The factor structure of mathematical abilities in Luxembourg’s national school monitoring: Its stability over elementary school and relations to, gender, language background, and SES

Scientific Conference (2021, July)

Mathematics skills are the fundament of modern societies, especially those based on a knowledge-economy. The age of digitalization renders mathematics education even more crucial since it builds the ... [more ▼]

Mathematics skills are the fundament of modern societies, especially those based on a knowledge-economy. The age of digitalization renders mathematics education even more crucial since it builds the starting point for all STEM-related fields. Consequently, mathematics is at the core of numerous educational Large-Scale Assessments on international (e.g. PISA, TIMSS) or national level (e.g. NAEP, NEPS, SNSA). Although the underlying test development frameworks are most often multi-dimensional or hierarchical, psychometric analyses usually focus on a single latent factor that represents a rather vague general mathematical ability. How and to what extent this simplification affects educational studies that rely on these data remains unclear. The present study takes Luxembourg’s national school monitoring program ÉpStan as example to tackle this question and clarify the consequences. ÉpStan’s mathematics test is conducted annually in elementary school Grades 1, 3, and 5 and is comprised of around 50 to 70 items. Since ÉpStan captures competencies of all students biyearly, each analysis will be based on the full cohort (n > 5000). First, we will investigate whether the curriculum-based test framework for mathematics can psychometrically be represented in a related (multi-dimensional) confirmatory factor model including the domains numbers & operations and space & form. This will be done in Grades 1, 3, and 5. Second, we will study the factor model’s cross-sectional stability within each Grade (over three consecutive years) and longitudinal stability between Grades. Finally, we will study the factors’ relations to students’ cognitive and sociodemographic characteristics and compare the results with correlations found using the most widely used one-dimensional model of mathematical abilities. Based on the results, we will discuss implications not only for educational studies that often uncritically make use of large-scale assessment data, but also highlight the consequences for group-level feedback that is based on such assessments. [less ▲]

A propensity score matching approach on predicting academic success of primary school students

Scientific Conference (2020, July)

School career and academic achievement are known to greatly affect an individual’s path through life (e.g., Trapmann, Hell, Weigand & Schuler, 2007; Jimerson, 2001). In Luxembourg, recent findings ... [more ▼]

School career and academic achievement are known to greatly affect an individual’s path through life (e.g., Trapmann, Hell, Weigand & Schuler, 2007; Jimerson, 2001). In Luxembourg, recent findings indicate that at school entrance (i.e., the beginning of Grade 1) the majority of the students achieve or even surpass the required minimum level of core competencies such as mathematics and early literacy (Hoffmann, Hornung, Gamo, Esch, Keller, & Fischbach, 2018). However, in Grade 3 (i.e., after the first two years of elementary school) many students do no longer achieve the required minimum level of competencies in math and literacy (ibid.). Especially students with another language background than (any of) the official languages in Luxembourg (Luxembourgish, German, and French) and those socio-economically disadvantaged were found to be more likely not to obtain the competency level (ibid.). The current study aims to investigate which specific factors may facilitate (or hinder) learning progression by using longitudinal data of the Luxembourg School Monitoring Programme Épreuves Standardisées from Grade 1 (2014, 2015) to Grade 3 (2016, 2017, 2018). More specifically, students with irregular pathways (i.e., those who experienced grade retention) will be identified as treatment group and compared to a stratified control group of students following regular pathways. For each student of the treatment group, one or more students from the control group will be matched through propensity score matching, a matching procedure based on logistic regression, according to different pre-sets of variables. In a second step, the two groups will be compared in regards to competency levels as well as to socio-emotional context variables such as family background, student-teacher interaction, and school satisfaction aiming at identifying characteristics potentially facilitating (or hindering) a student’s school career. [less ▲]

Predicting Academic Success in Early Primary School: A Propensity Score Matching Approach

Scientific Conference (2019, November 06)

Les compétences scolaires des enfants au début du cycle 2 de l'école fondamentale au Luxembourg et leur développement après deux ans.

Report (2018)

Ce chapitre présente les résultats de trois collectes de données (2014, 2015, 2016) des ÉpStan au cycle 2.1 et présente avec quelles compétences scolaires les élèves débutent leur scolarité au début du ... [more ▼]

Ce chapitre présente les résultats de trois collectes de données (2014, 2015, 2016) des ÉpStan au cycle 2.1 et présente avec quelles compétences scolaires les élèves débutent leur scolarité au début du cycle 2.1 et comment celles-ci évoluent sur deux ans. De manière générale, nos résultats montrent que les compétences disciplinaires du cycle 1 portant sur les trois domaines d’apprentissage observés (« compréhension de l’oral en luxembourgeois », « compréhension de l’écrit» et « mathématiques ») sont acquises. Au début du cycle 2.1, la majorité des élèves atteint le Niveau Avancé dans l’ensemble des trois domaines d’apprentissage considérés. Deux ans plus tard, au cycle 3.1, la répartition des élèves sur les différents niveaux de compétence est plus négative qu’au cycle 2.1 et ceci dans la mesure où moins d’enfants ont atteint le Niveau Socle dans l’ensemble des trois domaines d’apprentissage observés. Nos résultats montrent également que, dès le début de la scolarité, différents facteurs extrascolaires (tels que le statut socio-économique et le contexte linguistique) ont une influence extrêmement forte sur les résultats des épreuves et que cette influence augmente au fil des années. [less ▲]

Differential association of symbolic and non-symbolic numerical abilities in children with and without MLD – Evidence from large scale assessment data

