Mathematics and Education

A slow blog

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

Understanding Underrepresentation

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. . . is the title of my article in the Mathematical Intelligencer on the distribution of women in mathematics and other fields. I’ve posted the manuscript version here. Read the rest of this entry »

Written by CK

January 11, 2014 at 11:11 am

1 HIt, 1 Miss for the EMB Theory

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Simon Baron-Cohen’s Extreme Male Brain theory proposes that autistic people have an amplification of cognitive features considered typical of males. Associated with this conjecture about cognitive behavior are conjectures about brain anatomy, i.e., that brain regions which differ, on average, between the males and females whose brains have been studied, will also differ between autistic and non-autistic people.

Biological Sex affects the Neurobiology of Autism,” an article by Baron-Cohen and colleagues, describes findings from a study that examined brain anatomy via MRI scans. Read the rest of this entry »

Written by CK

August 20, 2013 at 2:32 pm

Posted in Baron-Cohen

Comments on Goodman’s “Comparison of Proposed US Common Core Math to Standards of Selected Asian Countries”

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Summary. In July of 2010, Jonathan Goodman published a comparison of Common Core State Standards with curriculum documents from several Asian countries (China, Hong Kong, Japan, Singapore, Taiwan). In my opinion, his analysis has some serious flaws. In this post, I give some examples. In an earlier post, I have given a brief overview of differences in national context, noting the different uses of standards and other documents in the U.S. and elsewhere. These different contexts and uses suggest how a U.S. reader’s expectations may lead to misinterpretation of documents from outside the U.S. In this post, I compare some of Goodman’s statements with the content of these documents in two ways: comments and detailed side-by-side comparisons. Read the rest of this entry »

Written by CK

August 4, 2013 at 4:12 pm

Comments on Milgram’s “Review of Final Draft Core Standards”

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Summary. In 2010 (apparently in June), Jim Milgram posted a review of the Common Core State Standards, comparing them with standards of high-achieving countries. In my opinion, his review misses some important details and makes some incorrect conclusions. In this post, I give some examples. In an earlier post, I have given a brief overview of differences in national context, noting the different uses of standards and other documents in the U.S. and elsewhere. These different contexts and uses suggest how a U.S. reader’s expectations may lead to misinterpretation of documents from outside the U.S. In this post, I discuss some assertions in the review and give some detailed side-by-side comparisons of comments with standards, teacher’s guides, and other documents. Read the rest of this entry »

Written by CK

August 4, 2013 at 3:55 pm

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