What to Do When a Group Gets Stuck Working on a Task

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.

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An Infinite Understanding

“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.

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As math graduate students, we often get teaching assignments from our departments, some of us tutor independently for financial reasons, and some volunteer to teach at local schools or libraries. Teaching is an inseparable part of our job/life. But that is where the consensus ends and we enter this wild jungle of ideas about (and debates over) math pedagogy, inquiry-based learning, proofs in math education, technology in math education, and so on. In this short note, I will not touch on any of these issues but rather share with you my own experience with reflecting on my teaching habits and trying to improve on them. Continue reading “SMART” »

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AMS Notices Spotlight August 2017

It’s hard to believe that a month has passed since the last AMS Notices Spotlight. But somehow, in the blink of an eye, it has and just last week the new AMS Notices came out. This month’s Notices feature some great articles about gravitational waves, a section specifically for graduate students, an article about The Global Math Project, and much more. Continue reading “AMS Notices Spotlight August 2017” »

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Adapting Problems to Improve their Groupworthiness

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” »

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