Tag Archives: math education

June 28, 2014, 9:57 am

Grand challenges for mathematics education

1054180042_90c9dace1c_mOn Twitter this week, someone sent out a link to this survey from the NCTM asking users to submit their ideas for “grand challenges” for mathematics education in the coming years. I forget the precise definition and parameters for a “grand challenge” and I can’t go back to the beginning of the survey now that I’ve completed it, but the gist is that a grand challenge should be “extremely difficult but doable”, should make a positive impact on a large group of mathematics students, and should be grounded in sound pedagogical research.

To that list of parameters, I added that the result of any grand challenge should include a set of free, open-source materials or freely-available research studies that anyone can obtain and use without having to subscribe to a journal, belong to a particular institution, or use a particular brand of published curricula. In other words, one…

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February 11, 2013, 7:45 am

Does Khan Academy help learners? A proposal

Last week’s flare-up over Khan Academy was interesting on a number of levels, one of which is that we got a new look at some of the arguments used in KA’s favor. Perhaps one of the most prominent defenses against KA criticism is: Khan Academy is free and really helps a lot of people. You can’t argue with the “free” part. On the other hand, the part about “helping” is potentially a very strong argument in KA’s favor —but there are two big problems with the way in which this is being presented by KA people.

First, the evidence is almost entirely anecdotal. Look through the Pacific Research Institute whitepaper, for example, and the evidence presented in KA’s favor is anecdotes upon anecdotes — possibly compelling, but isolated and therefore no more convincing than the critics. The reason that anecdotes are not convincing is because for every anecdote that…

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July 16, 2012, 3:02 pm

What does it mean for kids to be “ready” for math?

USA Today has this op-ed (h/t to Joanne Jacobs) from Patrick Welsh giving thoughts on why kids hate math:

I worry that we’re pushing many kids to grasp math at higher levels before they are ready. When they struggle, they begin to dread math, and eventually we lose thousands of students who could be the scientists and engineers of tomorrow. If we held back and took more time to ground them in the basics, we could turn them on to math.

We’re asking young kids to move up in mathematics too far, too soon, in other words. Patrick goes on to focus especially on a push in California to get more younger kids taking Algebra and cross-references it with a Duke University study showing negative effects of the same sort of program in North Carolina.

I’m in complete agreement with this op-ed, although thankfully I haven’t felt that push so much with my own kids, ages 3, 6, and 8. There have…

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June 14, 2012, 10:00 am

Calling all math people: ASEE 2013 is coming!

The following is a shameless plug for the Mathematics Division of the American Society for Engineering Education. I am the division’s program chair for next year’s conference in Atlanta, GA — the dates haven’t been released yet, but it’s always in the first half of June — which means I get to recruit presenters, set up the talks at the conference, and manage the logistics. The main thing is that we need presenters, and that’s the nature of the plug.

If you are an engineer with a passing interest in mathematics and its instruction, or a mathematics person with a passing interest in the education of engineers, this is the conference for you! And you should give a talk at the Atlanta conference. There are a number of reasons why:

  1. It’s a big conference, with over 4000 attending the 2012 meetings and about that many attending this year’s. Big stage for your ideas.
  2. It’s a different …

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January 17, 2012, 8:00 am

A new online community for peer instruction users

Peer Instruction has gotten a lot of attention lately thanks to this NPR piece, “Physicists Seek to Lose the Lecture as a Learning Tool”.  Now, Eric Mazur — widely credited with the invention of peer instruction — is helping to create an online community of peer instruction users at peerinstruction.net.

If you go to that web site and click “Join”, you’ll be taken to a Google Documents form that asks for some basic demographics, and you’ll be added to a mailing list. The site has not officially launched yet, but from my Twitter stream there appears to be some considerable interest.

I’m hopeful that peerinstruction.net will be a good resource and, especially, a support group and collaboration incubator for PI users across multiple disciplines. I especially hope there are some resources for helping students and university administrators learn about PI.

