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…

Cross-sectional and longitudinal data from students as they advance through the middle school years (grades 6-8) reveal insights into the development of students' pattern generalization abilities. As expected, students show a preference for lower-level tasks such as "reading the data," over more distant predictions and generation of abstractions.…

This study examined test-related experiences of enjoyment, anger, anxiety, and boredom in a sample of 2059 German school students (50% female) from grade 6, and how they relate to students' abstract reasoning ability (ARA). Emotions were assessed immediately before, during, and after a mathematics achievement test. Analysis of variance showed that…

Depression has been linked to cognitive deficits and learned helplessness models in various theories. To examine depression effects on abstract problem solving ability and the relationship between intelligence and anxiety, 66 of 303 college students (23 male, 43 female), evidencing least and most depressed states as assessed by the Beck Depression…

Studies exploring the transition from early to middle adolescence have found a significant increase in formal-operational thinking, but it is questionable whether the typical adolescent is capable of consistently applying formal operational logic. To examine the relationship between Piagetian-based training techniques and formal-operational…

Author attempted to outline a concept of logic that involves standards of correct reasoning as well as some idea of how these might be carried out in a classroom. (Author/RK)

In teaching symbolic logic to students not majoring in mathematics, one can appeal to simple arithmetic examples, set theory examples, and the use of conjunction and disjunction as aids in presenting the conditional. (SD)