Poster (2018, September)

Taking Language out of the Equation: The Assessment of Basic Math Competence Without Language

in Frontiers in Psychology (2018)

While numerical skills are fundamental in modern societies, some estimated 5–7% of children suffer from mathematical learning difficulties (MLD) that need to be assessed early to ensure successful ... [more ▼]

While numerical skills are fundamental in modern societies, some estimated 5–7% of children suffer from mathematical learning difficulties (MLD) that need to be assessed early to ensure successful remediation. Universally employable diagnostic tools are yet lacking, as current test batteries for basic mathematics assessment are based on verbal instructions. However, prior research has shown that performance in mathematics assessment is often dependent on the testee’s proficiency in the language of instruction which might lead to unfair bias in test scores. Furthermore, language-dependent assessment tools produce results that are not easily comparable across countries. Here we present results of a study that aims to develop tasks allowing to test for basic math competence without relying on verbal instructions or task content. We implemented video and animation-based task instructions on touchscreen devices that require no verbal explanation. We administered these experimental tasks to two samples of children attending the first grade of primary school. One group completed the tasks with verbal instructions while another group received video instructions showing a person successfully completing the task.We assessed task comprehension and usability aspects both directly and indirectly. Our results suggest that the non-verbal instructions were generally well understood as the absence of explicit verbal instructions did not influence task performance. Thus we found that it is possible to assess basic math competence without verbal instructions. It also appeared that in some cases a single word in a verbal instruction can lead to the failure of a task that is successfully completed with non-verbal instruction. However, special care must be taken during task design because on rare occasions non-verbal video instructions fail to convey task instructions as clearly as spoken language and thus the latter do not provide a panacea to non-verbal assessment. Nevertheless, our findings provide an encouraging proof of concept for the further development of non-verbal assessment tools for basic math competence. [less ▲]

Visuo-spatial abilities are key for young children’s verbal number skills

in Journal of Experimental Child Psychology (2018), 166C

Children’s development of verbal number skills (i.e, counting abilities and knowledge of the number names) presents a milestone in mathematical development. Different factors such as visuo-spatial and ... [more ▼]

Children’s development of verbal number skills (i.e, counting abilities and knowledge of the number names) presents a milestone in mathematical development. Different factors such as visuo-spatial and verbal abilities have been discussed to contribute to the development of these foundational skills. To understand the cognitive nature of verbal number skills in young children, the present study assessed the relation of preschoolers’ verbal and visuo-spatial abilities to their verbal number skills. In total, 141 children aged between five and six years participated in the present study. Verbal number skills were regressed on vocabulary, phonological awareness and visuo-spatial abilities, as well as verbal and visuo-spatial working memory in a structural equation model. Only visuo-spatial abilities emerged as a significant predictor of verbal number skills in the estimated model. Our results suggest that visuo-spatial abilities contribute to a larger extent to children’s verbal number skills than verbal abilities. From a theoretical point of view, these results suggest a visuo-spatial, rather than a verbal, grounding of verbal number skills. These results are potentially informative for the conception of early mathematics assessments and interventions. [less ▲]

LEARN Newsletter - Édition 2018

Book published by LEARN (2018)

The relevance of verbal and visuo-spatial abilities for verbal number skills – what matters in 5 to 6 year olds?

Poster (2017, September)

The acquisition of verbal number skills, as defined by the meaningful use of number words, marks a milestone in numerical development. In the present study, we were particularly interested in the question ... [more ▼]

The acquisition of verbal number skills, as defined by the meaningful use of number words, marks a milestone in numerical development. In the present study, we were particularly interested in the question, whether verbal number skills are primarily verbal in nature, or if they call upon visuo-spatial processes, reflecting a spatial grounding of verbal number skills. 141 five- to six-year old children were tested on a range of verbal (i.e. vocabulary, phonological awareness and verbal working memory) and visuo-spatial abilities (i.e. spatial perception, visuo-motor integration and visuo-spatial working memory). We were particularly interested in the predictive role of these abilities for children’s verbal number skills (as measured by different counting and number naming tasks). In a latent regression model, basic visuo-spatial abilities, measured by spatial perception and visuo-motor integration, emerge as the most important predictor of verbal number skills. This gives raise to the assumption, that verbal number skills are, despite their verbal nature, spatially grounded in young children. [less ▲]

Project NUMTEST: Assessing basic number competence without language

Poster (2017, May 31)

While numerical skills are fundamental in modern societies, some estimated 5-7% of children suffer from a mathematical learning disorder, called developmental dyscalculia (DD). Nevertheless, universally ... [more ▼]

While numerical skills are fundamental in modern societies, some estimated 5-7% of children suffer from a mathematical learning disorder, called developmental dyscalculia (DD). Nevertheless, universally valid diagnostic instruments are still lacking, as all current DD test batteries are based on language instructions. Consequently, their measurements are tightly linked to the specific language context of test administration and thus their results cannot easily be compared across countries. Here we are showing results of the first pilot study of a research project that aims to develop a test for basic math abilities that does not rely on language instruction and minimizes language use. To this aim, video and animation based instructions were implemented on touchscreen devices. A first version of the tasks has been tested with two samples of first grade children in Luxembourg’s fundamental schools, of which half completed the same tasks with traditional verbal instructions. Our results indicate that performance in the experimental group was similar or better than the control group using verbal instructions. Relationships between linguistic background and the sample’s performance on one hand and qualitative usability aspects of nonverbal task instruction and tablet-pc use with young children will be discussed. [less ▲]