This article describes a teaching experiment conducted in a seventh-grade classroom. It explores ways that students used four types of problem-solving knowledge through writing their responses to algebraic problems. The problems were presented to students in the geometric contexts of growth and change and size and shape. It was found that writing…

Manufacturing engineering provides a relevant context from which to envision interdisciplinary learning experiences because engineers integrate their knowledge and skills of manufacturing and algebra processes in order to plan the efficient manufacture of products. In this article, the author describes an interdisciplinary learning activity that…

The integration of history into educational practice can lead to the development of activities through the use of genetic "moments" in the history of mathematics. In the present paper, we utilize Oresme's genetic ideas--developed during the fourteenth century, including ideas on the velocity-time graphical representation as well as geometric…

Although much is known about the differences between expert and novice problem solvers, knowledge of those differences typically does not provide enough detail to help instructors understand why some students seem to learn physics while solving problems and others do not. A critical issue is how students access the knowledge they have in the…

Patterning is an essential skill in early mathematics learning, particularly in the development of spatial awareness, sequencing and ordering, comparison, and classification. This includes the ability to identify and describe attributes of objects and similarities and differences between them. Patterning is also integral to the development of…

Since the last decade, the use of computer algebra systems at the Hong Kong school level is still very limited. Among various reasons behind, the lack of exposure of this kind of software to local school teachers should be taken into account. In this article, we describe how to introduce MAPLE in a BEd module of a local teacher-training programme.…

This work addresses the subject of mathematics education at secondary schools from a current and stimulating point of view intimately related to computational science. Cryptology is a captivating way of introducing into the classroom different mathematical subjects such as functions, matrices, modular arithmetic, combinatorics, equations,…

This brochure is part of NAEPFACTS, a new series that briefly summarizes findings from the National Assessment of Educational Progress (NAEP). Course-taking is generally a powerful indicator of mathematics achievement. This occurs partially because students who are more proficient tend to take more mathematics classes and, at the eighth grade, the…

This book takes the position that the teaching of elementary linear algebra can be made more effective by emphasizing applications, exposition, and pedagogy. It includes the recommendations of the Linear Algebra Curriculum Study Group with their core syllabus for the first course, and the thoughts of mathematics faculty who have taught linear…

This article reports the results of a questionnaire applied to secondary school students (n=35) to explore efficiency in the resolution of equations in the domain of whole numbers and the spontaneous responses to problems leading to negative solutions. The most significant results obtained with the questionnaire are the lack of knowledge of the…

This book aims to present helpful, practical ideas and suggestions for mathematics teaching. Focus is on how teaching can be developed in a Rudolf Steiner (Waldorf) School and includes treatment of mathematical topics applicable to the 7-14 age group. Suggestions for curriculum and examples for children to work on are presented with a very wide…

Research indicates that students have great difficulty solving algebra word problems and that few high school seniors have mastered the fundamentals of algebra, let alone algebra problem-solving skills. Improving students' algebra problem solving skills is considered to be critically important by those who have worked on reforming mathematics…

In the United States female and male students supposedly have the same educational opportunities. Females continue to score below male students on the mathematics portions of standardized tests and less frequently choose mathematics-oriented careers. In this experimental study (n=95), 47 first-year algebra students participated in a month-long…

Use of the computer programs provided here in APL programming language can help students understand computational algorithms. (SD)

Some theorems concerning factorization of Pythagorean triples are presented. (SD)