This is a guide to using Maple in teaching fundamental calculus of one, two and three variables (limits, derivatives, integrals, etc.), also suitable for Maple beginners. It outlines one of the ways to effective use of computers in the teaching process. It scans advantages and disadvantages of using Maple in relation to students and teacher. The…

A number of ideas in complexity theory are reviewed and then it is shown that all known classes of complexity of really unmanageable problems have instances in education. These are common problems in the teaching of every branch of science, knowledge and human culture. Selected pedagogic problems classify as NP-harsh problems, i.e. NP-hard…

This note contains material to be presented to students in a first course in differential equations immediately after they have completed studying first-order differential equations and their applications. The purpose of presenting this material is four-fold: to review definitions studied previously; to provide a historical context which cites the…

Suggests that there is continued poverty in student understanding of proof. Reports on how proof attitudes could be inculcated in students by offering them a course design that is somewhat faithful to the historical genesis of modern mathematics. Contends that such a design can enable students to discover a sense of proof for themselves. (Contains…

Discusses a real-world problem-solving lesson that emerged when a high school math teacher used a motion detector with a CBL and graphing calculator to obtain the bounce data of a ping-pong ball. Describes the lesson in which students collect bad data then fill in the missing parabolas that result using critical components of parabolas and…

Presents a simple method for teaching the algebraic solution of cubic equations via completion of the cube. Shows that this method is readily accepted by students already familiar with completion of the square as a method for quadratic equations. (Author/KHR)

In this note involving mathematical induction, an identity involving the combinatorial numbers and the partial sums of the harmonic and related series is verified. (Author)

Dimension analysis is promoted as a technique that promotes better understanding of the role of units and dimensions in mathematical modeling problems. Dimensional analysis is shown to lead to interesting systems of linear equations to solve, and can point the way to more quantitative analysis. Two student problems are discussed. (Author/MM)

The purpose of this note is to give a construction method for measures of central tendency and dispersion of a set of data on the basis of some symmetric multivariate functions and distance functions. Several examples regarding the known and new measures are presented. (Author/MM)

Presents an integrated exposition of aspects of secondary school mathematics and a medical science specialty. Reviews clinical medical practice and theoretical and empirical literature in mathematics education and radiology to develop and pilot model integrative classroom topics and activities. Suggests mathematical applications in numeration and…

Presents a variety of examples of wrong proofs, misinterpreted definitions, and the mistaken use of theory. Examples are based on experience teaching mathematics to engineering students. Includes elementary examples and more advanced ones taken from different subjects. (Author)

Describes an exploration into the concept of the rate of convergence in a university classroom. It is well known in mathematics that this concept leads to a modern construction of infinitesimals and their orders. (Author)

Proposes the utilization of a spatial operational capacity model for the development of visual and spatial skills. Argues that it reflects the complexity of the interaction between physics/science and mathematics, and endeavors to assist in the design of appropriate learning activities and materials for the development of specific scientific…

Links the use of Computer Algebra Systems (CAS) to an existing classification scheme for mathematical tasks called the MATH Taxonomy. Illustrates through concrete examples how the goals of teaching and learning mathematics can be set using this classification together with the CAS. (Author/MM)

Gives concrete examples of examinations in which Computer Algebra Systems (CAS) can be used. Discusses the need to link the construction of the examination and evaluation of the exam scripts in terms of an existing classification scheme for mathematical tasks, the MATH Taxonomy. (Author/MM)