One of the things I love about teaching at a small school is that students find it easier to take risks and ask questions during class. Today, we were working on learning the Chain Rule in Calculus. One of the problems we reviewed involved using both the Chain Rule and the Quotient Rule. However, one of the students in my class raised her hand and asked if we could rewrite the quotient as a product and use the product rule instead. At this point, I told my students that they had a "Toolbox of Calculus Tools" at their disposal and that they could choose to do many of the problems in a variety of ways. In fact, one of the things that I love about math is that there are often a variety of approaches to solving a specific problem. We ended up working through the problem using both the Quotient Rule and the Product Rule and saw it resulted in equivalent forms of the solution.
I am curious as to which tools students would prefer to use when given the option. So, for our class opener on Monday (that's our next day of class - 5 days from today), I plan on giving students a few problems that lend themselves to using different tools in their Calculus Toolbox. It will be interesting to see which tools they choose.