Category Archives: High school

December 22, 2010, 12:00 pm

Misunderstanding mathematics

Plots of quadratic equations with discriminant...

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Robert Lewis, a professor at Fordham University, has published this essay entitled “Mathematics: The Most Misunderstood Subject”. The source of the general public’s misunderstandings of math, he writes, is:

…the notion that mathematics is about formulas and cranking out computations. It is the unconsciously held delusion that mathematics is a set of rules and formulas that have been worked out by God knows who for God knows why, and the student’s duty is to memorize all this stuff. Such students seem to feel that sometime in the future their boss will walk into the office and demand “Quick, what’s the quadratic formula?” Or, “Hurry, I need to know the derivative of 3x^2 – 6x +1.” There are no such employers.

Prof. Lewis goes on to describe some ways in which this central misconception is worked…

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June 4, 2010, 8:54 am

Plagiarism in high school

Turnitin logo
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About two dozen seniors at Hamilton Southeastern High School in the affluent northern suburbs of Indianapolis have been caught plagiarizing in a dual-enrollment college course, thanks to turnitin.com. Full story with video here, and there’s an official statement from the HSE superintendent on this issue here (.DOC, 20KB).

This would be an ordinary, though disappointing, story about students getting caught cheating if it weren’t for some head-scratchers here. First, this bit from the superintendent’s statement:

We took immediate action because the end of the school year was rapidly approaching. Several students were in danger of not graduating on time. We found a teacher who was willing to step up and administer a complete but highly accelerated online version of a class that would replace the credit that was lost due to cheating. Each student who wishes to graduate…

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March 31, 2010, 8:38 am

Indiana teacher licensing changes now official

The sweeping set of teacher licensing changes for Indiana, which I first blogged about here last July, has officially been signed into law. Frankly, I’m surprised, on two levels.

First, although this proposal flew mainly under the radar in Indiana, it was quite polarizing. The public, especially parents of school-aged kids, seemed mainly to be in favor of the bill; while teachers, teacher unions, and university education professors were quite vocally against it. Usually something this divisive doesn’t make it to being signed into law, or else it gets gutted and compromised first. But I can’t find any changes that were made between the bill and the law. It looks like what we saw is what we will get.

Second, it was pretty clear if you scratched the surface of this bill that one of its reasons for being was to put Indiana in a position to get Race to the Top money from the Federal…

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March 17, 2010, 8:26 pm

You can't become an expert in college

Cover of "Outliers: The Story of Success&...

Cover of Outliers: The Story of Success

Here’s something of an epiphany I had at the ICTCM while listening to Dave Pritchard‘s keynote, which had a lot to do with the differences between novice and expert behaviors in problem-solving.

Malcolm Gladwell, in his book Outliers, puts forth a now-famous theory that it takes at least 10,000 hours to become a true expert in a particular area, at the top of one’s game in a particular pursuit. That’s 10,000 hours of concentrated work in studying, practicing, and performing in some particular area. When we talk about “expert behavior”, we mean the kinds of behaviors that people who have put in their 10,000 hours exercise as second nature.

Clearly high school or college students who are in an introductory course — even Dave Pritchard’s physics students at MIT, who are likely…

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February 27, 2010, 6:32 am

Is Khan Academy the future of education?

Salman Khan is a former financial analyst who quit his day job so that he could form Khan Academy — a venture in which he makes instructional videos on mathematics topics and puts them on YouTube. And he has certainly done a prolific job of it — to the tune of over a thousand short videos on topics ranging from basic addition to differential equations and also physics, biology, and finance.  Amazingly, he does this all on his own time, in a remodeled closet in his house, for free:

I can attest to the quality of his linear algebra videos, some of which I’ve embedded on the Moodle site for my linear algebra course. They are simple without being dumbed down, and what he says about the 10-minute time span in the PBS story is exactly right — it’s just the right length for a single topic.

What do you think about this? What role do well-produced, short, simple, free video…

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January 30, 2010, 12:22 pm

Fractal Doritos!

Students and faculty at University Preparatory School in Redding, CA have created the world’s largest Sierpinski triangle constructed entirely out of Doritos. (Well, it’s probably the only one, but still.) It is 64 feet long and made out of 12,000 Doritos. This was done as an entry to the Doritos Crash the Superbowl contest. Watch, and be awed:

Can a 128-, 256-, etc. foot long Dorito Sierpinski triangle be far behind? I bet the parent company for Doritos would seriously consider some corporate sponsorship.

Thanks to Cory Poole, math and physics teacher at U-Prep, who sent this in. That’s a great, creative way to get students interested in math. (And you can eat it when it’s done.) There’s more on the video here.

January 26, 2010, 9:44 am

A school for grown-ups

My 6-year old is in kindergarten and fascinated by school and schoolteachers. Last week she asked me: “Daddy, are you a teacher?” I told her I was. “What’s your school?” I told her I teach at a college. “What’s a college?” I told her: “A college is a school for grown-ups.” And in that off-the-cuff answer, we have an economical way of describing the difference between college and pre-college education, and of encapsulating the hopes and goals of higher education.

College students, even the wide-eyed freshmen who show up every fall, are not kids. They are emerging adults, having worked 12 years for a high school education and who now enter a 4-5 year buffer zone before entering into the world with nothing more than the things they know, the experiences they’ve had, and the people around them. Therefore we college professors aren’t serving students if we treat them like kids, refer to …

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July 29, 2009, 1:33 pm

Big changes coming for Indiana teacher licensing?

Indiana Superintendent of Public Instruction Tony Bennett is announcing today a plan to overhaul the state’s system for teacher licensure. The announcement is here, and there are three PDF’s linked at the bottom of that page that go into more depth. [Update: There's now a 7-minute video of the press conference at this site as well.] And here’s an Indianapolis Star article (written prior to the announcement, so it’s a bit short on detail) that gives a thumbnail overview and some reactions from local education people. Those reactions seem pretty heated, and when you read the details of the program, you can begin to understand why.

The first point listed in the plan, and the one that seems to have the most impact, is that requirements for content knowledge for pre-service teachers are going to be ratcheted up several notches. Secondary education teachers will now be required to earn a…

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July 4, 2009, 3:19 pm

Changing the summit of math education?

Arthur Benjamin thinks that the current model of the mathematics curriculum — leading from arithmetic to algebra and ultimately to calculus — is flawed and needs to be changed. Watch this 3-minute TED talk for what he thinks ought to be the real summit of the mathematics curriculum:

[ted id=587]

I am in a great deal of agreement with Prof. Benjamin here. The secondary school math curriculum does indeed seem poised to point students towards calculus. While that is appropriate for some, it is not appropriate for all; while on the other hand, a better knowledge of discrete math, especially probability and statistics, would be appropriate for everybody.

Moreover, Prof. Benjamin did not stress one of the most important selling points for refocusing on discrete math: The mathematical background requirements are a lot lower than they are for calculus. Students currently have to take two…

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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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