The crucial role of language in mathematical development

Scientific Conference (2022, November 17)

Basic mathematics skills build on nonverbal number sense But these innate non-verbal skills are insufficient to develop symbolic exact number concepts and to learn arithmetic. Language development allows ... [more ▼]

Basic mathematics skills build on nonverbal number sense But these innate non-verbal skills are insufficient to develop symbolic exact number concepts and to learn arithmetic. Language development allows the acquisition of number words and math vocabulary, crucial for developing basic exact number concepts and arithmetic skills. This presentations highlights five key aspects on how language influences mathematical development. First, language is a building block for basic math skills. Second, number naming systems affect number transcoding. Third, multilingual students calculate better in the language in which they have learned numbers. Forth, children's home language influences their mathematics achievement. And finally, the mastery of the language of instruction has a strong impact on mathematics achievement. The implication of these key aspects are discussed with regard to education and instruction in schools. [less ▲]

Validation and Psychometric Analysis of 32 cognitive item models spanning Grades 1 to 7 in the mathematical domain of numbers & operations

Scientific Conference (2022, November)

Today’s educational field has a tremendous hunger for valid and psychometrically sound items to reliably track and model students’ learning processes. Educational large-scale assessments, formative ... [more ▼]

Today’s educational field has a tremendous hunger for valid and psychometrically sound items to reliably track and model students’ learning processes. Educational large-scale assessments, formative classroom assessment, and lately, digital learning platforms require a constant stream of high-quality, and unbiased items. However, traditional development of test items ties up a significant amount of time from subject matter experts, pedagogues and psychometricians and might not be suited anymore to nowadays demands. Salvation is sought in automatic item generation (AIG) which provides the possibility of generating multiple items within a short period of time based on the development of cognitively sound item templates by using algorithms (Gierl & Haladyna, 2013; Gierl et al., 2015). The present study psychometrically analyses 35 cognitive item models that were developed by a team of national subject matter experts and psychometricians and then used for algorithmically producing items for the mathematical domain of numbers & shapes for Grades 1, 3, 5, and 7 of the Luxembourgish school system. Each item model was administered in 6 experimentally varied versions to investigate the impact of a) the context the mathematical problem was presented in, and b) problem characteristics which cognitive psychology identified to influence the problem solving process. Based on samples from Grade 1 (n = 5963), Grade 3 (n = 5527), Grade 5 (n = 5291), and Grade 7 (n = 3018) collected within the annual Épreuves standardisées, this design allows for evaluating whether psychometric characteristics of produced items per model are a) stable, b) can be predicted by problem characteristics, and c) are unbiased towards subgroups of students (known to be disadvantaged in the Luxembourgish school system). After item calibration using the 1-PL model, each cognitive model was analyzed in-depth by descriptive comparisons of resulting IRT parameters, and the estimation of manipulated problem characteristics’ impact on item difficulty by using the linear logistic test model (LLTM, Fischer, 1972). Results are truly promising and show negligible effects of different problem contexts on item difficulty and reasonably stable effects of altered problem characteristics. Thus, the majority of developed cognitive models could be used to generate a huge number of items (> 10.000.000) for the domain of numbers & operations with known psychometric properties without the need for expensive field-trials. We end with discussing lessons learned from item difficulty prediction per model and highlighting differences between the Grades. References: Fischer, G. H. (1973). The linear logistic test model as an instrument in educational research. Acta Psychologica, 36, 359-374. Gierl, M. J., & Haladyna, T. M. (Eds.). (2013). Automatic item generation: Theory and practice. New York, NY: Routledge. Gierl, M. J., Lai, H., Hogan, J., & Matovinovic, D. (2015). A Method for Generating Educational Test Items That Are Aligned to the Common Core State Standards. Journal of Applied Testing Technology, 16(1), 1–18. [less ▲]

Validierung und psychometrische Analyse automatisch generierter Mathematikaufgaben im Bereich Zahlen und Operationen

Scientific Conference (2022, March 09)

Sprach- und Leseunterschiede zwischen portugiesischen Migrantenkindern mit und ohne Klassenwiederholung in Luxemburg.

in University of Luxembourg, LUCET; Ministère de l’Éducation nationale, de l’Enfance et de la Jeunesse, SCRIPT, (Eds.) Nationaler Bildungsbericht Luxemburg 2021 (2021)

