In my previous post, I discussed how to adapt a problem that you have found in order to make the problem groupworthy. One of the important things to consider when adapting real-world problems is to avoid giving step-by-step instructions and formulas to students. Instead, a teacher should maximize the opportunities for groups to make their own decisions about problems. In other words, in order to have challenging and productive group discussions, there must be an element of uncertainty so that students engage with the problem and with each other.
Continue reading “What to Do When a Group Gets Stuck Working on a Task” »
“Have you ever thought about how strange it is that we think about infinity every day, but most people think about it only on the rarest of occasions, if ever?” This is the text message I recently sent two of my close friends, who also happen to be mathematicians in my department. I was deep in the midst of studying for preliminary exams, trying to prove Riemann’s Theorem on removable singularities, when I started to think – really think – about infinity.
Continue reading “An Infinite Understanding” »
In my last blog post, I discussed the importance of using groupworthy tasks with your students. For a task to be groupworthy, it should satisfy three criteria: interdependence (the task is mathematically rich enough that students have to work together), multiple abilities (many different mathematical strengths are needed, e.g. verbal, written, spatial, visual), and multiple representations (e.g. graphical, numeric, linguistic and symbolic).
Many teachers do not have such groupworthy tasks in their curriculum, though, and do not have access to such problems. Many problems that we do have in our textbooks have potential; we just need to learn how to make them groupworthy. Continue reading “Adapting Problems to Improve their Groupworthiness” »