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April 2012, Volume 105, Issue 8


The Devil and Daniel’s Spreadsheet
Maurice J. Burke
A tool that combines the power of computer algebra and traditional spreadsheets can greatly enhance the study of recursive processes.
Second Look:
Recursive Reasoning

Multiple Proof Approaches and Mathematical Connections
Zhonghong Jiang and George E. O’Brien
Using technology to explore the Three Altitudes of a Triangle problem, students devise many proofs for their conjectures.

Don’t Fence Me In!
Harold Reiter, Arthur Holshouser, and Patrick Vennebush
This method for counting lattice octagons strengthens students’ counting skills and geometrical thinking.

Practicing Algebraic Skills: A Conceptual Approach
Alex Friedlander and Abraham Arcavi
Integrating procedures and thinking processes makes learning more meaningful.

Dragging and Making Sense of Invariants in Dynamic Geometry
Anna E. Baccaglini-Frank
In this activity, students learn to make conjectures about properties that do not change.

Enhancing Understanding of Transformation Matrices
Jonathan Dick and Maria Childrey
With the Common Core State Standards’ emphasis on transformations, teachers need a variety of approaches to increase student understanding.

Second Look - Recursive Reasoning

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.

Just Say Charge It!
The use of a recursive sequence with a graphing calculator to involve students in analyzing credit card debt.

Technology Tips: Using the Iterate Command to Construct Recursive Geometric Sketches
This month's article introduces readers to an advanced feature of the Geometer's Sketchpad: how to iterate geometric shapes to construct Baravelle spirals and Pythagorean trees. The "Surfing Note" sends readers to a site with applets that will generate fractals such as the Sierpinski gasket or the Koch snowflake.

Illuminations Lesson: Trout Pond

This investigation illustrates the use of iteration, recursion and algebra to model and analyze a changing fish population. Graphs, equations, tables, and technological tools are used to investigate the effect of varying parameters on the long-term population.

Algebra Standard for Grades 9-12
Instructional programs from prekindergarten through grade 12 should enable all students to—