Antônio ist ein Junge aus Luxemburg im schulpflichtigen Alter. Er wird demnächst Lesen und Schreiben lernen. Antônios Eltern sind Portugiesen, und zu Hause sprechen sie nur ihre Muttersprache. In Cycle 1 ... [more ▼]

Antônio ist ein Junge aus Luxemburg im schulpflichtigen Alter. Er wird demnächst Lesen und Schreiben lernen. Antônios Eltern sind Portugiesen, und zu Hause sprechen sie nur ihre Muttersprache. In Cycle 1 (Vorschule) hat Antônio Luxemburgisch sprechen gelernt. Seit er in der Vorschule mit der Sprache in Berührung gekommen ist, hat er sich einen großen Wortschatz in Luxemburgisch angeeignet. Wortschatzkenntnisse gehören zu den wichtigsten Voraussetzungen für das Lesen (Lervåg & Aukrust, 2010). Kinder, die das Lesenlernen mit umfangreicheren Wortschatzkenntnissen beginnen, haben bessere Chancen auf Lernerfolge beim Lesen. Für Kinder in Luxemburg ist es eine große Herausforderung, dass der Schriftspracherwerb in Deutsch erfolgt, das für die meisten von ihnen eine Fremdsprache ist, und nicht in Luxemburgisch, also der Sprache, die sie zuvor in Cycle 1 gelernt haben. [less ▲]

Nouveaux résultats longitudinaux issus du monitoring scolaire national ÉpStan en première et troisième année scolaire (cycles 2.1 et 3.1) : tendance négative au niveau du développement des compétences et redoublements inefficaces

in LUCET; SCRIPT (Eds.) Rapport national sur l’éducation au Luxembourg 2021 (2021)

Résultats du monitoring scolaire national ÉpStan dans le contexte de la pandémie de COVID-19

in LUCET; SCRIPT (Eds.) Rapport national sur l’éducation au Luxembourg 2021 (2021)

Résultats du monitoring scolaire national ÉpStan dans le contexte de la pandémie de COVID-19 (Matériels supplémentaires)

in LUCET; SCRIPT (Eds.) Rapport National sur l´Éducation au Luxembourg 2021 (2021)

Using Automatic Item Generation in the context of the Épreuves Standardisées (Épstan): A pilot study on effects of altering item characteristics and semantic embeddings

Scientific Conference (2021, November 11)

Assessing mathematical skills in national school monitoring programs such as the Luxembourgish Épreuves Standardisées (ÉpStan) creates a constant demand of developing high-quality items that is both ... [more ▼]

Assessing mathematical skills in national school monitoring programs such as the Luxembourgish Épreuves Standardisées (ÉpStan) creates a constant demand of developing high-quality items that is both expensive and time-consuming. One approach to provide high-quality items in a more efficient way is Automatic Item Generation (AIG, Gierl, 2013). Instead of creating single items, cognitive item models form the base for an algorithmic generation of a large number of new items with supposedly identical item characteristics. The stability of item characteristics is questionable, however, when different semantic embeddings are used to present the mathematical problems (Dewolf, Van Dooren, & Verschaffel, 2017, Hoogland, et al., 2018). Given culture-specific knowledge differences in students, it is not guaranteed that illustrations showing everyday activities do not differentially impact item difficulty (Martin, et al., 2012). Moreover, the prediction of empirical item difficulties based on theoretical rationales has proved to be difficult (Leighton & Gierl, 2011). This paper presents a first attempt to better understand the impact of (a) different semantic embeddings, and (b) problem-related variations on mathematics items in grades 1 (n = 2338), 3 (n = 3835) and 5 (n = 3377) within the context of ÉpStan. In total, 30 mathematical problems were presented in up to 4 different versions, either using different but equally plausible semantic contexts or altering the problem’s content characteristics. Preliminary results of IRT-scaling and DIF-analysis reveal substantial effects of both, the embedding, as well as the problem characteristics on general item difficulties as well as on subgroup level. Further results and implications for developing mathematic items, and specifically, for using AIG in the course of Épstan will be discussed. [less ▲]

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 ▲]

LEARN Newsletter - Editioun 2021

Book published by LEARN (2021)