Learning mathematics with shackles: How lower reading comprehension in the language of mathematics instruction accounts for lower mathematics achievement in speakers of different home languages.

Achievement in mathematics has been shown to partially depend on verbal skills. In multilingual educational settings, varying language proficiencies might therefore contribute to differences in mathematics achievement. We explored the relationship between mathematics achievement and language competency in terms of home language and instruction language proficiency in the highly multilingual society of Luxembourg. We focussed on third graders' linguistic and mathematical achievement and used data from the national school monitoring program from two consecutive years to assess the influence of children's language profiles on reading comprehension in German (the instruction language) and mathematics performance. Results were similar for both cohorts. Regression analysis indicated that German reading comprehension was a significant predictor of mathematics achievement when accounting for both home language group and socioeconomic status. Moreover, mediation analysis showed that lower mathematics achievement of students with a home language that is very different from the instruction language relative to the Luxembourgish reference group were significantly mediated by achievement in German reading comprehension. These findings show that differences in mathematics achievement between speakers of a home language that is similar to the instruction language and speakers of distant home languages can be explained by their underachievement in reading comprehension in the instruction language. Possible explanations for varying performance patterns between language groups and solutions are being discussed.

Sometimes More is Too Much: A Rejoinder to the Commentaries on Greiff et al. (2015).

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.