Explore, Conjecture, Connect, Prove: The Versatility of a Rich Geometry Problem
Robert Quinn, Tom Ball
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
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
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
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
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.