A first paper on the development of an algebraic representation of a simplicial complex K. (Author)

Demonstrates that using the elementary number theory in algebra classes helps students to use acquired algebraic skills as well as helping them to more clearly understand concepts that are presented. Discusses factoring, divisibility rules, and number patterns. (AIM)

Ploynomials which can be used to calculate the number of ways of coloring hexagonal patterns are presented. (SD)

Using sequential chains of regular n-gons in a row with one side touching, as for example, one triangle, two triangles, three triangles, and so on, students graph the length of the perimeter versus the number of n-gons and determine the functional relationship for different values of n. (MKR)

Described are patterns in Pascal's triangle which are obtained when the entries are reduced modulo a prime number. (MM)

Outlines a lesson on the Fibonacci and Lucas sequences that captures student interest by presenting the opportunity for computation practice, mental mathematics, and proof for algebra students. Discusses an extension for solving simultaneous equations. (YDS)

Describes how student thinking about geometric patterns can be used to develop algebraic reasoning and to make sense of mathematical notation and symbols. (Contains 11 references.) (YDS)

Many mathematics educators have lost sight of the critical importance of the mathematical understanding which underlies procedural competence, in part because we do not have a language to refer to this kind of understanding. The modal way of categorizing mathematical knowledge--conceptual and procedural knowledge--is limited in that: (a) it is…

Demonstrates how students' power to recognize and express patterns and generality can be exploited in a variety of different ways that are connected to both arithmetic and algebra. Uses the Tunja sequence approach to teach multiplication of negative numbers and simplification of factors. (KHR)

Shares the results of some of the algebraic-thinking pattern problems presented in "Principles and Standards for School Mathematics." (KHR)

Describes students' generalization strategies and justifications as they engage in patterning activities. (YDS)

Demonstrates how to extend student awareness of a common computational pattern into the realm of algebraic thinking through carefully selected, sequenced activities and guided discussion. (YDS)

Describes how students can be guided to find an explicit rule for a pattern from a recursive rule. (YDS)

Helps students develop new insights into mathematical relationships through alternative representations. Examines patterns, symbolic, and functions approaches. (Contains 11 references.) (YDS)