What are you learning?
If you ever needed a REASON to calculate the highest point of a parabola that opens downward, here’s one.
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Futurist Peter Bishop was one of the keynote presenters at MichMATYC 2010 this year. He spoke to us about what a futurist does, and shifted our paradigms about how to look at data trends to one that is more mindful of the cone of plausibility. Don’t know what that is? Well, watch the talk! If you don’t have a lot of time, then watch the last 20 minutes. You can also get the slides here.
If you’re interested in the other sessions at MichMATYC 2010, many of the slide decks are posted in the Resources Tab of the MichMATYC 2010 Website.
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I let my students use Wolfram Alpha when they are in class and when they are doing their homework (um, how would I stop them?). Because of this, I’ve had to shift how I assess on more formal assignments. For the record, it’s the same adjustment you might make if you were using ANY kind of Computer Algebra System (CAS).
The simplest shift is to stop asking for the answers to problems, and just give the students the answers. After all, they live in a world where they CAN easily get the answers, so why pretend that it’s the answers that are important? It’s the mathematical thinking that’s important, right? Giving the students the answers turns problems into “proofs” where the evaluation (grade) is based on the thought-process to get from start to finish. It also eliminates the debate about whether to award points for a correct answer with no correct process.
Here are two examples of problems from a recent Calculus exam (old and new wording).
I wish I had thought to do this years ago, because students who insist on just doing the “shortcut” (and not learning what limits are all about) now have nothing to show for themselves (the answer, after all, is right THERE).
Again, a student that knows the derivative rules might get the right answer, but the right answer is now worth zero points. The assessment is now clearly focused on the mathematical thinking using limits.
Another reason that I really like this is that it allows students to find mistakes that they are capable of finding “in the real world” where they can quickly use technology to get an answer. They are now graded solely on their ability to explain, mathematically, the insides of a mathematical process.
Wolfram Alpha also allows me to pull real-world data into my tests much faster. Here’s a question about curve shape (the graph is just a copy/paste from W|A):
If you haven’t begun to think about how assessment should change in a world with ubiquitous and free CAS, you should. You don’t have to change all your problems, but I think some of them should change. Otherwise, we’re just testing students on the same thing that a computer does, and that doesn’t sit well with me. If you can be replaced by a computer, you’re likely to be replaced by a computer. Let’s make sure we’re teaching students how to think mathematically, not how to compute mathematically.
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I just finished watching the TED Talk by David McCandless called “The Beauty of Data Visualization” and it is stunningly awesome! In the talk, he discusses the importance of understanding the relativeness of data when it is reported in the news. “Visualizing information is a form of knowledge compression” where we squeeze enormous amount of information and understanding into a small space. McCandless was not trained in graphic design, but “”being exposed to all this media over the years had instilled a kind of dormant design literacy in me.” He says he is something of a “data detective” (see his graph “Mountains out of Molehills” in the talk for an example).
Edward Tufte also discusses the importance of data visualization, but he is something of a technology Luddite. David’s interactive digital data visualization “Snake Oil” is simply awesome and demonstrates a path that “information supergraphics” could take if Tufte were to embrace technology instead of just bashing it (I went to one of Tufte’s workshops last year and I can tell you that the only “good technology” was his iPhone).
If there was ever a video to show a math or statistics class at the beginning of the semester, this might be it. Of course, then you’ll actually have to DO some data visualization during the semester, but hey – it will keep you honest!
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The talk is titled “Computing a Theory of Everything”
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For a few months now, the NYT Opinionator Blog has been hosting a series of pieces that do a phenomenally good job of explaining mathematics in layman’s terms.
The latest article is about Calculus (with a promise of more to come): Change We Can Believe In is written by Steven Strogatz, an Applied Mathematician at Cornell University.
There are several other articles in this series, and if you haven’t been reading them, you really should go check them out. Assign them. Discuss them in your classes.
Given the discussions we’ve been having about teaching Series and Series approximations lately on Facebook, Twitter, and LinkedIn, I wonder if he’d consider writing an article explaining “Why Series?” to students.
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