The impact of instructor pedagogy on college calculus students’ attitude toward mathematics

College calculus teaches students important mathematical concepts and skills. The course also has a substantial impact on students’ attitude toward mathematics, affecting their career aspirations and desires to take more mathematics. This national US study of 3103 students at 123 colleges and universities tracks changes in students’ attitudes toward mathematics during a ‘mainstream’ calculus course while controlling for student backgrounds. The attitude measure combines students’ self-ratings of their mathematics confidence, interest in, and enjoyment of mathematics. Three major kinds of instructor pedagogy, identified through the factor analysis of 61 student-reported variables, are investigated for impact on student attitude as follows: (1) instructors who employ generally accepted ‘good teaching’ practices (e.g. clarity in presentation and answering questions, useful homework, fair exams, help outside of class) are found to have the most positive impact, particularly with students who began with a weaker initial attitude. (2) Use of educational ‘technology’ (e.g. graphing calculators, for demonstrations, in homework), on average, is found to have no impact on attitudes, except when used by graduate student instructors, which negatively affects students’ attitudes towards mathematics. (3) ‘Ambitious teaching’ (e.g. group work, word problems, ‘flipped’ reading, student explanations of thinking) has a small negative impact on student attitudes, while being a relatively more constructive influence only on students who already enjoyed a positive attitude toward mathematics and in classrooms with a large number of students. This study provides support for efforts to improve calculus teaching through the training of faculty and graduate students to use traditional ‘good teaching’ practices through professional development workshops and courses. As currently implemented, technology and ambitious pedagogical practices, while no doubt effective in certain classrooms, do not appear to have a reliable, positive impact on student attitudes toward mathematics.     

Ultraviolet emission spectra of sunbeds

It is well known that UV radiation contributes to the development of skin cancer. Exposure to solar radiation is predominantly responsible for the high incidence rate of skin cancer, but there are also indications that sunbeds are involved. The aim of the present investigation was to determine the UV emission spectra of sunbeds. It included the most common sunbed models, which cover more than 50% of the Swiss market. The UV emission spectra of sunbeds have special characteristics and are different from the sun spectrum, which can be seen in high-resolution spectral measurements. Sunbed emission spectra are similar to the sun spectrum in the UVB (280-320 nm) range but reach values 10 to 15 times higher in the UVA (320-400 nm) range. An average erythema-effective irradiance of 0.33 W/m2 was determined for sunbeds. This corresponds to a UV index of 13, which is significantly higher than the UV index of 8.5 of the high summer sun at noon at intermediate latitudes. The measurements were spread over the whole effective area of the sunbeds, and an inhomogeneous distribution of the irradiances with variations of up to 30% from the average value was found.     

Dark induction of haem oxygenase messenger RNA by haematoporphyrin derivative and zinc phthalocyanine; agents for photodynamic therapy.

Haematoporphyrin derivative is one of the main drugs currently used in clinical trials involving photodynamic therapy of cancer, and zinc phthalocyanine is being considered as one of several possible alternatives. We show that incubation of cultured human fibroblasts populations with either of the two drugs will lead to a sharp increase in the accumulation of the messenger RNA corresponding to haem oxygenase. Only cells incubated with haematoporphyrin derivative show additional enhancement of expression of this specific gene on exposure to red light. Since haem oxygenase induction appears to be a specific stress response that may be involved in cellular defence, such observations should be confirmed under conditions which would allow the clinical implications to be fully evaluated.     

Change of Base in Bailey Pairs

Versions of Bailey's lemma which change the base from q to q ² or q ³ are given. Iterates of these versions give many new versions of multisum Rogers-Ramanujan identities.     

Elementary Proofs of Identities for Schur Functions and Plane Partitions

We use elementary methods to prove formulas that represent sums of restricted classes of Schur functions as ratios of determinants. This includes recent formulas for sums over bounded partitions with even parts and sums over bounded partitions whose conjugates have only even parts. All of these formulas imply plane partition generating functions.     

Elementary Proof of MacMahon's Conjecture

Major Percy A. MacMahon's first paper on plane partitions [4] included a conjectured generating function for symmetric plane partitions. This conjecture was proven almost simultaneously by George Andrews and Ian Macdonald, Andrews using the machinery of basic hypergeometric series [1] and Macdonald employing his knowledge of symmetric functions [3]. The purpose of this paper is to simplify Macdonald's proof by providing a direct, inductive proof of his formula which expresses the sum of Schur functions whose partitions fit inside a rectangular box as a ratio of determinants.     

An easy proof of the Rogers-Ramanujan identities

A proof of the Rogers-Ramanujan identities is presented which is brief, elementary, and well motivated; the “easy” proof of whose existence Hardy and Wright had despaired. A multisum generalization of the Rogers-Ramanujan identities is shown to be a simple consequence of this proof.     

Extension of the partition sieve

We demonstrate the correspondence which lies behind certain partition identities used by Andrews in his partition sieve. This leads to an extension of his methods and a generalization of his results.