In a repeated measures design (pretest, posttest, 1-year follow-up) with 161 3rd-grade students, the authors compared 2 curricula on floating and sinking within constructivist learning environments, varying in instructional support. The 2 curricula differed in the sequencing of content and the teacher's cognitively structuring statements. At the posttest, both instructed groups showed significant gains on a test on understanding the concepts of density and buoyancy force as compared to a baseline group without instruction. One year later, the group of high instructional support was superior to the group of low instructional support on the reduction of misconceptions and the adoption of scientific explanations. Thus, instructional support within constructivist learning environments fostered elementary schoolchildren's conceptual change in the domain of physics.

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Conceptual change requires learners to restructure parts of their conceptual knowledge base. Prior research has identified the fragmentation and the integration of knowledge as 2 important component processes of knowledge restructuring but remains unclear as to their relative importance and the time of their occurrence during development. Previous studies mostly were based on the categorization of answers in interview studies and led to mixed empirical results, suggesting that methodological improvements might be helpful. We assessed 161 third-graders' knowledge about floating and sinking of objects in liquids at 3 measurement points by means of multiple-choice tests. The tests assessed how strongly the children agreed with commonly found but mutually incompatible statements about floating and sinking. A latent profile transition analysis of the test scores revealed 5 profiles, some of which indicated the coexistence of inconsistent pieces of knowledge in learners. The majority of students (63%) were on 1 of 7 developmental pathways between these profiles. Thus, a child's knowledge profile at a point in time can be used to predict further development. The degree of knowledge integration decreased on some individual developmental paths, increased on others, and remained stable on still others. The study demonstrates the usefulness of explicit quantitative models of conceptual change. The results support a constructivist perspective on conceptual development, in which developmental changes of a learner's knowledge base result from idiosyncratic, yet systematic knowledge-construction processes.

Previous research has emphasized the importance of language for learning mathematics. This is especially true when mathematical problems have to be extracted from a meaningful context, as in arithmetic word problems. Bilingual learners with a low command of the instructional language thus may face challenges when dealing with mathematical concepts. At the same time, speaking two languages can be associated with cognitive benefits with regard to attentional control processes, although such benefits have only been found in highly proficient bilinguals. In the present study, we attempted to disentangle the effects of bilingual proficiency on mathematical problem solving in Turkish-German bilingual elementary school students. We examined whether the positive cognitive effects of bilingualism could be found not only in highly proficient bilinguals but also in students with an immigrant background and a low command of the instructional or native language. Our findings emphasize the importance of language proficiency for mathematics problem solving, as shown by the predictive value of students' proficiency in the language of testing (German/Turkish) for their performance on mathematical word problems. No additional effect of the language of instruction (German) was found for problem solving in the bilingual students' native language (Turkish). Furthermore, bilinguals gained scores comparable to those of their monolingual peers on word problems that required attentional control skills although performing significantly below their monolingual classmates on ordinary word problems, suggesting that bilinguals have an advantage when it comes to attentional control. Finally, bilingual students with a relatively high command of the instructional language performed better on word problems presented in German than on those presented in Turkish, thus facing cognitive costs when transferring knowledge from one language to the other. Implications of our findings for bilingual education are discussed.

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