A new study published today in BioMed Central’s open access journal Behavioral and Brain Functions [Devine A, Fawcett K, Szűcs D, Dowker A (2012), Gender differences in mathematics anxiety and the relation to mathematics performance while controlling for test anxiety. Behavioral and Brain Functions (in press; still was not online at time of writing).] reports that a number of school-age children suffer from mathematics anxiety and, although both genders’ performance is likely to be affected as a result, girls’ maths performance is more likely to suffer than boys’.
A word problem from the Khan Academy
Last year, I was asked by my American colleagues to give my assessment of mathematical material on the Khan Academy website. Among other things I looked for the so-called “word problems” and clicked on a link leading to what was called there an “average word problems” but happened to be a “word problem about averages”. It appears that the problem there changed since last year. I reproduce here the old one, it is more of interest for discussion of “word problems”.
Gulnar has an average score of \( 87\) after \( 6\) tests. What does Gulnar need to get on the next test to finish with an average of \( 78\) on all \( 7\) tests?
D. Pierce, Induction and Recursion, The De Morgan Journal, 2 no. 1 (2012), 99-125.
From the Introduction:
In mathematics we use repeated activity in several ways:
- to define sets;
- to prove that all elements of those sets have certain properties;
- to define functions on those sets.
These three techniques are often confused, but they should not be. Clarity here can prevent mathematical mistakes; it can also highlight important concepts and results such as Fermat’s (Little) Theorem, freeness in a category, and Goedel’s Incompleteness Theorem.
The main purpose of the present article is to show this.
In the `Preface for the Teacher’ of his Foundations of Analysis of 1929, Landau discusses to the confusion just mentioned, but without full attention to the logic of the situation. The present article may be considered as a sketch of how Landau’s book might be updated.
A paper by Alicia Chang, Catherine M. Sandhofer, and Christia S. Brown. Journal of Language and Social Psychology, December 2011 vol. 30 no. 4 440-450. Published online before print August 25, 2011, doi: 10.1177/0261927X11416207.
Despite dramatically narrowing gender gaps, women remain underrepresented in mathematics and math-related fields. Parents can shape expectations and interests, which may predict later differences in achievement and occupational choices. This study examines children’s early mathematical environments by observing the amount that mothers talk to their sons and daughters (mean age 22 months) about cardinal number, a basic precursor to mathematics. In analyses of naturalistic mother–child interactions from the Child Language Data Exchange System (CHILDES) database, boys received significantly more number-specific language input than girls. Greater amounts of early number-related talk may promote familiarity and liking for mathematical concepts, which may influence later preferences and career choices. Additionally, the stereotype of male dominance in math may be so pervasive that culturally prescribed gender roles may be unintentionally reinforced to very young children.
Even [when their children are] as young as 22 months, American parents draw boys’ attention to numerical concepts far more often than girls’. Indeed, parents speak to boys about number concepts twice as often as they do girls. For cardinal-numbers speech, in which a number is attached to an obvious noun reference — “Here are five raisins” or “Look at those two beds” — the difference was even larger. Mothers were three times more likely to use such formulations while talking to boys.
And this is from my collection of testimonies made by professional research mathematicians about their earliest exposure to mathematics (I collect such stories for my forthcoming book Shadows of the Truth):
My Mother told me the following story. When I was about two and a half a small flock of birds flew overhead. I said: “Look, there are two and three birds”. I didn’t yet know the number five but I understood simple counting.
What mattered was that Mother found this conversation significant. And yes, of course, she was talking to a boy …
R. Howe, Three pillars of first grade mathematics. The De Morgan Journal 1 no. 1 (2011), 3-17. PDF file of the paper.
Abstract. This note presents a proposal for a coherent approach to mathematics instruction in first grade. The 3 pillars indicated in the title are
- a robust understanding of the operations of addition and subtraction;
- instruction in arithmetic computation that emphasizes place value issues;
- building a strong connection between arithmetic as used in counting, and as used in linear measurement.
The proposal is highly compatible with the recently published (in the US) Common Core State Standards for mathematics, but places more emphasis on connections between topics than might be evident from a casual reading of those standards.
Roger Evans Howe is the William R. Kenan Jr. Professor of Mathematics at Yale University. He is well known for his contributions to representation theory, and in particular for the notion of a reductive dual pair, sometimes known as a Howe pair, and the Howe correspondence. He has been a member of the National Academy of Sciences since 1994. He is also a member of the American Academy of Arts and Sciences. In 2006 he was awarded the American Mathematical Society Award for Distinguished Public Service in recognition of his “multifaceted contributions to mathematics and to mathematics education.”
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