A key part of the practice of chemistry is the analysis of chemical composition, including through gravimetric analysis and spectrophotometry. However, the complexity of doing multiple calculations to obtain analytical evidence, such as that required to determine an empirical formula, presents a challenge if such analytical methods are to be…

The use and understanding of mathematics is a crucial component of the physical sciences. Much work has been done in physics education research and science education more broadly to determine persistent difficulties with mathematics. This work has led to the development of numerous problem solving strategies aimed at helping learners approach…

Trends in the curriculum reform propose that algebra should be taught throughout the grades, starting in elementary school. The aim should be to decrease the discontinuity between the arithmetic in elementary school and the algebra in upper grades. This study was conducted to investigate and characterise upper elementary school students…

Failure rates in first year calculus courses are high in most post-secondary institutions across North America and other parts of the world. This Inukshuk-funded open education project involved the development of five stand-alone pre-calculus learning modules. The design and revision phases of this project occurred between the fall of 2007 and…

Curriculum materials' developers typically assume the existence of certain general social-educational classroom practices and norms. Conversely, the current study addresses the effects of context on curriculum enactment, focusing on the interrelations between teacher, class and curriculum materials. Each of the two case studies presented herein…

Describes how the cubic formula can be presented easily at the precalculus level, shows how to verify that the formula is correct, and identifies when it is profitable to use. (KHR)

Examines how selected U.S. and Asian mathematics curricula are designed to facilitate students' understanding of the arithmetic average. Discusses similarities and differences of learning goals, focuses, and concepts among U.S. commercial, Asian, and U.S. reform curriculum series. (Author/KHR)

This article "opens up" the study of the relationship between quadrilaterals and circles to two sets of quadrilaterals--those that can be drawn either inside (cyclic) or outside (tangential) a circle (or both). Of course, "all" triangles are both cyclic and tangential. Or, to use the traditional Euclidean language for triangles, a unique…

This set of transparencies shows how the manipulation of combinatorial structures in the context of modern combinatorics can easily lead to interesting teaching and learning activities at every level of education from elementary school to university. The transparencies describe: (1) the importance and relations of combinatorics to science and…

The method used in a Soviet technological institute to plan instructional programs cooperatively, in order to avoid duplication of effort and streamline the training process, involves evaluation of curriculum's relevance by experts in each discipline. (MSE)

Described is a graduate level engineering course on functional analysis offered at Purdue University. The course restricts itself to linear problems, specifically analysis of linear operators on vector spaces. Key applications in the course demonstrating the utility of abstract formulations are presented. (BT)

Proposed is a gradual transition from arithmetic to the idea of an equation with variables in the elementary grades. Vertical and horizontal formats of open sentences, the instructional sequence, vocabulary, and levels of understanding are discussed in this article. (KR)

Discusses the emergence of chaos as a major scientific subject and its place in historical, scientific, and technological context. Three sections provide (1) an overview of the scientific paradigm; (2) a review of the ideology of classical mechanics; and (3) examples of classical systems behaving in peculiar, nonintuitive manners. (MDH)

Designed as an avenue of communication for mathematics educators concerned with the views, ideas, and experiences of two-year college students and teachers, this journal contains articles on mathematics exposition and education and regular features presenting book and software reviews, classroom activities, instructor experiences, and math…

Designed as an avenue of communication for mathematics educators concerned with the views, ideas, and experiences of two-year college students and teachers, this journal contains articles on mathematics exposition and education, and regular features presenting book and software reviews and math problems. In addition to regular features such as…