Mathematics and Education

A slow blog

The Tyranny of the Mean

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In the appendix footnote 3 of a forthcoming 2015 article, Ceci and Williams state:

Many commentators have opined that female scientists are superior to their male counterparts, and therefore the fact that they are hired at the same rate as men obscures the fact that they should be hired at even higher rates, if merit was the basis for hiring.

Ceci and Williams give three quotes intended as examples of this argument. One comes from my blog post The Pipeline and The Trough. However, as I stated in a later post, I did not give this argument.

So why do Ceci and Williams think I did? The answer may lie in “the tyranny of the mean”—the assumption that the mean for a set, e.g., “female scientists,” is the same as the mean of a subset, e.g., “female applicants for a given job.” Read the rest of this entry »

Written by CK

October 19, 2015 at 4:22 pm

Grade 4 and 8 NAEP Objectives Outside the Common Core

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This is a guest post by Jason Zimba.

Created in the late 1960s, the National Assessment of Educational Progress (NAEP) today measures U.S. achievement in mathematics, reading, science, U.S. history, and other subjects. The most recent framework for the mathematics assessment is described in a document published in 2014 by the National Assessment Governing Board and entitled Mathematics Framework for the 2015 National Assessment of Educational Progress. Below, I list assessment targets from the NAEP Mathematics Framework that are outside the expectations in the Common Core State Standards for Mathematics (CCSS-M). Read the rest of this entry »

Written by CK

October 15, 2015 at 4:45 pm

A Female Advantage in Academic Hiring?

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In their recent Proceedings of the National Academy of Sciences article about tenure-track hires, Williams and Ceci say:

A number of audits of hiring by universities have been reported in the past two decades and these have reported either a neutral playing field in non-mathematical fields . . . , or, more commonly, a pronounced female hiring advantage in math-intensive fields. . . . Here is what we know about the female advantage in real-world hiring of tenure-track applicants in STEM fields in the United States and Canada: There is a female advantage in all large-scale studies dating back to the 1980s. (SI Appendix, p. 26, emphasis added)

Williams and Ceci quantify “female preference” as the ratio of female hires to female applicants. However, they do not compute these ratios for the “audit studies” they cite. This post makes some of those computations.

Interestingly, three of the eight studies cited come from Canada, but some large-scale audit studies of United States universities are not mentioned. This post examines a few of the studies that could have been cited, finding that the claim above is not supported and offering an alternative explanation for the statistics in the US audit studies.

Update (August 2015): Ceci makes an assumption explicit (see comments section here and further discussion below).

Iqbal 2000 Fig 1Update (July 2015): The three Canadian studies concern hiring in the 1980s and 1990s. During this period, the gender distribution of Canadian faculty hires may have been affected by a “brain drain” to the United States. Studies note that PhDs were overrepresented among these migrants. What is known suggests that a very large proportion of these PhDs were male and among “the best and the brightest.” Thus, faculty hiring patterns in Canada and the United States may differ. Moreover, an exodus of men may be a factor in the apparent overrepresentation of women as hires in Canada. Further discussion is below.

Figure from Iqbal, M. (2000). Brain drain: Empirical evidence of emigration of Canadian professionals to the United States. Canadian Tax Journal, 48(3), 674–688.

Read the rest of this entry »

Written by CK

May 11, 2015 at 3:14 pm

Save the Phenomena!

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Last Halloween, the psychologists Wendy Williams and Stephen Ceci wrote an op-ed in New York Times claiming that “academic science isn’t sexist.” Among other things, they suggest that bias doesn’t occur in hiring, writing of “alleged” hiring bias. In a longer article, Ceci and three co-authors claim that “the evidence in support of biased hiring as a cause of under-representation is not well supported, and even points in the opposite direction.” The same evidence is interpreted as a “female hiring advantage” in Williams and Ceci’s “2:1 Faculty Preference for Women on STEM Tenure Track.”

I think the reason why this evidence “points in the opposite direction” is that Ceci et al. do not “save the phenomena” by accounting for crucial details of the findings they cite. Thus, these findings may not be consistent with the findings of Williams and Ceci’s experimental study. This raises concerns about the ecologically validity of the experimental study, e.g., that it may be not realistic to assume that a strong female applicant will often be described as “creative” or “a powerhouse.”

Here are details. Read the rest of this entry »

Written by CK

April 14, 2015 at 4:33 pm

Who is the Most “Mathematically-intensive” of Them All?

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Well, mathematics, of course. But what comes after that? Engineering, computer science, or economics perhaps? Answers differ, even according to the same definition of “mathematically intensive.” Read the rest of this entry »

Written by CK

November 7, 2014 at 2:10 pm

Unfinished Business from 300 BC

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The double meaning of “ratio” in U.S. school mathematics is a phenomenon that goes back as far as Euclid. On the one hand, a ratio of two numbers is written as a pair, e.g., 3 to 1. On the other, a trigonometric ratio is a single number, e.g., the sine of pi/6 is one half—not 1 to 2. (Ratios of more than two numbers do not have this double interpretation, so are not part of this discussion.) Read the rest of this entry »

Written by CK

September 29, 2014 at 3:24 pm

Comments on Ravitch’s MLA Speech

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The historian Diane Ravitch gave a speech to the Modern Language Association on January 11 about the past, present and future of the Common Core State Standards which was posted on a Washington Post blog. There’s a lot to like about the speech when it comes to rethinking uses of tests and test scores. I’ve been in favor of caution about testing since at least 1999 (see my article here).

However, the speech has some statements that are unclear, appear unaware of research in mathematics education, or seem uninformed. Some concern:

Characteristics of standardized tests.

Field testing standards.

Developmental appropriateness of the CCSS.

Development of the CCSS.

Details are below. Read the rest of this entry »

Written by CK

February 13, 2014 at 9:09 am


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