From time to time, I’m going to add websites or problems that I think challenge visitors in rich ways. One of my very favorites is a little wonder called “Petals around the rose”. There is a nice implementation by Lloyd Barrett on his website. Prepare to spend some time on this, and don’t bother going if you’d ever contemplate doing a web search for solutions. If it takes you a week to solve, it’s a well-spent week. It took me several days (so no, I don’t want to hear about it if you solve it simply after visual inspections 🙂 ). There are several problem solving aspects that I think make this a rich experience… [No spoilers below]
Over the years, I’ve developed a number of questions/suggestions I often use in assisting students in the development of new problem-solving strategies. The goal is to guide students find strategies for approaching novel problems (the good kind, where you aren’t just adjusting for different values, but are really trying to figure out something ‘new’). Continue reading
We all want our students to ‘think critically’ and ‘become better problem solvers’. But what does that mean, and how do we scaffold and provide opportunities developing problem-solving strategies? Obviously, this question is deeper and wider than a single blog post, but I wanted to put my first card on the table. First and foremost, this must all begin with ‘legitimate’ problems. To me, this means ones where a student must reach beyond plug-and-play; there must be elements of identifying which information is useful, choosing approaches that attack weak points of the problem, finding their own path rather than following ones already mapped out. Two cases that I think exemplify ‘real’ problems are Petals around the rose and (surprise surprise) my own PatternMaster.
The rest of this introductory post is dedicated to a distillation of George Polya’s advice to young mathematicians