In this paper, the authors investigate the consequences of curricular intensification by examining changes in the social organization of schooling and student achievement in one California school district. The authors' analyses consider the following three research questions: (1) What effect did 8th grade curricular intensification have on…

When hoping to initiate or sustain students' interest in mathematics teachers should always consider relevance, relevance to students' lives and in the middle and later years of instruction in high school and university, accessibility. A topic such as the mathematics behind networks science, more specifically scale-free graphs, is up-to-date,…

This article describes a professional development initiative for fifteen mathematics teachers in the use of dynamic geometry software GeoGebra. A four-day introductory workshop was given in Nepal to provide an overview of GeoGebra and its possible integration in the teaching/learning of secondary school mathematics there. Teachers' impressions and…

Lim and Leek (2012) presented a formalization of information along object contours, which they argued was an alternative to the approach taken in our article (Feldman & Singh, 2005). Here, we summarize the 2 approaches, showing that--notwithstanding Lim and Leek's (2012) critical rhetoric--their approach is substantially identical to ours,…

In this study, we explored the structural relationship between the students' perceived use of cognitive and metacognitive reading strategies (CMRS) and their reading comprehension of geometry proof (RCGP), and we also examined the differences in students' perceived use of reading strategies among the poor, moderate and good comprehenders. A sample…

For students who have difficulty envisioning how the mathematics that they are learning is used outside the classroom, an adventure as field mathematicians can be enlightening. Measuring stream discharge is a field experience that allows students to engage in a hands-on (and boots-on) real-world, problem-solving activity and that integrates…

Students often view mathematics as a set of unrelated facts and procedures and fail to make the connections between and among related topics. One role of a teacher is to help students understand that mathematics is an interrelated discipline. Another role is to assist students in the scaffolding of their knowledge so that they can make connections…

Nowadays, computer aided design (CAD) is widely used by designers. Would children learn to draw more easily and more efficiently if they were taught with computerised tools? To answer this question, we made an experiment designed to compare two methods for children to do the same drawing: the classical "pen and paper" method and a CAD…

Although teachers' professional knowledge and instructional beliefs are known to have a variety of subcomponents, research on the structure and interrelations of these subcomponents is relatively scarce. This article presents some findings of a preliminary, quantitative empirical study examining the relationships between mathematics teachers'…

The goal of this study was to examine the pathways to being college ready in mathematics. Students who enter high school already having demonstrated mathematics proficiency on a standardized test in the 8th grade have already taken a significant step towards being college ready. The best scenario is to enter high school proficient in mathematics…

This dissertation is devoted to a history of the New York State elementary school teacher certification requirements, specifically in mathematics, during the nineteenth century. In the last half of nineteenth century, teacher education and uniform certification procedures were beginning to become the norm in the educational systems throughout the…

Many problems of electric field strength on a boundary between two media require college-level mathematical analysis. However, when the boundary between media is represented by a sphere or a flat plane, these types of problems can be solved algebraically, placing them within reach of high school students. This article presents a solution analysis…

A well-documented experience of students of elementary Euclidean geometry is "seeing" a geometric result and being sure about its truth; this sort of experience gives rise to the notion of geometrical visualisation that is developed here. In this essay a philosophical argument for the epistemic potential of geometrical visualisation is reviewed,…

Biangular coordinates specify a point on the plane by two angles giving the intersection of two rays emanating from two fixed poles. This is a dual of Cartesian coordinates wherein a point on the plane is described by two distances. Biangular coordinates, first written about in 1803 in France, were subsequently studied in Britain at the end of the…

In this paper, we investigate university students' interaction in an attempt to construct a model of elliptic geometry. In order to study the several ways in which geometrical meaning is produced through context and practices, we introduce three different types of use of geometrical concepts, namely as (1) elements of representation of spatial…