Early number competence, grounded in number-specific and domain-general cognitive abilities, is theorized to lay the foundation for later math achievement. Few longitudinal studies have tested a comprehensive model for early math development. Using structural equation modeling and mediation analyses, the present work examined the influence of kindergarteners’ nonverbal number sense and domain-general abilities i.e., working memory, fluid intelligence, and receptive vocabulary) and their early number competence (i.e., symbolic number skills) on first grade math achievement (arithmetic, shape and space skills, and number line estimation) assessed one year later. Latent regression models revealed that nonverbal number sense and working memory are central building blocks for developing early number competence in kindergarten and that early number competence is key for first grade math achievement. After controlling for early number competence, fluid intelligence significantly predicted arithmetic and number line estimation while receptive vocabulary significantly predicted shape and space skills. In sum we suggest that early math achievement draws on different constellations of number-specific and domain-general mechanisms.

In this rejoinder, we respond to two commentaries on the study by Greiff, S.; Stadler, M.; Sonnleitner, P.; Wolff, C.; Martin, R. Sometimes less is more: Comparing the validity of complex problem solving measures. Intelligence 2015, 50, 100–113. The study was the first to address the important comparison between a classical measure of complex problem solving (CPS) and the more recent multiple complex systems (MCS) approach regarding their validity. In the study, we investigated the relations between one classical microworld as the initially developed method (here, the Tailorshop) with three more recently developed multiple complex systems (MCS; here, MicroDYN, Genetics Lab, and MicroFIN) tests. We found that the MCS tests showed higher levels of convergent validity with each other than with the Tailorshop even after reasoning was controlled for, thus empirically distinguishing between the two approaches. The commentary by Kretzschmar and the commentary by Funke, Fischer, and Holt expressed several concerns with how our study was conducted, our data was analyzed, and our results were interpreted. Whereas we acknowledge and agree with some of the more general statements made in these commentaries, we respectfully disagree with others, or we consider them to be at least partially in contrast with the existing literature and the currently available empirical evidence.

Le présent article analyse les changements qui ont été introduits dans les enquêtes comparatives internationales (plus spécifiquement celles de l’OCDE) par suite de l’introduction du testing assisté par ordinateur. On passera en revue les différents instruments de mesure administrés par ordinateur qui ont été utilisés dans les différents cycles de ces enquêtes et on discutera si elles ont réellement impliqué une valeur ajoutée, notamment par le fait de fournir des données sur des compétences qui sont inaccessibles à travers des instruments classiques sous format papier-crayon. On analysera également les relations spécifiques que les mesures assistées par ordinateur entretiennent avec des variables d’arrière-fond tel le genre. Finalement, l’article mettra en évidence les défis et les risques qui sont associés avec une introduction de plus en plus massive d’instruments de mesure assistés par ordinateur, notamment en ce qui concerne deux aspects majeurs: la nécessité de garder une continuité dans les compétences mesurées en vue de mettre en évidence des évolutions, et le manque de cadres théoriques adéquats pour la mise en oeuvre efficace des mesures assistées par ordinateur.