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The important role that metacognition plays as a predictor for student mathematical learning and for mathematical problem-solving, has been extensively documented. But only recently has attention turned to primary grades, and more research is needed at this level. The goals of this paper are threefold: (1) to present metacognitive framework during mathematics problem-solving, (2) to describe their multi-method interview approach developed to study student mathematical metacognition, and (3) to empirically evaluate the utility of their model and the adaptation of their approach in the context of grade 2 and grade 4 mathematics problem-solving. The results are discussed not only with regard to further development of the adapted multi-method interview approach, but also with regard to their theoretical and practical implications.
Does competent bilingualism entail advantages for the third language learning of immigrant students?
(2018)
This study examined the role of immigrant bilingualism in third language learning (L3 = English). It focused on the respective effects of students' competence in the minority language (L1 = Turkish or Russian) and language of instruction (L2 = German). We analyzed a sample of 8752 German 10th-grade students (N = 7964 monolinguals, N = 436 Turkish-German students, N = 352 Russian-German students) and drew on standardized tests in L1, L2, and L3. OLS-regression models showed L3 advantages for balanced bilinguals at a high level in both language groups compared to their average monolingual peers when third variables were controlled, while advantages in the L2 dominant bilinguals could only be observed in the Russian-German sample. Balanced bilinguals at a low level and L1 dominants attained lower L3 levels than monolinguals. However, comparisons with comparably high proficient monolinguals, as well as further analyses with the bilingual samples separately, revealed that only L2 competence – and not L1 competence – explained immigrant students' L3 proficiency. Our findings indicate that the advantages of immigrant bilinguals in L3 learning mainly depend on their competence in the language of instruction.
This study examined a theoretical model hypothesizing that reading strategies mediate the effects of intrinsic reading motivation, reading fluency, and vocabulary knowledge on reading comprehension. Using path analytic methods, we tested the direct and indirect effects specified in the hypothesized model in a sample of 1105 fifth-graders. In addition to standardized tests and questionnaires, we administered a performance test to assess students' proficiency in the application of three reading strategies. The overall fit of the model to the data was good. Both cognitive (fluency and vocabulary) and motivational (intrinsic reading motivation) variables had an indirect effect on reading comprehension through their influence on reading strategies. Reading strategies had a unique effect on reading comprehension and partially mediated the effects that cognitive and motivational variables had on fifth-graders' reading achievements.
Nonsymbolic numerical magnitude processing skills are assumed to be fundamental to mathematical learning. Recent findings suggest that visual–spatial skills account for associations between children’s performance in visually presented nonsymbolic numerical magnitude comparison tasks and their performance in visually presented arithmetic tasks. The aim of the current study was to examine whether associations between children’s performance in visually presented tasks assessing nonsymbolic numerical magnitude processing skills and their performance in tasks assessing early mathematical skills, which do not involve visual stimulation, may also be mediated by visual–spatial skills. This line of reasoning is based on the assumption that children make use of mental visualization processes when working on tasks assessing early mathematical skills, such as knowledge of the sequence of number words, even when these tasks do not involve visual stimulation. We assessed 4- to 6-year-old children’s performance in a nonsymbolic numerical magnitude comparison task, in tasks concerning knowledge of the sequence of number words, and in a developmental test to assess visual–spatial skills. Children’s nonsymbolic numerical magnitude processing skills were found to be associated with their number word sequence skills. This association was fully mediated by interindividual differences in visual–spatial skills. The effect size of this mediation effect was small. We assume that the ability to construct mental visualizations constitutes the key factor underlying this mediation effect.
This article describes architectural extensions for a dynamically scheduled processor to enable three different operation modes, ranging from high-performance, to high-reliability. With minor extensions of the control path, the resources of the super-scalar data-path can be used either for high-performance execution, fail-safe-operation, or fault-tolerant-operation. Furthermore, the online error-correction capabilities are combined with reconfiguration techniques for permanent fault handling. This reconfiguration can take defective components out of operation permanently, and can be triggered on-demand during runtime, depending on the frequency of online corrected faults. A comprehensive fault simulation was carried out in order to evaluate hardware overhead, fault coverage and performance penalties of the proposed approach. Moreover, the impact of the permanent reconfiguration regarding the reliability and performance is investigated.