Archives for math



Does Math Make Research “Better”?

Yes — if you don’t know much math, that is. A new study finds that even academic scholars perceived research to be of higher quality if there’s some math involved — even if the math makes no sense. The experiment threw an irrelevant mathematical equation into research paper abstracts, and asked scholars of different fields to evaluate the quality of the research:

Mathematics is a fundamental tool of research. Although potentially applicable in every discipline, the amount of training in mathematics that students typically receive varies greatly between different disciplines. In those disciplines where most researchers do not master mathematics, the use of mathematics may be held in too much awe. To demonstrate this I conducted an online experiment with 200 participants, all of which had experience of reading research reports and a postgraduate degree (in any subject).

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Ending the Math Wars in a Treaty of QAMA

As a country, we are often at war. If it’s not against Germany, England, terrorism, or Grenada, it’s the war on poverty (that’s gone so well), the war on cancer (ditto), and, of particular interest to me, the Math Wars, which have been raging for decades. On one side, the traditionalists insist on drilling and back to basics, “on behalf of sanity and quality in math education.” On the other side, the reformers insist on conceptual understanding using computers and calculators, to “promot[e] the rational reform of mathematics education.”

Both are half-right and half-crazy. As the reformers say, students need to understand what the mathematics means. Students whose word problem for “6 x 3 = 18″ is of the form “There were 6 ducks, and 3 more showed up, so 6 times 3 is 18,” understand little. (See “Children Learning Multiplication, Part 1,” in the articles by Professor Thomas C. O’Brien.) As the traditionalists say, using computers for everything leads to needing a calculator to compute what 6.5 x 10 is.

However, there’s a tool to combine the merits of both sides: the Quick, Approximate, Mental Arithmetic (QAMA) calculator. Read More »



The Best Third-Grade Teacher Ever

One of the most important economic issues we face today is how much to spend on education, both individually and as a society. As tax revenues decline due to demographic changes and deteriorating business conditions, municipalities have to make tough choices about which programs to cut, and education is often an early victim. Because we don’t yet have good measures of all the future benefits produced by better education today, school programs are easy targets for cost-cutting measures, especially in lower-income regions where parents are focused on meeting more basic needs and less likely to put up a fight. But experiments like Geoffrey Canada’s Harlem Children’s Zone hint at the enormous impact that early educational support can have on lifetime achievement.

I have my own example: Mrs. Ficalora, the best third-grade teacher ever. Read More »



Raising Money to Teach Math

A reader named Karim Kai Ani writes:

Guy walks into a bar and says, “We’ve got this math curriculum that everyone is saying is the bomb (a dangerous thing to say when you have my name, but go with me), and we’re Kickstarting a video series to offer teachers a new vision of what it means to teach math.”

And the waitress says, “You should see if the dudes from Freakonomics would tweet about it. Didn’t they mention Mathalicious on their blog once?”

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What Teachers Think About Girls’ Math Skills

A disheartening new study by Catherine Riegle-Crumb and Melissa Humphries finds that teachers discount the math skills of white females, even when girls’ grades and test scores indicate a comparable level of skill.  Here’s the abstract:

This study explores whether gender stereotypes about math ability shape high school teachers’ assessments of the students with whom they interact daily, resulting in the presence of conditional bias. It builds on theories of intersectionality by exploring teachers’ perceptions of students in different gender and racial/ethnic subgroups and advances the literature on the salience of gender across contexts by considering variation across levels of math course-taking in the academic hierarchy. Analyses of nationally representative data from the Education Longitudinal Study of 2002 (ELS) reveal that disparities in teachers’ perceptions of ability that favored white males over minority students of both genders are explained away by student achievement in the form of test scores and grades.

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The Mathematics of Magic

I don’t particularly like math.  I’ve never been a fan of magic either.  For some reason, however, when I heard about a new book entitled Magical Mathematics written by two first-rate mathematicians, Persi Diaconis and Ron Graham, I felt compelled to buy it and read it.

I have to say that it is really good, and I would highly recommend it to any nerd.  It is a really artful melding of card tricks that are remarkable, with explanations of the underlying math concepts that are at one level so simple and clear that almost anyone could get the basic intuition for what they are talking about, but at another level so deep and difficult that it is probably hopeless for someone like me to ever truly understand.  Read More »



UCLA’s Crime Fighting Mathematicians

A team of mathematicians at UCLA have created an algorithm that can identify with relative accuracy which Los Angeles gang is responsible for an unsolved crime. When tested against cases with a known culprit, the mathematicians could correctly list the gang rivalry involved (out of the three most likely rivalries) about 80 percent of the time. Of these options, they ranked the responsible gang first about 50 percent of the time.

To develop their technique, the mathematicians studied a combination of solved and unsolved gang crimes throughout East L.A. over ten years. Explaining the process, author Andrea Bertozzi, director of applied mathematics at UCLA, says:

If police believe a crime might have been committed by one of seven or eight rival gangs, our method would look at recent historical events in the area and compute probabilities as to which of these gangs are most likely to have committed crime.

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Memorizing the Digits of Pi

Pi is an irrational number. Which means that as a decimal, it goes on forever. What’s the best way to memorize this infinite chain of numbers? How about music? Or poetry? Read More »