Considers the value of preschool children saying the Pledge of Allegiance daily in their classrooms. Suggests that there may be better ways to help children grasp abstract concepts like patriotism and to provide developmentally appropriate ways to explore the symbol of the flag. (LB)

Discusses children's use of metaphors to create meaning, using as an example the pragmatic and "scientific" ways in which preschool children explain thunder and lightning to themselves. Argues that children are being shortchanged by modern scientific notions of abstractness and that they should be encouraged to create their own explanations of…

Presents some methods for describing and referring to mathematical objects and consistently and unambiguously signaling the logical structure of mathematical arguments. Presents the problems involved in referring to mathematics objects and properties. Discusses certain individual words used to communicate the logical structure of mathematical…

This study examined above-grade-level abstract reasoning abilities of 150 students (grades 2-6). Understanding of abstract concepts varied by age for only four of eight subscales or concepts: probability, proportion, momentum, and frames of reference. Performance varied widely within age level for the understanding of volume, correlation,…

Utilizes a psychological-constructivist perspective to examine the transitions that students make from arithmetic to algebra in the context of problems that, from an expert's perspective, involve the concept of linear inequality. Reports that students who completed a transition to algebra operated at higher levels of reflective abstraction than…

Investigates the concepts of ratio and proportion constructed by grade 9 students by investigating their proportional reasoning schemes and procedures on three types of tasks: missing value, numerical comparison, and qualitative reasoning. Indicates that students frequently used additive reasoning--that is, a comparison of two numbers by…

Aims to acquire better understanding of how informal learning experiences may interface with classroom science instruction by investigating one aspect of science learning, that of scientific reasoning ability. Investigates possible differences in students' scientific reasoning abilities relative to their informal learning environments, classroom…

Evaluates the thinking of third grade students in relation to an instructional program in probability which was informed by a research-based framework that included a description of students' probabilistic thinking. Reveals that overcoming misconceptions in sample space, applying both part-part and part-whole reasoning, and using invented language…

While teaching, teachers need to access both their knowledge of mathematics and knowledge of pedagogy. Practice-based materials afford teachers opportunities to reason about both mathematics and pedagogy within the context of teaching. Accepted systems exist for explaining and reasoning in the domain of mathematics; logic, procedures, and…

There is a growing interest in the mathematics education community in the notion of abstraction and its significance in the learning of mathematics. "Reducing abstraction" is a theoretical framework that examines learners' behavior in terms of coping with abstraction level. It refers to situations in which learners are unable to manipulate…

Literature on relational reasoning mainly focuses on the performance question. It is typically argued that problem difficulty relies on the number of ''mental models'' compatible with the problem. However, no study has ever investigated the wording of conclusions that participants formulate. In the present work, we analyze the relational terms…

The purpose of this study was to examine the perceived reasons of pre-service music educators (undergraduate music majors preparing to teach music) for preferring three distinctive pieces with traditional roots in East Asia. The selected pieces were foreign to research participants in the US. Pre-service music educators (N = 66) listened to a…

Abstract algebra courses tend to take one of two pedagogical routes: from examples of mathematics structures through definitions to general theorems, or directly from definitions to general theorems. The former route seems to be based on the implicit pedagogical intention that students will use their understanding of particular examples of an…

When worthwhile mathematical tasks are used in classrooms, they should also become a crucial element of assessment. For teachers, using these tasks in classrooms requires a different way to analyze student thinking than the traditional assessment model. Looking carefully at students' written work on worthwhile mathematical tasks and listening…

"What does deep ethical understanding look like and how can we measure the progression of this aptitude?" Qualitative and quantitative data collected from students in Contemporary Moral Problems courses over two successive semesters revealed that the development of moral reasoning skills is a slow process. The progression of moral…