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March 2009, Volume 102, Issue 7

FEATURES

The Infinite Hotel
Jeffrey J. Wanko
The short story “Welcome to the Hotel Infinity” uses the analogy of a hotel with an infinite number of rooms to help explain the concept of the cardinality of different infinities. This article provides a historical context for the debate between George Cantor and Leopold Kronecker (who are characterized in the short story) and it describes the author’s use of this history and short story in teaching difficult concepts about infinity.

Using Lesson Study and Four-Column Lesson Planning with Preservice Teachers
Michael Matthews, Christopher Hlas, Teresa Finken
Four-column lesson planning, an adaptation of lesson study, for preservice secondary school teachers. Four-column plans, an integral part of Japanese lesson study, have been less emphasized in the United States. This article presents study results indicating how these teachers were affected by this lesson study adaptation: They were more student centered and valued collaboration more than before the lesson study.

Rare and Exotic Probability Bugs
James Kennis
Examining some of the various judgmental errors and rationales that high school students make when attempting to solve basic probability exercises. Many of these errors allow the students to arrive a correct answer and, thus, need to be examined more closely.

Tangent Lines without Derivatives for Quadratic and Cubic Equations
William Carroll
In the quadratic equation, y = ax<sup>2</sup> + bx + c, the equation y = bx + c is identified as the equation of the line tangent to the parabola at its y–intercept. This is extended to give a convenient method of graphing tangent lines at any point on the graph of a quadratic or a cubic equation.

Rethinking the Teaching of Systems of Equations
Jérôme Proulx, Mary Beisiegel, Helena Miranda, Elaine Simmt
Exploring the conceptual richness of systems of equations through a discussion of various aspects that could enhance its study.