proof E is a Borel set: for each n ∈ N, On is open as the union of open sets. Therefore E is the countable intersection of open sets, thus is a Borel set. E is of the second category: we first prove that O n is nowhere dense. Indeed, we have for all qk ∈ Q, B(qk, 1 n2k ) ⊂ On, thus qk ∈ int(On). Therefore Q ⊆ int(On), therefore R = cl(Q) ⊆ cl(int(On)), i.e. cl(int(On)) = R. Taking complements, ...

Underperformance in math is a problem with increasing prevalence, complex etiology, and severe repercussions. This study examined the etiological heterogeneity of math performance in a sample of 264 pairs of 12-year-old twins assessed on measures of math achievement, numerosity and math anxiety. Latent profile analysis indicated five groupings of individuals representing different patterns of m...

In two experiments, we explored how the situation model of a math story problem impacts math problem performance. Participants completed multiplication story problems in which a set of objects was associated with or dissociated from a protagonist, making them more or less accessible in memory during answer retrieval. On the basis of previous findings that the sum of two numbers interferes with ...

This paper introduces a benchmark problem library for mechanized math technologies including computer algebra and automated theorem proving. The library consists of pre-university math problems taken from exercise problem books, university entrance exams, and the International Mathematical Olympiads. It thus includes problems in various areas of pre-university math and with a variety of difficu...

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We shall prove an existence inequality for two maps on Banach algebra, withan example and in sequel we have some results on R and Rn spaces. This waycan be applied for generalization of some subjects of mathematics in teachingwhich how we can extend a math problem to higher level.

We tested whether informing women about stereotype threat is a useful intervention to improve their performance in a threatening testing situation. Men and women completed difficult math problems described either as a problem-solving task or as a math test. In a third (teaching-intervention) condition, the test was also described as a math test, but participants were additionally informed that ...