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.
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.
Tongta Somchaipeng, Tussatrin Kruatong, and Bhinyo Panijpan
Students use balls and disks to prove the general formulas for sums of squares and cubes.
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.
Cindy M. Cherico
Simulating a real-world marketing situation, students examine the mathematical calculations that play an integral part in product design.