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August 2007, Volume 101, Issue 1


Explore, Conjecture, Connect, Prove: The Versatility of a Rich Geometry Problem
Robert Quinn, Tom Ball
A rich geometry problem and discussion of its solution. Preservice teachers are challenged to prove their conjecture in a  variety of mathematically correct justifications. The authors demonstrate that mathematical rigor is possible at a variety of student ability levels.

Humanizing Calculus
Michelle Cirillo
The history and the mathematics used by Newton and Leibniz in their invention of calculus. The exploration of this topic is intended to show students that mathematics is a human invention. Suggestions are made to help teachers incorporate the mathematics and the history into their own lessons.

Promoting Equity in Mathematics: One Teacher's Journey
Alan Tennison
The impact of using a problem-based curriculum in a heterogeneous classroom environment in a pilot program. The author finds tracking does not offer challenges to minority and struggling students. A problem based curriculum provides equity for all students.

Discovering the Magic of Magic Squares
Ingrid Semanišinová, Marián Trenkler
A collection of problems that allow students to investigate magic squares and Latin squares, formulate their own conjectures about these mathematical objects, look for arguments supporting or disproving their conjectures, and finally establish and prove mathematical assertions. Each problem is completed with commentary and/or experience from the classroom.

Eliciting Students' Beliefs about Who Is Good at Mathematics
Shelby Morge
A series of activities designed to elicit students' mathematics-related beliefs, particularly those related to gender. As a result of the activities, females in upper-level classes rated themselves as having less confidence than males, and viewing a movie clip was sufficient for some students to modify their descriptions of someone who is good at mathematics.

A Model for Constructing Higher-Level Classroom Assessments
Truus Dekker
The use of a Dutch pyramid model that may help teachers design assessment problems that go beyond procedural operations. The author offers a design for producing a balanced, time restricted test, which reflects conceptual understanding as well as factual and procedural knowledge.