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)

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)

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)

Investigates ways to analyze change in various contexts. Focuses on computer technology providing contexts for children's investigations of patterns of change and helping to develop foundational ideas of algebra and calculus. Discusses relationships between patterns of change, fundamental algebraic notions as linear and nonlinear functions, and…

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.…

Explores the attempts of a group of preservice elementary school teachers to generalize a repeating visual number pattern. Discusses students' emergent algebraic thinking. Indicates that students' ability to express generalities verbally was not accompanied by algebraic notation, but participants often perceived complete and accurate solutions…

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)

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…