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)

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)

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)

Shows how all primitive Pythagorean triples can be generated from harmonic sequences. Use inductive and deductive reasoning to explore how Pythagorean triples are connected with another area of mathematics. (KHR)

Presents a project that addresses several components of the Algebra and Communication Standards for Grades 9-12 presented in Principles and Standards for School Mathematics (NCTM, 2000). Describes doing mathematical modeling and using the language of mathematics to express a recursive relationship in the perimeter and area of the Koch snowflake.…

The ability to use algebra in describing and analyzing real-world situations is becoming a basic skill for all students. The main focus of this book is on patterns, functions, and relationships. Information and ideas on how algebraic thinking can be developed in the years leading to a formal algebra course are included. K-8 teachers are offered a…

Three examples are given illustrating the use of the calculator in problems where determining patterns and making conjectures are stressed. (MP)

Presents a quilting problem that engages students at many levels, has multiple possible solution paths, lends itself to a variety of representations, and connects many mathematical ideas. (KHR)

Describes an investigation-based, lecture-free first-year algebra course in which students are responsible for compiling their own textbooks. Discusses the purpose and procedures of the activity. Includes student worksheets. (KHR)

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)

Presents a project used to help students make connections between linear and exponential models and between arithmetic and geometric sequences. (KHR)

The purpose of this article is to highlight and discuss the role of language as the link between experiences with number patterns and the emergence of algebraic notation. Discussed is a recommended approach. A sample of a written student response is provided. (CW)

Presents suggestions for developing algebraic concepts beginning in the early grades to develop a gradual building from informal to formal algebraic concepts that progresses over the K-12 curriculum. Includes suggestions for representing relationships, solving equations, employing meaningful applications of algebra, and using of technology. (MDH)

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)