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 ▲]

Early Childhood Education and Care in Luxembourg - Is attendance influenced by immigration background and socioeconomic status?

Poster (2022, November 10)

For decades, researchers have been raising awareness of the issue of educational inequalities in the multilingual Luxemburgish school system. Especially children from families with a migration background ... [more ▼]

For decades, researchers have been raising awareness of the issue of educational inequalities in the multilingual Luxemburgish school system. Especially children from families with a migration background or a lower socio-economic status show large deficits in their language and mathematics competences in comparison to their peers. The same applies to children who do not speak Luxemburgish or German as their first language (Hornung et al., 2021; Sonnleitner et al., 2021). One way to reduce such educational inequalities might be an early and extensive participation in early childhood education and care (ECEC). Indeed, participation in ECEC was found to be positively connected to language and cognitive development in other countries, especially for children from disadvantaged families (Bennett, 2012). However, these children attend ECEC less often (Vandenbroeck & Lazzari, 2014). There are indications that lower parental costs might go hand in hand with a greater attendance of ECEC in general (for a Luxembourgish study, see Bousselin, 2019) and in particular by disadvantaged families (Busse & Gathmann, 2020). The aim of this study is to spotlight the attendance of ECEC in Luxembourg during the implementation of the ECEC reform after 2017 which increased free ECEC hours for all families from 3 to 20 hours a week. We draw on a large dataset of about 35.000 children from the Épreuves Standardisées (ÉpStan, the Luxemburg school monitoring programme) from 2015 to 2021 and investigate which children attend any kind of regulated ECEC service (public, private or family daycare) in which intensity, taking socio-economic and cultural family factors into account. The findings might help to understand in which contexts ECEC attendance should be further encouraged. Implications for future policy decisions are discussed with the goal of further promoting equal educational opportunities for all children. [less ▲]

Development of a test battery to diagnose specific learning disorder in reading in a multilingual education context

Scientific Conference (2022, November 10)

Providing timely and adequate support to children experiencing difficulties in reading and writing is key to minimize the impact on children’s academic achievements, social and emotional well-being ... [more ▼]

Providing timely and adequate support to children experiencing difficulties in reading and writing is key to minimize the impact on children’s academic achievements, social and emotional well-being, particularly for children with specific learning disorders. However, the diagnostic process is especially challenging in Luxembourg’s multilingual educational system with changing instruction languages (Luxembourgish, German, French) and multilingual population. The chosen language of the diagnostic tool is usually identical to the main language of instruction at school, which at time of diagnosis (typically grade 3) is German. This may especially affect the diagnosis of children who do not speak German or Luxembourgish at home as data from the Luxembourgish national school monitoring program reveals significant differences in German reading comprehension in grade 3 depending on the language spoken at home (Hoffmann et al., 2018; Martini et al., 2021). Furthermore, the diagnostic tools currently employed in Luxembourg are developed in countries with primarily one language of instruction, challenging the validity of the diagnostic process in a multilingual population (Ugen et al., 2021). The aim of the current project is to develop a diagnostic tool adapted to the Luxembourgish educational curriculum, that takes children’s potential proficiency differences in the test language into account in the instructions, tasks and resulting norms. This way, over-diagnosis of reading and writing disorders in children who do not speak the main language(s) of instruction at home and underdiagnosis of children who do, can be avoided. The developed test battery assesses children’s performance in key domains relevant for reading and writing comprising phonological skills, (non)word and text reading (fluency and accuracy), reading comprehension, writing, and vocabulary. We will present the pre-test results of 9 sub-tests completed by 214 children, providing the first insights into the test development and validation process.   References Hoffmann, D., Hornung, C., Gamo, S., Esch, P., Keller, U., & Fischbach, A. (2018). Schulische Kompetenzen von Erstklässlern und ihre Entwicklung nach zwei Jahren. In T. Lentz, I. Baumann, & A. Küpper (Eds.), Nationaler Bildungsbericht (pp. 84–96). University of Luxembourg & SCRIPT. Martini, S., Schiltz, C., Fischbach, A., & Ugen, S. (2021). Identifying Math and Reading Difficulties of multilingual children: Effects of different cut-offs and reference group. In M. Herzog, A. Fritz-Stratmann, & E. Gürsoy (Eds.), Diversity Dimensions in Mathematics and Language Learning (pp. 200–228). De Gruyter Mouton. Ugen, S., Schiltz, C., Fischbach, A., & Pit-ten Cate, I. M. (2021). Einleitung: Lernstörungen im multilingualen Kontext – Eine Herausforderung. In Ugen, S., Schiltz, C., Fischbach, A., & Pit-ten Cate, I. M. (Eds.), Lernstörungen im multilingualen Kontext. Diagnose und Hilfestellungen (pp3-7). Luxembourg: Melusina Press. [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 ▲]

Number transcoding in bilinguals—A transversal developmental study

in PLoS ONE (2022), 17(8), 0273391

Number transcoding is the cognitive task of converting between different numerical codes (i.e. visual “42”, verbal “forty-two”). Visual symbolic to verbal transcoding and vice versa strongly relies on ... [more ▼]

Number transcoding is the cognitive task of converting between different numerical codes (i.e. visual “42”, verbal “forty-two”). Visual symbolic to verbal transcoding and vice versa strongly relies on language proficiency. We evaluated transcoding of German-French bilinguals from Luxembourg in 5th, 8th, 11th graders and adults. In the Luxembourgish educational system, children acquire mathematics in German (LM1) until the 7th grade, and then the language of learning mathematic switches to French (LM2). French `70s `80s `90s are less transparent than `30s `40s `50s numbers, since they have a base-20 structure, which is not the case in German. Transcoding was evaluated with a reading aloud and a verbal-visual number matching task. Results of both tasks show a cognitive cost for transcoding numbers having a base-20 structure (i.e. `70s, `80s and `90s), such that response times were slower in all age groups. Furthermore, considering only base-10 numbers (i.e. `30s `40s `50s), it appeared that transcoding in LM2 (French) also entailed a cost. While participants across age groups tended to read numbers slower in LM2, this effect was limited to the youngest age group in the matching task. In addition, participants made more errors when reading LM2 numbers. In conclusion, we observed an age-independent language effect with numbers having a base-20 structure in French, reflecting their reduced transparency with respect to the decimal system. Moreover, we find an effect of language of math acquisition such that transcoding is less well mastered in LM2. This effect tended to persist until adulthood in the reading aloud task, while in the matching task performance both languages become similar in older adolescents and young adults. This study supports the link between numbers and language, especially highlighting the impact of language on reading numbers aloud from childhood to adulthood. [less ▲]

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

Scientific Conference (2022, March 09)

Ready for the future? – The third Education Report for Luxembourg (Supplement)

E-print/Working paper (2022)

The influence of tens and units inversion in a two-digit number matching task in German and French monolinguals and bilinguals

Poster (2022)

Artificial intelligence and machine learning: an introduction for orthopaedic surgeons

in Knee Surgery, Sports Traumatology, Arthroscopy (2022), 30

Différences de performance dans les compétences langagières et en lecture entre élèves à parcours scolaire régulier et irrégulier, issus de familles immigrées portugaises au Luxembourg.

in University of Luxembourg, LUCET; Ministère de l’Éducation nationale, de l’Enfance et de la Jeunesse, SCRIPT (Eds.) Rapport national sur l’éducation au Luxembourg 2021 (2021)