This study examines prospective elementary teachers' growth and development of competencies, conceptions, and perceptions of mathematical modelling in a mathematics content course for elementary teachers. A series of lessons were implemented that engaged students in the modelling process through modelling tasks. The goal was to capture prospective…

This study investigates prospective elementary and secondary school mathematics teachers' ways of reasoning about differentiability at a point and corner points while working on a mathematical modelling activity. Adopting a multiple-case study design, the participants of the study were 68 prospective elementary school mathematics teachers enrolled…

Forming part of a wider research study, the current study investigated prospective middle school mathematics teachers' ways of covariational reasoning on tasks involving simultaneously changing quantities. As the introductory theme of a larger unit on derivative, a model development sequence on covariational reasoning was designed and experimented…

The purpose of the study was to investigate the effects of the instruction with mathematical modeling on pre-service mathematics teachers' mathematical modeling performance. The participants were 24 pre-service elementary mathematics teachers. A mixed method approach was used to conduct the research. Each week, the participants were given two…

The development of mathematical thinking plays an important role on the solution of problems faced in daily life. Determining the relevant variables and necessary procedural steps in order to solve problems constitutes the essence of mathematical thinking. Mathematical modeling provides an opportunity for explaining thoughts in real life by making…

This article examines how visual representations may mediate the teaching and learning of mathematics over time in Japanese elementary classrooms. Using the Zone of Proximal Development Mathematical Learning Model (Murata & Fuson, 2006; Fuson & Murata, 2007), the process of mediation is explicated. The tape diagram, a central visual…

Interventions that aim to promote social competence, reduce problem behavior, and improve school climate are common at all levels of schooling. This whole-school focus, coupled with researchers' concerns about contamination or spillover effects in evaluations that randomly assign classrooms or students to conditions, as well as advances in…

Two competing longitudinal models, the latent growth curve model and the Simplex model, are used to represent the Matthew effect hypothesis (K. Stanovich, 1986) that the gap between good and poor readers increases with time. Theoretical and empirical arguments support the Simplex model, although it is argued that it should be refined and…

Reports on a study comparing the use of Multi-base arithmetic blocks (MAB) and an alternative, LAB (linear arithmetic blocks) on the basis of epistemic fidelity and accessibility for students. Use of LAB was associated with more active engagement by students and deeper discussion. (Author/MM)

Empirical estimates of production frontiers and average production functions performed for selected public elementary school districts in California support the hypothesis of an optimal school size model. Some policy implications of the results are briefly analyzed. Appended are 16 references. (MLF)

Describes several activities of the Data and Chance program involving third and fourth graders. Students use real-life situations to investigate probability. (MKR)

Discusses a classroom-teaching example provided in this issue. Comments that teachers, using curricular materials and activities, adapt, elaborate on, or invent the context of learning in ways that ensure that students study important central concepts in science and mathematics, and that the understandings students develop are accurate and rich.…

Presents examples of direct modeling and invented strategies of students for problem solving. Teachers are encouraged to capitalize on children's abilities to use these invented strategies and in time guide the student toward a standard, more efficient strategy. (AIM)

Discusses the concept of three-dimensional perspective. Presents some assessment tasks to help develop perspective and describes student responses. (Author/NB)

Presents a variety of activities in which 4th grade students investigate prisms and pyramids by building models from folded paper and drinking straws. (Author/NB)