When I was younger, I used to have something called a “Trap Club.” If this sounds dangerous, it probably was. I used to create all sorts of traps for people to fall into. The traps all started with a single question: I wonder how I can trap my friend? Traps had to be uniquely designed for each individual. After all, some people may be smarter or quicker than others. I began by creating my own detailed blueprints, and it wasn’t until the design was perfect that I was able to start collecting the needed materials and build the traps. (Don’t worry, no one really got hurt.)
In the same way that I made my blueprints, mathematicians often create a model before they arrive at a solution. Similarly, mathematical models are also dependent on the context of the situation. And like my initial question, mathematical modeling also begins with a simple act of wondering. Curiosity and wonders lead us to think, “How?” How can I figure out the number of candles on a birthday cake? How can I determine the number of candies in a jar? Will the basketball make it to the hoop? Asking students to wonder is a great hook. Our wonders grip us until a solution is found. So I was thrilled to watch the new video series, Modeling With Mathematics. See how the teachers get students to wonder, how the students are actively engrossed, and their positive reactions after they notice or derive a solution!