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November 2004, Volume 98, Issue 4

 FEATURES Developing Mathematical Power by Using Explicit and Recursive ReasoningJohn LanninThe use of a variety of tasks that encourage students to examine the advantages and limitations of recursive and explicit reasoning. The authors discuss the reasoning for employing different types of reasoning and how to encourage students to justify their thinking. Patterns Jumping Out of a Simple Checker PuzzleSusan G. StaplesIn this article, we consider the generalization of a “solitaire checker puzzle” from the book More Joy of Mathematics, by Theoni Pappas (1991). In addition to presenting the solution to the general case, we shall also investigate the attractive patterns that emerge during the process of solving the puzzle, as well as in analyzing the minimal solutions of various cases. Fractal Patterns and Chaos GamesRobert L. DevaneyOne of the most wonderful ways to introduce students in middle school or secondary school to the beauty and excitement of contemporary mathematics is to involve them in the many variations of the “chaos game” which produces such intriguing fractal patterns as the Sierpinski triangle and the Koch curve. Pattern BustingThomas DenceEven though sequences of numbers may follow an apparent pattern for a long period, that doesn't mean the pattern will continue forever. Geometric and algebraic sequences are used in examples as well as trig functions and prime number patterns. Patterns in Perfect Squares: An Activity for Exploring Mathematical ConnectionsJeff Farmer, Andrew NeumannA versatile mathematical problem that begins by asking students to find patterns in a list of perfect squares. The representations and explanations of those patterns can lead to connections between many mathematical concepts. The patterns are represented algebraically, geometrically, and pictorially. Patterns with multiples and arrangements are explored while developing reasoning and communication. Drug Levels and Difference EquationsKathleen AckerStudents examine details of Tylenol. Using difference equations students develop mathematical models for the amount of a drug in the body after a single dose and after multiple doses. They compare other data about the drug and create geometric growth models.

 Departments Editorial/From the EditorsFrom the Editors: Patterns: Revitalizing Recurring Themes in School Mathematics Reader ReflectionsReader Reflections - November 2004 Delving DeeperDelving Deeper: Kaprekar's Constant Calendar ProblemsCalendar Problems - November 2004 Activities (for students)Activities for Students: Unit Fractions and Their Basimal Representations: Exploring Patterns Mathematical LensMathematical Lens: Chandelier in Marriott Courtyard Hotel, Philadelphia For Your Information/Products/PublicationsFor Your Information - November 2004