The importance of developing reasoning and justification has been highlighted in "Principles and Standards for School Mathematics" (NCTM 2000). The Common Core State Standards for Mathematics (CCSSI 2010) further reiterates the importance of reasoning and proof in several standards for mathematical practice. Students of all grades are…

What is the role of patterns in developing algebraic reasoning? This important question deserves thoughtful attention. In response, this article examines some differing views of algebraic reasoning, discusses a controversy regarding patterns, and describes how three types of patterns--in contextual problems, in growing geometric figures, and in…

This article draws out many mathematical ideas connected with a familiar game often used by middle school teachers. (Contains 5 figures and 1 table.)

Patterning is an essential skill in early mathematics learning, particularly in the development of spatial awareness, sequencing and ordering, comparison, and classification. This includes the ability to identify and describe attributes of objects and similarities and differences between them. Patterning is also integral to the development of…

Pattern work is now undertaken as early as kindergarten, and both researchers and teachers have discovered that children engage in pattern work with great enthusiasm and innate ability. Having some flexibility in pattern perception and selecting mathematically useful patterns require some training, although there is nothing particularly algebraic…

Curiosities offer an interesting alternative to traditional methods of attacking problems. An illustrative situation is given, with graphical, computer, and analytical methods used to solve the problem. (MNS)

Some activities are provided to help students develop a conceptual understanding of perimeter, area, and volume, as well as developing skills in spatial visualization and formulating generalizations. (MNS)

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)

Briefly presented are suggestions on using exercises in number patterns in second-year algebra and factoring quadratics in a 10th-grade enrichment class. (MNS)

Discusses the importance of identifying and describing the pattern by students in algebra class. Provides some examples showing the usefulness of the method seeing the pattern from mathematical materials. (YP)

Described are two examples involving recursive mathematical sequences designed to integrate a holistic approach to learning algebra. These examples promote pattern recognition with algebraic justification, full class participation, and mathematical values that can be transferred to other situations. (MDH)

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…

Presented are problem-solving experiences with area, volume, and algebraic expresssions resulting from data collection. Three worksheets are included for students in grades 7-12. (MNS)