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

Reviews an alternative patterning approach and highlights the difficulties it can present when students lack the requisite skills and knowledge of processes. Describes how this approach can be used to introduce elementary algebraic ideas and offers recommendations for establishing these important understandings. (ASK)

Students use a series of isosceles right triangles constructed on a geoboard to discover patterns and form generalizations. (MP)

Students examined patterns emerging when numbers placed at vertices in a braided pattern were summed. (SD)

Describes an activity in which students, grades 7-12, explore patterns and properties of repunits, an integer written as a string of ones. Includes extensions for exploring algebraic justifications. (MKR)

Describes a card trick that provides opportunities for students to discover patterns, work with variables, create tables, and ponder mathematics. Students at various levels of ability are able to enjoy the trick, and mathematical discourse is promoted within the classroom. (AIM)

The ability of students to sort cards based on surface features and deep patterns is investigated. The effect of the presence of variables and what makes a pattern difficult or easy for students to recognize are discussed. Study revealed that students are unsuccessful at making connections between expressions, sentences, and sequences which share…

Explores algebraic thinking as children search for patterns while collecting, organizing, and graphing data and as they derive equations describing relationships found in the data. (ASK)

Presents a brief definition and examples of residue designs while sharing some of the algebraic thought that a student used to form generalizations about the patterns discovered during the investigations of residue designs. (ASK)

This collection of activities resulted from a visit by the Polish author to the Teachers' Center Project at Southern Illinois University at Edwardsville in 1980. The set of 30 activity sheets involve blocks with various types of patterns depicted. Directions for using each sheet and questions to be answered are then given. Elementary school…

How to find and classify positive integral solutions to 1/a + 1/b = 1/c in beginning and advanced algebra classes is described. The computer finds the solutions, but students practice algebraic manipulation as they analyze the solutions for patterns. Extensions to challenge more capable students are included. (MNS)

Provided is a teacher's guide for a problem-solving activity that establishes a link between number patterns and geometry by focusing on the development of recurrence relations established when generating central polygonal numbers. Reproducible worksheets and a 3.0 BASIC program for the activity are given. (MDH)