Knowing and Teaching Middle School Mathematics: A Professional Development Course for In‐Service Teachers

This article describes a professional development course intended to improve the content understanding of middle school mathematics teachers. The design of the course included three professional learning strategies: problem solving, examination of student thinking, and discussion of research. The concepts studied in the course included multi‐digit subtraction, multi‐digit multiplication, operations with fractions, and concepts of area and perimeter. Results from pre‐ and post‐tests administered to the nineteen participants indicate a significant increase in the mean score for each concept and document growth in the teachers' content understanding. In particular, their solutions moved from primarily procedural to more conceptual. Responses to an open‐ended survey indicate other important aspects of the professional development. Examples of teachers' work and comments are included.     

The determination of diborane (B2H6) in gas mixtures

Summary A fast and sensitive method is described for the determination of diborane in diborane-gas mixtures. The precision of the method in the 100-ppm range is ±2%. The analysis takes about 70 min to perform. No such retention problems occur as can do in the mass spectroscopy and infrared analysis methods. It is shown that diborane stored in a pressure gas-container slowly decomposes.

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Zusammenfassung Ein rasches und empfindliches Verfahren zur Bestimmung von Diboran in Gasgemischen wurde beschrieben. Dessen Genauigkeit beträgt im 100 ppm-Bereich ±2%. Eine Analyse dauert etwa 70 min. Retentionsprobleme wie bei der Massenspektrometrie oder der IR-Analyse treten hier nicht auf. In Druckflaschen aufbewahrt, zersetzt sich Diboran langsam.

     

LIGHT-INDUCED CONFORMATIONAL CHANGES IN CATTLE RHODOPSIN AS PROBED BY MEASUREMENTS OF THE INTEFFACE POTENTIAL

Abstract— A novel technique of capacitative coupling of oriented rhodopsin at a polar/apolar interface allows the time resolved investigation of conformational changes following a flash. Electric signals arise as a consequence of changes of the interface potential. A signal occurring within milliseconds behaves like the R₂-phase of the "early receptor potential" (= ERP). This response is interpreted as a conformational change of rhodopsin. No correlation of this signal is found to the spectroscopically defined metarhodopsin I-metarhodopsin II transition.
The temperature dependence of the conformational change coincides with the temperature dependence of the latency of the 'a-wave' of the electroretinogram, reported by Arden and Ikeda (1968). It is suggested that the command step of visual excitation is the conformational change and not one of the spectroscopically defined photolysis steps of rhodopsin.
Analysis of slower electrical signals following the fast response is in accordance with the model of a light-induced pore formation.     

Abtrennung von Submikrogramm-Mengen Arsen aus Ammomumfluoridlösungen

Arsenic has been separated from NH₄F solutions by coprecipitation with MnO(OH)₂, which is formed within the solution by addition of stoichiometric amounts of MnSO₄ and KMnO₄. The precipitate is dissolved in HC1 and As determined by known methods.     

Formal Total Synthesis of Kendomycin by Way of Alkyne Metathesis/Gold Catalysis

In an attempt to study the ability of the latest generation of alkyne metathesis catalysts to process sterically hindered substrates, two different routes to the bacterial metabolite kendomycin ( 1 ) were explored. Whereas the cyclization of the overcrowded arylalkyne 39 and related substrates turned out to be impractical or even impossible, ring closure of the slightly relaxed diyne 45 was achieved in excellent yield under notably mild conditions with the aid of the molybdenum alkylidyne 2 endowed with triphenylsilanolate ligands. The resulting cycloalkyne 46 was engaged into a gold‐catalyzed hydroalkoxylation, which led to benzofuran 47 that had already previously served as a late‐stage intermediate en route to 1 .     

Rho(0) meson production in the pp-->pppi(+)pi(-) reaction at 3.67 GeV/c

Total and differential cross sections for the exclusive reaction pp-->pp rho observed via the pi(+)pi(-) decay channel have been measured at p(beam)=3.67 GeV/c. The observed total meson production cross section is determined to be (23.4+/-0.8+/-8) mu b and is significantly lower than typical cross sections used in model calculations for heavy-ion collisions. The differential cross sections measured indicate a strong anisotropy (approximately cos(theta(CM)(rho)) in the rho(0) meson production.     

Universal properties of two-dimensional boson droplets

We consider a system of N nonrelativistic bosons in two dimensions, interacting weakly via a short-range attractive potential. We show that for N large, but below some critical value, the properties of the N-boson bound state are universal. In particular, the ratio of the binding energies of (N+1)- and N-boson systems, B(N+1)/B(N), approaches a finite limit, approximately 8.567, at large N. We also confirm previous results that the three-body system has exactly two bound states. We find for the ground state B(0)(3)=16.522 688(1)B2 and for the excited state B(1)(3)=1.270 409 1(1)B2.