, and word problems as applications of the numerical and arithmetical knowledge and skills.

The CLIA-model: A framework for designing powerful learning environments for thinking and problem solving

A major challenge for education and educational research is to build on our present understanding of learning for designing environments for education that are conducive to fostering in students self-regulatory and cooperative learning skills, transferable knowledge, and a disposition toward competent thinking and problem solving. Taking into account inquiry-based knowledge on learning and recent instructional research, this article presents the CLIA-model (Competence, Learning, Intervention, Assessment) as a framework for the design of learning environments aimed to be powerful in eliciting in students learning processes that facilitate the acquisition of productive knowledge and competent learning and thinking skills. Next, two intervention studies are described that embody major components of this framework, one focussing on mathematical problem solving in primary school, and a second one relating to self-regulatory skills in university freshmen. Both studies were carried out in parallel with the development of the framework, and were instrumental in identifying and specifying the different components of the model. They yielded both promising initial support for the model by showing that CLIA-based learning environments are indeed powerful in facilitating in students the acquisition of high-literacy learning results, especially the acquisition and transfer of self-regulation skills for learning and problem solving.RésuméUn défì important pour l’éducation et la recherche pédagogique est de développer en partant de notre compréhension actuelle de l’apprentissage des environnements éducationnels susceptibles de promouvoir chez les étudiants des habiletés d’apprentissage autorégulatrices et collaboratives, des connaissances transférables, et une disposition orientée vers le raisonnement et la résolution de problèmes compétents. Tenant compte des résultats de la recherche sur l’apprentissage et l’enseignement, cet article présente le modèle “CLIA (Competence, Learning, Intervention, Assessment)” comme cadre de référence pour concevoir des environnements d’apprentissage visés à stimuler chez les étudiants des processus d’apprentissage qui facilitent l’acquisition de connaissances productives et des habiletés compétentes d’apprentissage et de raisonnement. Ensuite, deux recherches d’intervention sont présentées qui représentent les composantes majeures du modèle CLIA: une expérience porte sur la résolution de problèmes mathématiques dans l’enseignement primaire, et la seconde a pour objet les habiletés autorégulatrices chez des étudiants en première année de l’université. Ces recherches ont été réalisées en parallèle avec le développement du modèle, et ont été instrumentales pour l’identification et la spécification des différentes composantes du modèle. Les deux investigations ont apporté du support initial pour le modéle en montrant que des environnements d’apprentissage basés sur le cadre de référence CLIA sont en effet stimulants pour faciliter chez les étudiants l’acquisition de résultats d’apprentissage d’ordre supérieur, spécialement l’acquisition et le transfert d’habiletés d’autorégulation de l’apprentissage et de la résolution de problèmes.

Influence of the semantic structure of word problems on second graders' eye movements

This study used the technique of eye-movement registration to examine the influence of the semantic structure of one-step addition and subtraction word problems (simple vs. complex) on the eye-fixation patterns of 10 high-ability and 10 low-ability second graders. We investigated the effects of the factors semantic complexity and ability level on response time and on the amount and proportion of fixation time spent on words and on numbers in the problem. For a subgroup of 10 children, we analyzed the data for two substages separately: an initial systematic reading phase and the rest of the solution process

Study time and test performance as a function of test expectations

Abstract Study time and test performance change as a function of subjects expecting either open questions or a multiple-choice test on the contents of a history text. After studying a first history text, the subjects immediately received a test consisting of either open questions or multiple-choice items. They were led to expect the same type of test on a second text. Study time on Text 2 was self-paced, and the type of test was either the expected or unexpected one (either open questions or a multiple-choice test). The main hypothesis was confirmed that subjects consider open questions a more demanding test than a multiple-choice test. Accordingly, subjects expecting open questions on Text 2 used more study time and performed better on both types of test than did subjects expecting a multiple-choice test. Internal analyses revealed that the differences on study time and test achievement between the two expectation conditions occurred only when the subjects were thoroughly acquainted with the processing requirements of the learning material and its expected test.