Dearest readers, It’s been too long. Habib and I have been hard at work improving the site in ways large and small and have ambitious plans underway for 2013. In the meantime, I want to take the opportunity to feature great work from a friend-of-friend, Zak Ringelstein, co-founder and CEO of United Classrooms ( www.uclass.org). UClass is a free platform that connects K-12 classrooms worldwide. Zak and his co-founder Leah are former Teach for America and Teach for All Corps members who were inspired by their own experience to create an international platform for teachers and students. In their recent Tedx, Zak and Leah speak out against a restrictive educational culture driven by multiple-choice assessments, and call teachers to open their classrooms to a broader and richer experience befitting future world-changers. On a personal note, I am optimistic that the forthcoming Common Core assessments will be less restrictive. I’m also excited about UClass as an opportunity for students to create content for an authentic audience. I look forward to seeing it develop and encourage you to check it out.
This week, I stumbled upon an article about the math department at Milton Academy. The article describes Milton's transition from textbooks to a homegrown curriculum, and it is full of energy and hope. Here are some reflections from Milton teachers: “We spend less time on the repetitive practice of skills, in the abstract, and more on presenting a stream of situations.”
"The fight is won or lost far away from witnesses . . . long before I dance under those lights."
- Muhammad Ali
Teaching is a form of leadership, and teaching - like all leadership - depends on belief. Great teachers believe in what they are selling - not just in the abstract idea of what they are selling (education, mathematical literacy), but in the actual product (this unit on fractions, this problem I am presenting or assigning right now). In other words, great teachers only sell to students what they've sold to themselves.
When we're sharing a lot of information, it is important to share using appropriate units. The appropriate unit tends to be the smallest unit that is still a complete experience – small because small is easy to process, easy to use, easy to mix and match.
In the music industry, the appropriate unit is the song. A song is a complete experience, and anything less than a song is not. All of us have greatly benefited from sharing music at the level of the song. We can now assemble playlists of just the songs that we like. We can use software programs to create radio stations based on our current favorites.
In math education, the appropriate unit is the problem. A problem – from the perspective of the solver - is a complete experience, and anything less than a problem is not. Usually, when we distribute problems, we bundle them together. Publishers bundle them into books. Sharing sites (like BetterLesson and ClaCo) bundle them into lessons and worksheets. At Opus, we think that it is time to unbundle.
“All of us who do creative work, we get into it because we have good taste. But there is this gap. For the first couple years you make stuff, it's just not that good. It's trying to be good, it has potential, but it's not. And your taste is why your work disappoints you.”
-Ira Glass Last year at Match and this year at Opus, my creative works have been math problems. Like Ira, I have enough taste to know that they're not that good. But I also worry that taste won't be enough to close the gap. Taste is too vague. I need something definite to aspire to. So, in the past few days, I buckled down and wrote out my criteria. Hopefully they'll be helpful to you, and to me.
This week I discovered “The Exeter Series” by Glenn Waddell. For me, this was a “You've got a friend” moment (not my generation, but I definitely caught the allusion, Lee). If there's one thing in the field of education that gets me fired up, it is good thinking on the problems and questions that we pose to our students. And, if that's what you're into, it doesn't get much better than Glenn's “Exeter Series” and the object of that series, Exeter's math curriculum. Exeter in BriefI am not an Exeter expert, but for the sake of a starting point (and to expose any misinterpretations), here's my understanding of their approach:
Last week I stumbled upon A Mathematician's Lament by Paul Lockhart, a beautifully written and provocative essay on K-12 Mathematics Education. Many aspects of the essay resonated with me. But something about it did not sit right. I read Keith Devlin's follow-up column, and this comment by Keith best captured my discomfort: “Paul's approach is geared to developing in his pupils a love for mathematics as an enjoyable and challenging intellectual pursuit . . . But mathematics has another face. It is one of the most influential and successful cognitive technologies the world has ever seen. Tens of thousands of professionals the world over use mathematics every day, in science, engineering, business, commerce, and so on. They are good at it, but their main interest is in its use, not its internal workings. For them, mathematics is a tool. Even if they had an interest in investigating the inner workings of that tool (and there are plenty who claim they do not), they do not have the time . . . I fear that Paul's approach would not serve those individuals particularly well . . . Industry needs few employees who understand what a derivative or an integral are, but it needs many people who can solve a differential equation.”
I’m writing problems to seed Opus, a free and open-submission problem bank for K-12 teachers. My friend and I started Opus in May, and we are hard-at-work inputting problems, trying to push it to the point where it is worthy of a community.
As I write more and more problems, I am running up against a definite hierarchy of problem-writing difficulty. It goes: procedural, conceptual, applied, from easiest to hardest.
Here are my latest attempts (posted to Opus):
Submitted as an entry in the MathTwitterBlogosophere New Blogger Initiation:First, a confession: I am not a math teacher. I will understand if being a math teacher is viewed as a non-negotiable prerequisite for participation in the mathtwitterblogosphere, and will accept my excommunication. Otherwise, please read on: Last year, I was a Match Corps member at Match Middle School in Boston, MA. As the Algebra TA at Match, I was responsible for writing the math tutorials for our eighth graders, and it forced me to think about the problems that we give our students, and the work that they evoke. Early in the year, I had creative ambitions, but they were clumsily executed and incredibly time-consuming. By midway through the year, I could efficiently produce error-free scaffolded assignments, which seemed to mostly fulfill the primary goal of tutorial: high repetition procedural practice. But I was dissatisfied. Students were getting better procedurally (important), but they were totally missing the relevance of mathematics (very important). I wanted to communicate that math is a language that we use to represent real situations, and to solve real problems, but there's no way to communicate that without giving students real problems, and it's hard to come up with real problems in real time.
Compelling questions are open-ended: - How can Americans reduce their impact on the environment?
- What should the speed limit be on American highways?
- Is Facebook stock over-valued?
Open-ended questions provoke thought. They engage the user in an iterative process of questioning, assuming, estimating, and calculating. In his TED Talk, Dan Meyer makes an important point: we don’t give these types of questions to American math students. Instead, we give them closed-ended questions, questions that already have an answer, and that have been constructed to funnel students towards the answer.
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