The mathematical concept of slope can be made real through a set of simple, inexpensive, and safe experiments that can be conducted in the classroom or at home. The experiments help connect the idea of slope with physical phenomena related to surface tension. In the experiments, changes in surface tension across the surface of the water, which correspond to greater slopes on the graph, lead to increased motion of the fluid. The mathematical content, targeted to middle school and high school students, can be used in a classroom or workshop setting and can be tailored to a single session of thirty to ninety minutes.
The relationship between a midpoint and an average showcases the interplay between procedural knowledge and conceptual knowledge in learning mathematics for teaching.
When understood and applied appropriately, mathematics is both beautiful and powerful. As a result, students are sometimes tempted to extend that power beyond appropriate limits. In teaching statistics at both the high school and college level, I have found that one of students' biggest struggles is applying their understanding of probability to make appropriate inferences.
Jeffrey J. Wanko, Michael Todd Edwards, and Steve Phelps
The Measure-Trace-Algebratize (MTA) approach allows students to uncover algebraic relationships within familiar geometric objects.
Adam Poetzel, Joseph Muskin, Anne Munroe, and Craig Russell
Using simple materials, a Mathematica software application, and their knowledge of function transformations, students design and create real mathematical sculptures.
Harold Reiter, Arthur Holshouser, and Patrick Vennebush
This method for counting lattice octagons strengthens students' counting skills and geometrical thinking.
Walter J. Whiteley and Ami Mamolo
Investigating rates of change in volume without calculation leads to an enriched sense of the optimization process and encourages reflection and connection among different approaches.