This case study examines the salient features of two individuals' reasoning when confronted with a task concerning the cardinality and associated cardinal number of equinumerous infinite sets. The APOS Theory was used as a framework to interpret their efforts to resolve the "infinite balls paradox" and one of its variants. These cases…

This study aims to examine the enhancement of mathematical reasoning ability through reflective learning. This study used quasi-experimental method with nonequivalent pretest and posttest control group design. The subject of this study were students of Mathematics Education Program in one of private universities in Palembang, South Sumatera,…

This study's hypotheses were that (a) word-problem (WP) solving is a form of text comprehension that involves language comprehension processes, working memory, and reasoning, but (b) WP solving differs from other forms of text comprehension by requiring WP-specific language comprehension as well as general language comprehension. At the start of…

We present a synthesis of findings from constructivist teaching experiments regarding six schemes children construct for reasoning multiplicatively and tasks to promote them. We provide a task-generating platform game, depictions of each scheme, and supporting tasks. Tasks must be distinguished from children's thinking, and learning situations…

When students reason during school science, they often refer to conceptions that are derived from out-of-school experiences and are poor proxies for science orthodoxy. However, for some areas of science, these conceptions represent only a proportion of students' full conceptual knowledge, for tacit understanding exists that is superior to the…

Tasks that develop spatial and algebraic reasoning are crucial for learning and applying advanced mathematical ideas. In this article, the authors describe how two early childhood teachers used stories as the basis for a unit that supports spatial reasoning in kindergartners and first graders. Having mathematical experiences that go beyond…

Early language development is characterized by predictable changes in the words children produce and the complexity of their utterances. In infants, these changes could reflect increasing linguistic expertise or cognitive maturation and development. To disentangle these factors, we compared the acquisition of English in internationally-adopted…

The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) identifies the strategic use of appropriate tools as one of the mathematical practices and emphasizes the use of pictures and diagrams as reasoning tools. Starting with the early elementary grades, CCSSM discusses students' solving of problems "by drawing." In later…

We followed established best practices in concept inventory design and developed a 12-item inventory to assess student ability in statistical reasoning in biology (Statistical Reasoning in Biology Concept Inventory [SRBCI]). It is important to assess student thinking in this conceptual area, because it is a fundamental requirement of being…

Abstraction is one of the methods for learning knowledge with using mental processes that cannot be obtained through experiment and observation. RBC model that is based on abstraction in the process of creating knowledge is directly related to mental processes. In this study, the RBC model is used for the high school students' processes of…

Building on the multidimensional framework of epistemic cognition proposed by Greene et al. ("Educational Psychologist" 43:142--160, 2008), this study examined beliefs about justification of knowledge claims in science among 65 Norwegian 10th graders. The first research question asked whether beliefs in personal justification,…

In the authors' examination of various instructional programs, they observed that most provide all the necessary data to solve proportion problems, employ compatible numbers that are usually unrealistic, present numbers (data) in the order in which they are to be manipulated, discuss contexts that cannot be easily replicated, and present…

Proportional reasoning is important for informed decisions in proportional problem situations. This paper reports on mathematical content knowledge related to proportional reasoning of second-year, pre-service teachers. Responses to two ratio items provide insights into their correct method of solutions and common misconceptions. Anchor Points…

The Common Core State Standards emphasize students writing analytically in response to texts. Questions remain about the nature of instruction that develops students' text-based writing skills. In the present study, we examined the role that writing task quality plays in students' mastery of analytic text-based writing. Text-based writing tasks…

We use a longitudinal national dataset to explore the direct and conditional effects of fraternity/sorority membership on students' educational outcomes in the 4th year of college. Controlling for a variety of potentially confounding variables, including pretest measures of the outcomes, we find no direct effect of fraternity/sorority membership…