Reacts to an article published in a previous issue of this journal on the effects of graphing calculators and computer algebra systems (CAS) on students' manual calculation skills. Asks enthusiasts of CAS to learn from history and avoid pitfalls. (ASK)

Describes activities for Technical Algebra, which provides students an opportunity to solve algebraic problems through a hands-on, instructional process. (MKR)

College students (n=32) in their first abstract algebra course were asked to list elements and find the product of 2 elements in the dihedral group D4. Most students found solutions using a combination of visual approaches and analytic strategies. Proposes an alternative model, the Visualizer/Analyzer model, which assumes visualization and…

Introduces an algebra lesson plan on two people saving money over the course of a week and the problems they encounter for early elementary school students. (YDS)

Discussion of XML focuses on a description of Tequyla-TX, a typed text retrieval query language for XML documents that can search on both content and structures. Highlights include motivations; numerous examples; word-based and char-based searches; tag-dependent full-text searches; text normalization; query algebra; data models and term language;…

One of the workshops at the 10th SNM Stowarzyszenie Nauczcieli Matematyki (SNM) conference was entitled: Do we really need algebra? The workshop members were given several problems to consider. By doing these problems and reflecting on them the participants explored some important aspects of the question posed. Moreover they became aware of a…

The Chebyshev polynomials named after a Russian mathematician, Pafnuty Lvovich Chebyshev, have various mathematical applications. A process for obtaining Chebyshev polynomials, and a mathematical inquiry into the patterns they generate, is presented.

An attempt to implement problem solving as a teacher of ninth grade algebra is described. The problems selected were not general ones, they involved combinations and represented various situations and were more complex which lead to the discovery of Steiner triple systems.

Participants at the Summer Institute Pattern Exploration: Integration Math and Science in the Middle Grades used and developed a method treat arithmetic, algebra and geometry as one entity. The use of iterative geometric constructions is seen to reinforce the concepts of exponents, ratios and algebraic expressions for the nth stage of the…

In addition to looking for applications that can be profitably examined algebraically, numerically and geometrically it is also helpful to use ideas that typical students might find interesting. Most secondary students are eager to obtain their driving license and part of becoming a good driver is understanding how long it takes to stop your…

The author examined the effect of demographic variables and attitudes on achievement of 8th-grade algebra students. Participants (N = 107) in 4 classes completed a questionnaire that determined demographic characteristics. They also completed attitude scales at the beginning and end of the school year. Dependent measures were the North Carolina…

Eigenvalue is an important concept in Linear Algebra. It is well known that the eigenvectors corresponding to different eigenvalues of a square matrix are linear independent. In most of the existing textbooks, this result is proven using mathematical induction. In this note, a new proof using Vandermonde determinant is given. It is shown that this…

The matrix diagonalization method is used to solve a limit problem.

It is shown that the symbols for the fundamental units of mechanics, namely length, time and mass, are capable of a meaningful interpretation as positive real parameters. Then a suitable parameter domain allows one to take the derived units into account. The formal manipulations usually carried out with symbols of physical quantities, involving…

In this note it is shown that the Moore-Penrose inverse of real 3 x 3 matrices can be expressed in terms of the vector product of their columns. Moreover, a simple formula of a generalized inverse is presented, which also involves the vector product.