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Gender differences in math: Cultural, not biological

This report Frinom the Atlanta Journal-Constitution, citing an article in the June 1 Proceedings of the National Academy of Sciences, says that differences between boys’ and girls’ performance on standardized mathematics tests correlates with the level of gender equity and other socio-cultural factors in the country in which the test was taken.
The study’s co-author says:

“There are countries where the gender disparity in math performance doesn’t exist at either the average or gifted level. These tend to be the same countries that have the greatest gender equality,” article co-author Janet Mertz, an oncology professor at the University of Wisconsin-Madison, said in a university news release.[…]

“If you provide females with more educational opportunities and more job opportunities in fields that require advanced knowledge of math, you’re going to find more women learning and performing very well in mathematics,” Mertz said.

The study goes on to cite the US as a country where there is a relatively high degree of gender equity and hence a relatively equal performance on standardized tests between boys and girls, with more and more girls taking advanced courses in science and math. But, importantly, the study also warns that

“U.S. culture instills in students the belief that math talent is innate; if one is not naturally good at math, there is little one can do to become good at it,” Mertz said. “In some other countries, people more highly value mathematics and view math performance as being largely related to effort.”

This is a point well worth noting. What will it take for the culture in the US to get away from the idea that you’re either born with mathematical ability or born without it — in other words, mathematical predestination?

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A calculus thought experiment

On Twitter right now I am soliciting thoughts about calculus courses, the topics we cover in them, and the ways in which we cover them. It’s turning out that 140 characters isn’t enough space to frame my question properly, so I’m making this short post to do just that. Here it is:

Suppose that you teach a calculus course that is designed for a general audience (i.e. not just engineers, not just non-engineers, etc.). Normally the course would be structured as a 4-credit hour course, meaning four 50-minute class meetings per week for 14 weeks. Now, suppose that the decision has been made to cut this to TWO credit hours, or 100 minutes of contact time per week for 14 weeks.

Questions: What topics do you remove from the course? What topics do you keep in the course at all costs? And of those topics you keep, do you teach them the same way or differently? If differently, then how would you do it? Finally, would there be anything NEW you’d introduce in the course that would be pertinent for a 2-hour course that wouldn’t show up in a 4-hour version of that course?

Keep Twittering your comments to me at @RobertTalbert, or comment below. I’ll sum them up later.

UPDATE: I also meant to say, feel free to play with the assumptions I am making here. For example, if it’s impossible to think of a 2-hour calculus course, change that to a 3-credit course and see if you can come up with anything.

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You’re missing all the excitement…

…if you’re not following my family blog, The Talbert Five. Just click it.

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Ten rules for financing a transition to academia

My latest post at the Young Mathematicians Network blog is on how to get from graduate school to your first academic job without hopelessly screwing yourself over financially speaking, like I did. It takes some time for the post to appear on the YMN web site, so I will include it below the fold for CO9s readers (I should call this “premium content”!). Continue reading

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Top of the charts

You have to love this:

song chart memes
more graph humor and song chart memes

I’m not sure how I made it this far without GraphJam. Briliant stuff.

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Questions about the algebra course

Jackie asked a series of good questions about the textbook-free modern algebra course and some of the student outcomes I was seeing in it. I tried to respond to those in the comments, but things started to get lengthy, so instead I will get to them here.

Do you think the results are only a result of a textbook free course?

To repeat what I said in the comments: I think the positives in the course come not so much from the fact that we didn’t have a textbook, but more from the fact that the course was oriented toward solving problems rather than covering material. There was a small core of material that we had to cover, since the seniors were getting tested on it, but mostly we spent our time in class presenting, dissecting, and discussing problems. We didn’t cover as much as I would have liked, but this is a price I decided to pay at the outset.

Most traditional textbooks don’t lend themselves well to this kind of class design. The ratio of text to problems in a typical textbook is probably something like 5:1 — a lot higher than that in some books. When you have a book in the course, it almost forces itself into the center of the class universe and everything tends to revolve around it, and take on its flavor. When the book spends most, almost all, of its pages on stuff for students to read rather than on problems for students to solve, then I guess it’s possible to have a problem-solving oriented class, but you’re going to be swimming upstream the whole way.

It works better, I think, to have no central book — and instead, provide problems via the course notes with just enough information to solve the problems. And if the students need more information, make it an assignment for library research or web queries.

Were there any negative outcomes? Anything you didn’t like as a result of choosing to structure the course in this manner?