August 11, 2010, 8:35 am

Student (mis)understanding of the equals sign

Interesting report here (via Reidar Mosvold) about American students’ misunderstanding of the “equals” sign and how that understanding might feed into a host of mathematical issues from elementary school all the way to calculus. According to researchers Robert M. Capraro and Mary Capraro at Texas A&M,

About 70 percent of middle grades students in the United States exhibit misconceptions, but nearly none of the international students in Korea and China have a misunderstanding about the equal sign, and Turkish students exhibited far less incidence of the misconception than the U.S. students.

Robert Capraro, in the video at the link above, makes an interesting point about the “=” sign being used as an operator. He makes a passing reference to calculators, and I wonder if calculators are partly to blame here. After all, if you want to calculate 3+5 on a typical modern calculator, what do…

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August 8, 2010, 12:47 pm

Calculus and conceptual frameworks

Image via http://www.flickr.com/photos/loopzilla/

I was having a conversation recently with a colleague who might be teaching a section of our intro programming course this fall. In sharing my experiences about teaching programming from the MATLAB course, I mentioned that the thing that is really hard about teaching programming is that students often lack a conceptual framework for what they’re learning. That is, they lack a mental structure into which they can place the topics and concepts they’re learning and then see those ideas in their proper place and relationship to each other. Expert learners — like some students who are taking an intro programming course but have been coding since they were 6 years old — have this framework, and the course is a breeze. Others, possibly a large majority of…

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December 19, 2008, 9:54 am

What does academic rigor look like?

I got an email from a fellow edu-blogger a couple of days ago asking for my input on the subject of academic rigor. Specifically this person asked:

Is the quest for more rigor an issue for you? Is it good, bad, meaningless? What does rigorous teaching look like in your classroom?

I hope she doesn’t mind my sharing the answer, because after writing it I thought it’d make a good blog post. I said:

For me, “rigor” in the context of intellectual work refers to thoroughness, carefulness, and right understanding of the material being learned. Rigor is to academic work what careful practice and nuanced performance is to musical performance, and what intense and committed play is to athletic performance. When we talk about a “rigorous course” in something, it’s a course that examines details, insists on diligent and scrupulous study and performance, and doesn’t settle for a mild or  informal…

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November 9, 2008, 9:13 pm

Straight talk on constructivism

Hat tip to Darren at Right on the Left Coast for this article, which starts off saying in a plainspoken way:

Here are two of the clues to America’s current mathematics problem:
1.”Student-centered” learning (or “constructivism”)
2.Insufficient practice of basic skills

The article then goes on to say, of constructivism:

In small doses, constructivism can provide flavor to classrooms, but some math professors have told me the approach seems to work better in subjects other than math. That sounds reasonable. The learning of mathematics depends on a logical progression of basic skills. Sixth-graders are not Pythagorus [sic], nor are they math teachers.

That’s right. Constructivism, when used with the right kinds of students and in the right ways, can be quite effective. But it’s important to remember that not all students are ready for this, and not all material is taught effectively …

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October 15, 2008, 8:54 pm

Technology in proofs?

We interrupt this blogging hiatus to throw out a question that came up while I was grading today. The item being graded was a homework set in the intro-to-proof course that I teach. One paper brought up two instances of the same issue.

  • The student was writing a proof that hinged on arguing that both sin(t) and cos(t) are positive on the interval 0 < t < π/2. The “normal” way to argue this is just to appeal to the unit circle and note that in this interval, you’re remaining in the first quadrant and so both sin(t) and cos(t) are positive. But what the student did was to draw graphs of sin(t) and cos(t) in Maple, using the plot options to restrict the domain; the student then just said something to the effect of “The graph shows that both sin(t) and cos(t) are positive.”
  • Another proof was of a proposition claiming that there cannot exist three consecutive natural numbers such that the …

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