Preservice Elementary Teachers' Use of Mathematics in a Project‐Based Science Approach

The use of a project‐based science (PBS) approach to teaching encourages students to integrate mathematics and science in meaningful ways as they create projects. As a beginning study of how students use mathematics in such an approach, an analysis of 23 projects developed by preservice elementary teachers enrolled in an elementary science course was conducted. Findings showed that students made a number of different types of mathematical errors and underutilized data representation and summary forms. Implications included the importance of developing methods for supporting the use of mathematical tools in utilizing a project‐based approach and considering ways that such tools mediate scientific thinking.     

Connection machine simulation of ultrasonic wave propagation in materials III: The three-dimensional case

A formalism for the simulation by parallel processing of the propagation of ultrasonic pulses of arbitrary shape (i.e. not restricted to continuous waves) in complex media is presented. Recursive relationships yielding the time evolution of the displacement field are derived for both homogeneous and heterogeneous materials. In the latter case, formulas for cross-points at the intersection of up to eight different materials are obtained. A few examples of numerical results obtained with the proposed method are shown to demonstrate its applicability and efficiency. The problem of visualization of the results is also briefly discussed.     

Structure of the crystal solvate of the dipyridinium salt of 2,2′-bis[1,3-bis(dicyanomethylene)indane] with acetonitrile

L. Ya. Karpov Physical Chemical Research Institute. Translated from Zhurnal Strukturnoi Khimii, Vol. 32, No. 3, pp. 141–144, May–June, 1991.     

Influence of solute mobility on dislocation motion I. Basic model

Dislocation motion in the real lattice of alloys is highly complex. In a certain temperature range the dynamic strain ageing phenomena have been reported. In this paper the influence of mobile solute atoms (as obstacles) on the motion of dislocation is analysed. Both processes are assumed to be thermally activated. A new model based on this assumption is proposed. The dislocation velocity and the friction stress (due to solute-dislocation interactions) are calculated. A change in the friction stress caused by solute mobility is discussed.     

Diazabicycloalkanes with nitrogen atoms in bridgehead positions. 15. Reactions of benzo[b]-1,4-diazabicyclo[2.2.2]octene monoquaternary salt derivatives with nucleophilic reagents

Monoquaternary salt derivatives of benzo[b]-1,4-diazabicyclo[2.2.2]octene react with piperidine and sodium methoxide or 4-tert-butylthiophenoxide to give primarily N,N-disubstituted tetrahydroquinoxalines. Rate constants have been measured for these bimolecular reactions. Based on their levels of reactivity, these quaternary salts behave as typical alkylating agents.For communication 14, see [1].Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 7, pp. 966–972, July, 1987.     

The homotopy categorical crossed module of a CW-complex

Crossed modules have longstanding uses in homotopy theory and the cohomology of groups. The corresponding notion in the setting of categorical groups, that is, categorical crosses modules, allowed the development of a low-dimensional categorical group cohomology. Now, its relevance is also shown here to homotopy types by associating, to any pointed CW-complex (X,∗), a categorical crossed module that algebraically represents the homotopy 3-type of X.