Generating scenarios of addition and subtraction: A study of Japanese university students

Students are presented with problems involving three scenario types of addition and subtraction in elementary mathematics: one dynamic (Change) and two static (Combine, Compare). Previous studies have indicated that the dynamic type is easier for school children, whereas the static types are more difficult and comprehended only gradually throughout elementary grades. However, these differences in scenario difficulty have not be adequately investigated in adults to ascertain whether they persist in adults who have used the operations for a long period of time. This study examined this with Japanese university students (ages 18–23 years). In Study 1, 99 participants were provided with one numerical equation and one picture representing one of the three scenario types, and were instructed to generate a single scenario. In Study 2, 97 participants were provided with one numerical equation and were instructed to recall the various scenario types that they had encountered previously and to generate multiple scenarios of diverse types. Results indicated that participants found the dynamic scenario types easier than static ones, and they tended to understand the given information of static types by interpreting them in dynamic forms (Study 1). In addition, they strongly preferred generating scenarios of dynamic type over static types (Study 2). Implications for mathematics learning are discussed.     

The basis step in the construction of the principle of mathematical induction based on APOS theory

Using APOS theory as the framework along with a case study from a perspective within the methodological design of APOS theory, this study presents a cognitive model of the Principle of Mathematical Induction (PMI) in higher education. Based on evidence from university classrooms and the result of an initial measurement, the genetic decomposition designed by Dubinsky and Lewin for this concept was reformulated, introducing and defining the basis step in the PMI as a mental process. Using this reformulated genetic decomposition, the productions of four university students are analysed in order to support or refute the constructions it proposes. The results show that the reformulated genetic decomposition is viable and that the inclusion of the basis step as a mental process was seen in the cognitive model of the PMI shown by the students. The instruments used provide activities for a teaching sequence for the PMI at university level.     

Berkeley and Its Physics Heritage

I first sketch the settlement of Berkeley, California, the founding of the University of California at Berkeley, and the origin of its Department of Physics. I then discuss the pivotal role that Ernest O. Lawrence (1901–1958) and his invention and subsequent development of the cyclotron played in physics at Berkeley after his arrival there in 1928 through the Second World War and beyond. I close by commenting on the Lawrence Hall of Science, the educational center and science museum conceived as a living memorial to Lawrence.     

Vibrational spectra of ethyl iodedes

The infrared spectra of CH₃CH₂I, CD₃CH₂I, and CH₃CD₂I of the vapors and the solids at 170°C have been recorded from 4000-200 cm^?1. The Raman spectra of the liquids and vapors have also been recorded and depolarization values have been measured. Assignment of the eighteen fundamental vibrations has been based on depolarization values, band contours, group-frequency correlations, and normal coordinate calculations. A critical discussion of the CH stretching assignments in CH₃CH₂X molecules is presented.     

On the nature of excited electronic states in cyanine dyes: implications for visual pigment spectra

CNDO/S CI calculations are carried out on polyenes and on cyanine dyes. In contrast to polyenes, doubly excited configurations have a strong effect on the first optically allowed excited state in cyanines. Protonated Schiff bases of retinal are closely related to cyanine dyes, with important consequences for models of visual pigment spectra and photochemistry.     

Ab initio calculations of the equilibrium geometry of cis and trans methylglyoxal using the force method

Ab initio calculations of the equilibrium ground-state conformation of trans-methylglyoxal, CH₃COCHO, have been carried out using the gradient method and a 4-3 IG basis set. The results are compared with experiment and with a theoretical geometry computed using an STO-3G basis set, and the more usual stepwise optimization of the parameters. The molecular orbital energies, dipole moment and ionization energy are calulated. Calculations are also carried out on the cis-isomer and the barrier to cis-trans isomerization is obtained.     

Crystal structure of dimeric p-phenoxyphenyltellurium(IV) trichloride

p-PhOC₆H₄TeCl₃ crystallises with a dimeric molecular unit. The two approximately square pyramidal coordination polyhedra are linked trans to each other through two bridging chlorine atoms. The dimeric units are further connected through Te…Cl secondary interactions producing a distorted octahedral geometry about each tellurium atom. The crystals are triclinic, space group P$\text{1}$, with unit cell dimensions a 8.521(2), b 10.917(2), c 14.813(2) Å, α 81.84(1), β 83.38(1), γ 88.41(1)°, V 1353.4(4) ų and Z = 2(dimers) from 3887 observed reflections [I > 3σ(I)], R = 0.0359.     

Vibrational frequencies, force constants, mean amplitudes, shrinkage effects and thermodynamic functions for monohaloacetylenes

Harmonic force fields are developed for the monohaloacetylenes on the basis of recent vibrational spectra of H-CC-I and previously published spectra of H-CC-X (X = F, Cl, Br). Mean amplitudes of vibration and Bastiansen-Morino shrinkage effects are reported for monohaloacetylenes and their deuterated derivatives. Thermodynamic functions are listed for monoiodoacetylene.