There are some important algebra topics, in rings and particularly in fields, that are not going to get the time they really deserve. And I had to cut short or cut out some topics in group theory that are normally standard fare. At least, I see this as a negative; whether it really makes a difference in the long run is yet to be determined.

The way I select students to do course tasks in class basically involves randomly ordering the students and having them attempt the problems one after the other. It seemed like several times, students who had not presented much ended up first on the list on the days they didn’t have something and last on the list on the days they did. Call it bad luck or Murphy’s Law or what-have-you; but I didn’t like how there was no mechanism for making sure the lower-scoring students got more chances to work.

Some students in the class still struggle with basic problem-solving skills and writing proofs. I think they have enough education to carry out successful problem-solving on proofs most of the time. But not having me lecture has meant that they don’t get to see professionally put-together proofs very often unless they go do some reading.

And I think that this course structure caused stress and even ill will among the students who were not used to having so much personal responsibility in their college work. I think that’s an unintended consequence of implementing a course design that is basically sound; I regret that it happened, and I’d like students to have a more uniformly positive experience in the class, but I’m not going to change the basic course design.

Would you do this again?

You bet, although I believe this way of running the class works in some situations and wouldn’t work in others. I thought about running my differential equations class next semester like this, but that course is so focused on methods that a blind application of this course structure onto that course doesn’t seem appropriate. Maybe I’ll come up with some variant that works.

What would you keep the same? What would you change?

I would definitely keep my method for assigning problems to students, my rubric for grading course tasks, and just the overall procedure for running the class sessions that I used. And I’d keep the feature where students get to choose the weights on the various assessments.

I’d do a little more with the course wiki. Right now students are expected to write up their solutions to course note tasks on the wiki, but there is no point value in doing so nor a penalty for not doing so. The exams are open-wiki, though, so there is some incentive for writing results up well. But I think I would make the posting of solutions mandatory and enforce the rule.

I’d also try to have a complete set of notes before the course began. I have been writing things as I go, and it’s led to some snafus I could have avoided.

I might try writing the course notes so that rings and fields come first.

I’d seriously consider having proof techniques be offered as the subject of weekly help sessions or additional course work. Some students are still struggling with basic problem-solving techniques, and they really need more help than what they are asking for.

That’s that for the questions. Any more?

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iWork ‘08 brief once-over

Apple just made major updates to the software I probably use the most, namely iWork and particularly Keynote. I downloaded the 30-day trial (which makes me wonder why we can’t just download software from Apple) and have given Pages and Keynote a very (VERY) brief once-over. I hope to have more later. But for now, here are some first impressions.

They are really pushing Pages now as a word processor. Before, it was a little hard to know exactly what it was. Is it a word processor? Is it desktop publishing? Is it something in between? We didn’t really know, and I hardly ever used it unless I had a document to print that had a lot of graphics in it. But now, check out the updated toolbar:
Pages Screenshot

Mercifully, you can now adjust stuff like font size, typeface, aligment, etc. from the toolbar — no more click, click, click to navigate through those damnable Inspectors to do such simple stuff. Just like… a word processor. And just so you don’t forget, it tags the name of the document with (Word Processing) at the top. Actually this appears to be because you can switch between “word processing” mode and some other kind of mode (“page layout”?). I didn’t play with it long enough to find out the difference.

I made out a document in Pages ’08 just to see what it was like, and the experience was pretty much the same as with Pages ’06. One thing I was thankful for was this commonly-used Inspector item for laying out objects within a document:
Pages Screenshot 2

In ’06, the choices here were “moves with text” or “fixed on page”. The latter option confusingly meant that the object being selected could be moved around and the text would wrap with it, which to me is the opposite of something being fixed on a page. “Floating” is a much better term for this.

Keynote ’08 has some nice new themes to it and has the feature I have been secretly wishing for ever since I started using Keynote: The ability to animate an object along a user-defined path. There is also a new option that lets you export a presentation directly to YouTube — which is nice, but won’t the screen resolution be terrible?

There are more features to boot, and I hope to delve deeply into them later.

Finally, there is a new spreadsheet package with iWork called Numbers. From the Apple tutorials, it sounds… rudimentary. There are all sorts of media-rich enhancements, like the ability to edit images right in the spreadsheet, but honestly, I use a spreadsheet for number-crunching and data analysis. All I can say is, if it doesn’t do multiple forms of regression, it ain’t a spreadsheet, and I don’t care how media-rich it is. We’ll see how it stacks up to Excel pretty soon.

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