War and Pieces
Tolstoy's analogy of the correct interpretation of history as similar to following the laws of math and physics. Provides lesson plans and alternatives for calculus students studying intervals and integration. An interdisciplinary approach to integrals.
Note: Figures Not Drawn to Scale
Mathematical problems that include a visual representation with the note "Figure not drawn to scale" are analyzed. Strategies that students can use in solving such problems are discussed. Also presented are sample tasks that include a figure not drawn to scale for teachers to use in their own classrooms. Ideas for teaching students to interpret figures not drawn to scale.
Exploring Nonconvex, Crossed, and Degenerate Polygons
How interactive software can be used to extend mathematical conjectures and theorems to non-convex, crossed, and degenerate polygons. The author demonstrates investigating Napoleon's Theorem with Geometer's Sketchpad.
Copernican Mathematics: Calculating Periods and Distances of the Planets
How Copernicus found the periods and relative distances of the planets. Using provided data, students will be able to discover his methods and make their own calculations of planetary parameter using circles, angles and arcs, algebra formulas, and trig functions. Students also discuss data sources and opportunities for error. Oppportunities for teaching the lesson to different levels is discussed.
Examining Students' Reluctance to Use Graphs
Frances Van Dyke, Alexander White
What students do not understand about graphing and why they remain reluctant to use it for problem solving at the calculus level. The authors point out that graphing was not developed until the 17th century. Conclusions are that students lack understanding in the concept of function, the Cartesian connection, and the mathematical description of change.
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