The purpose of this study was to investigate students' conceptions about watersheds. Specifically: (1) What are students' conceptions of a watershed? and (2) In what ways might students' conceptions vary by grade level and community setting? This study was descriptive in nature and reflected a cross-age design involving the collection of…

Instructional strategies for teaching concepts have long been identified. Less commonly studied is a learner's level of confidence and certitude in their knowledge based upon exposure to these instructional treatments. This experimental research study used an instrument referred to as the Spatial Probability Measure (SPM) to solicit levels of…

Many teachers administer a force concept test such as the Force Concept Inventory (FCI) to their students in an effort to evaluate and improve their instructional practices. It has been commonly assumed that looking at class normalized gains allows teachers to compare their courses with other courses. In this paper we present evidence to suggest…

Much of the difficulty that students encounter in the transition from arithmetic to algebra stems from their early learning and understanding of arithmetic. Too often, students learn about the whole number system and the operations that govern that system as a set of procedures to solve addition, subtraction, multiplication, and division problems.…

Busy educators find it difficult to work creatively in conditions imposed by ill-conceived, politically charged reform initiatives such as the No Child Left Behind Act. In order to keep up with research findings, emerging theories and practical recommendations in the creativity literature, they need accessible, highly condensed distillations of…

The paper reports on a study of five pupils' (13-14 years old) learning about freshwater pollution and related theoretical concepts such as drainage basin and water pollution. Much of the instruction is devoted to fieldwork conducted at a polluted lake and other practical activities designed to promote the pupils' understanding of the central…

The inertial balance is one device that can help students to quantify the quality of inertia--a body's resistance to a change in movement--in more generally understood terms of mass. In this hands-on activity, students use the inertial balance to develop a more quantitative idea of what mass means in an inertial sense. The activity also helps…

"Working Smarter, Not Harder: Reaching the Tough to Teach" is the topic of an exclusive four-part series by Sylvia Rockwell for the "Kappa Delta Pi Record." Part I describes the characteristics of students at risk of school failure, provides an overview of research-based principles found to be effective with all students and essential for students…

Building a repertoire of teaching skills means organizing instructional strategies in some meaningful way. In this brief essay, the author recommends that beginning teachers develop a repertoire comprised of a mix of strategies from each of Joyce, Weil, and Calhoun's (2004) categories: three strategies from the Cognitive Family (Concept…

One of the important phenomena observed in the learning of mathematics is compartmentalization. This phenomenon occurs when a learner has two different, potentially contradictory schemes in his or her cognitive structure; in a typical case, a student deals with the same mathematical concept in an inconsistent or incoherent way, or activates a less…

This paper considers mathematical abstraction as arising through a natural mechanism of the biological brain in which complicated phenomena are compressed into thinkable concepts. The neurons in the brain continually fire in parallel and the brain copes with the saturation of information by the simple expedient of suppressing irrelevant data and…

Sociocultural and cognitive perspectives hold to epistemically different views on knowledge acquisition and change. While sociocultural perspectives point to social experience as the principal source of knowledge, cognitive perspectives emphasize the importance of the individual mind and reasoning as the primary source of knowledge. Herein, I…

This study presents the results of a partial credit Rasch analysis of in-depth interview data exploring statistical understanding of 73 school students in 6 contextual settings. The use of Rasch analysis allowed the exploration of a single underlying variable across contexts, which included probability sampling, representation of temperature…

The basic assumption of this paper is that mathematics and history of mathematics are both forms of knowledge and, therefore, represent different ways of knowing. This was also the basic assumption of Fried (2001) who maintained that these ways of knowing imply different conceptual and methodological commitments, which, in turn, lead to a conflict…

The perspective of situated learning offers a theoretical framework for understanding the dialectical relations between the social and the individual dimensions of classroom microculture. The purpose of this article is to show how sociomathematical norms constructed during whole-class discussions provide a reference for the elaboration of…