In order to get undergraduates interested in mathematics, it is essential to involve them in its "discovery". In this paper, we will explain how technology and the knowledge of lower dimensional calculus can be used to help them develop intuition leading to their discovering the first derivative rule in multivariable calculus. (Contains 7 figures.)

In this note it is shown how closed sums of infinite series may be used to construct efficient economized formulas for microstrip electrical impedances. (Contains 1 figure.)

This note considers the problem of determining, for fixed k and m, all values of r, 0 [less than] r [less than] [empty set](m), such that k[superscript [empty set](m)+1] [equivalent to] k[superscript r](mod m). More generally, if k, m and c are given, necessary and sufficient conditions are given for k[superscript c] [equivalent to] k[superscript…

The definition of "definition" cannot be taken for granted. The problem has been treated from various angles in different journals. Among other questions raised on the subject we find: the notions of "concept definition" and "concept image", conceptions of mathematical definitions, redefinitions, and from a more axiomatic point of view, how to…

Trapezoids help in understanding the role of definition in mathematics in investigating other mathematical ideas and in understanding the examples of symbolic manipulation and multiple representations. Trapezoids offers additional exposure to a polygon that gets little attention in the school curriculum yet provides for a number of rich…

This report describes results from field-testing of POWERSOURCE[C] formative assessment alongside professional development and instructional resources. The researchers at the National Center for Research, on Evaluation, Standards, & Student Testing (CRESST) employed a randomized, controlled design to address the following question: Does the…

Young Filipino children are expected to solve mathematical word problems in English, a task which they typically encounter only in schools. In this exploratory study, task-based interviews were conducted with seven Filipino children from a public school. The children were asked to read and solve addition and subtraction word problems in English or…

This research was conducted during an after-school partnership between a University and school district in an economically depressed, urban area. The school population consists of 99% African American and Latino students. During the informal after-school math program, a group of 24 6th-grade students from a low socioeconomic community worked…

This paper reports on a case-study design experiment in the domain of fraction as number-measure. We designed and implemented a set of exploratory tasks concerning comparison and ordering of fractions as well as operations with fractions. Two groups of 12-year-old students worked collaboratively using paper and pencil as well as a specially…

Written by a social worker for social work students, this is a nuts and bolts guide to statistics that presents complex calculations and concepts in clear, easy-to-understand language. It includes numerous examples, data sets, and issues that students will encounter in social work practice. The first section introduces basic concepts and terms to…

Big things come in small packages. This saying came to the mind of the author after he created a simple math review activity for his fourth grade students. Though simple, it has proven to be extremely advantageous in reinforcing math concepts. He uses this activity, which he calls "Show What You Know," often. This activity provides the perfect…

The focus of this paper is on student interpretation and usage of the existence and uniqueness theorems for first-order ordinary differential equations. The inherent structure of the theorems is made explicit by the introduction of a framework of layers concepts-conditions-connectives-conclusions, and we discuss the manners in which students'…

This article provides activities that merge two fascinating mathematical topics: the Mayan system of numeration and magic squares. (Contains 3 figures.)

The study addresses the relational reasoning of different-aged children and how addition reasoning is related to problem-solving skills within addition and to reasoning skills outside addition. Ninety-two 5- to 8-year-olds were asked to solve a series of conceptually related and unrelated addition problems, and the speed and accuracy of all…

In this paper, departments are urged to consider implementing the type of changes proposed in Beyond Crossroads in College Algebra. The author of this paper is chair of the Curriculum Renewal Across the First Two Years (CRAFTY) Committee of the Mathematical Association of America. The committee has members from two-year colleges, four-year…