Developing Mathematical Power by Using Explicit and Recursive Reasoning
The 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 Puzzle
Susan G. Staples
In 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 Games
Robert L. Devaney
One 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.
Even 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 Connections
Jeff Farmer, Andrew Neumann
A 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 Equations
Students 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.