Nonparametric regression as an example of model choice

Nonparametric regression can be considered as a problem of model choice. In this paper we present the results of a simulation study in which several nonparametric regression techniques including wavelets and kernel methods are compared with respect to their behaviour on different test beds. We also include the taut-string method whose aim is not to minimize the distance of an estimator to some ?true? generating function f but to provide a simple adequate approximation to the data. Test beds are situations where a ?true? generating f exists and in this situation it is possible to compare the estimates of f with f itself. The measures of performance we use are the L2 and the L1 norms and the ability to identify peaks. --

Constructing a regular histogram : a comparison of methods

Even for a well-trained statistician the construction of a histogram for a given real-valued set is a sifficult problem. It is even more difficult to construct a fully automatic procedure which specifies the number and widths of the binss in a satisfactory manner for a wide range of data sets. In this paper we compare several histogram construction methods by means of a simulation study. The study includes plug-in methods, cross-validation, penalized maximum likehood and the taut string procedure. Their performance on different test beds is measured by the Hellinger distance and the ability to identify the modes of the underlying density. --regular histogramm,model selection,penalized likehood,taut-string

Nr. 14/2011The benchden Package: Benchmark Densities for Nonparametric Density Estimation

The benchden package: Benchmark densities for nonparametric density estimatio

Cracking percent problems in different formats: The role of texts and visual models for students with low and high language proficiency

International audienceStudents with low academic language proficiency are often considered to meet specific comprehension challenges with word problems. But how do conceptual and reading challenges interfere in these situations? We approach this question by investigating how performance depends on the problem format for different problem types. A test with N=250 students investigates cracking percent problems in pure, text, and visual format. The results show that text formats are most difficult for elementary problem types, whereas (context t can enhance the accessibility for more complex problem types. Item difficulties differ similarly for students with high and low language proficiency, hence reading challenges seem as crucial as conceptual challenges. A deeper analysis shows specific linguistic challenges with the expressions reduced to and reduced by

Cracking percent problems in different formats: The role of texts and visual models for students with low and high language proficiency

International audienceStudents with low academic language proficiency are often considered to meet specific comprehension challenges with word problems. But how do conceptual and reading challenges interfere in these situations? We approach this question by investigating how performance depends on the problem format for different problem types. A test with N=250 students investigates cracking percent problems in pure, text, and visual format. The results show that text formats are most difficult for elementary problem types, whereas (context t can enhance the accessibility for more complex problem types. Item difficulties differ similarly for students with high and low language proficiency, hence reading challenges seem as crucial as conceptual challenges. A deeper analysis shows specific linguistic challenges with the expressions reduced to and reduced by

Which factors coincide with mathematical learning gains in bilingual classrooms?

Although bilingual mathematical learning opportunities have often been requested for multilingual students, little quantitative evidence has been provided that activating two languages has measurable effects on learning gains. This study uses data from a bilingual teaching intervention to investigate which factors coincide most with the mathematical learning gains in conceptual understanding of fractions. Students’ individual and family characteristics have been assessed and participation and language use have been coded in ~95h videotaped teaching-learning processes. A regression analysis shows that students’ learning gains can best be explained by students’ German language proficiency and their use of Turkish and mixed mode, while talking time did not coincide with learning gains. Thus, the connection of languages seems to be even more important for mathematical learning gains than the isolated use of home languages or active participation

Which factors coincide with mathematical learning gains in bilingual classrooms?

Although bilingual mathematical learning opportunities have often been requested for multilingual students, little quantitative evidence has been provided that activating two languages has measurable effects on learning gains. This study uses data from a bilingual teaching intervention to investigate which factors coincide most with the mathematical learning gains in conceptual understanding of fractions. Students’ individual and family characteristics have been assessed and participation and language use have been coded in ~95h videotaped teaching-learning processes. A regression analysis shows that students’ learning gains can best be explained by students’ German language proficiency and their use of Turkish and mixed mode, while talking time did not coincide with learning gains. Thus, the connection of languages seems to be even more important for mathematical learning gains than the isolated use of home languages or active participation

Which factors coincide with mathematical learning gains in bilingual classrooms? German language proficiency and mixed language use

International audienceAlthough bilingual mathematical learning opportunities have often been requested for multilingual students, little quantitative evidence has been provided that activating two languages has measurable effects on learning gains. This study uses data from a bilingual teaching intervention to investigate which factors coincide most with the mathematical learning gains in conceptual understanding of fractions. Students’ individual and family characteristics have been assessed and participation and language use have been coded in ~95h videotaped teaching-learning processes. A regression analysis shows that students’ learning gains can best be explained by students’ German language proficiency and their use of Turkish and mixed mode, while talking time did not coincide with learning gains. Thus, the connection of languages seems to be even more important for mathematical learning gains than the isolated use of home languages or active participation