Mother and Child Emotions during Mathematics Homework

Mathematics is often thought of as a purely intellectual and unemotional activity. Recently, researchers have begun to question the validity of this approach, arguing that emotions and cognition are intertwined. The emotions expressed during mathematics work may be linked to mathematics achievement. We used behavioral measures to identify the emotions expressed by U.S. mothers and their 11-year-old children while solving pre-algebra tasks in the home. The most notable positive emotions displayed by mothers and children included positive interest, affection, joy, and pride, whereas the most notable negative emotions expressed included tension, frustration, and distress. Reflecting the social aspects of doing homework together, mothers' and children's emotions were highly correlated. Independent of pre-existing differences in knowledge, children's emotions were associated with their performance on a mathematics post-test: tension was linked to poorer performance while positive interest, humor, and pride were linked to better performance. We found no evidence of gender differences in the emotions while working the tasks, although boys responded with more tension following an incorrect solution than did girls.     

Guest Commentary

Abstract

Clustering and Classification edited by P. Arabie, L. J. Hubert, and G. De Soete, River Edge, New Jersey: World Scientific, 1996, 490 pp., $109 hardcover, $61 paperback. Reviewed by Jon R. Kettenring

Statistics as Principled Argument by Robert P. Abelson, Hillsdale, New Jersey: Lawrence Erlbaum Associates, 1995, 221 pp. Reviewed by Edward J. Shoben     

Decarboxylative ipso Amination of Activated Benzoic Acids

In the presence of a bimetallic Pd/Cu system with 1,10‐phenanthroline as the ligand and either air or N‐methylmorpholine N‐oxide as the oxidant, electron‐deficient benzoic acids undergo oxidative decarboxylative coupling with unprotected amines. This operationally simple aniline synthesis is widely applicable with respect to the amine and gives good yields, even on multigram scale. The orthogonality of this reaction to other Pd‐catalyzed cross‐couplings allows the concise synthesis of multisubstituted arenes by sequential C?C, C?Cl, and C?N functionalizations. Mechanistic investigations suggest the intermediacy of a hypervalent Pd species.     

(19)F-(19)F and (19)F-(1)H spin-spin coupling constants in cyclic FH polymers (FH)(n), n=2-6

Spin-spin coupling constants (2h)J(F-F), (1)J(F-H), and (1h)J(H-F) have been obtained for cyclic complexes (FH)(n), with n=2-6, from ab initio equation-of-motion coupled cluster singles and doubles (EOM-CCSD) calculations. Although both the Fermi-contact (FC) term and (2h)J(F-F) increase and become positive as the cluster size increases, the FC term is not a good quantitative approximation to (2h)J(F-F). The paramagnetic spin-orbit (PSO) and spin-dipole (SD) terms which contribute to (2h)J(F-F) appear to be sensitive to the orientation of the hydrogen-bonded pair. However, the large increase in the FC term and (2h)J(F-F) as the size of the cluster increases is due primarily to the reorganization of sigma electron densities in both ground and excited states, and is another manifestation of cooperativity effects in hydrogen-bonded cyclic polymers. The FC term and (1)J(F-H) always increase upon complex formation, but (1)J(F-H) increases only slightly as the size of the cluster increases due to a concurrent decrease in the PSO term. The changes in (1)J(F-H) as a function of polymer size reflect the polarization of electron density away from H and toward F in the ground state, and the electron reorganization which occurs in the excited states which couple to the ground states through the FC and PSO operators. The FC term is a good approximation to (1h)J(H-F), and is always negative, indicating that the hydrogen bonds in the FH clusters are traditional hydrogen bonds.     

Calculated coupling constants 1J(X–Y) and 1K(X–Y), and fundamental relationships among the reduced coupling constants for molecules HmX–YHn,with X,Y ═ 1H, 7Li, 9Be, 11B, 13C, 15N, 17O, 19F, 31P, 33S,and 35Cl

Equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) calculations have been performed to determine coupling constants ¹J(X–Y) for 65 molecules H_mX–YH_n, with X,Y ═ ¹H, ⁷Li, ⁹Be, ¹¹B, ¹³C, ¹⁵N, ¹⁷O, ¹⁹F, ³¹P, ³³S, and ³⁵Cl. The computed ¹J(X–Y) values are in good agreement with available experimental data. The reduced coupling constants ¹K(X–Y) have been derived from ¹J(X–Y) by removing the dependence on the magnetogyric ratios of X and Y. Patterns are found for the reduced coupling constants on a ¹K(X–Y) surface that are related to the positions of X and Y in the periodic table.     

Easily immobilized di- and tetraphosphine linkers: rigid scaffolds that prevent interactions of metal complexes with oxide supports

Di- and tetraphosphines with rigid phenyl-, biphenyl-, and tetraphenylstannane, -silane, and -methane scaffolds, and various substituents R, have been synthesized and immobilized via triethoxysilane-propagated formation of one or two surface-bound phosphonium moieties. The remaining phosphine groups can be coordinated to metal complexes. All the detective work and proof is done by solid-state NMR spectroscopy.     

Covalency in the f element-chalcogen bond. computational studies of M[N(EPR2)2]3 (M = La, Ce, Pr, Pm, Eu, U, Np, Pu, Am, Cm; E = O, S, Se, Te; R = H, (i)Pr, Ph)

The geometric and electronic structures of the title complexes have been studied using scalar relativistic, gradient-corrected density functional theory. Extension of our previous work on six-coordinate M[N(EPH 2) 2] 3 (M = La, Ce, U, Pu; E = O, S, Se, Te), models for the experimentally characterized M[N(EP (i)Pr 2) 2] 3, yields converged geometries for all of the other 4f and 5f metals studied and for all four group 16 elements. By contrast, converged geometries for nine-coordinate M[N(EPPh 2) 2] 3 are obtained only for E = S and Se. Comparison of the electronic structures of six- and nine-coordinate M[N(EPH 2) 2] 3 suggests that coordination of the N atoms produces only minor changes in the metal-chalcogen interactions. Six-coordinate Eu[N(EPH 2) 2] 3 and Am[N(EPH 2) 2] 3 with the heavier group 16 donors display geometric and electronic properties rather different from those of the other members of the 4f and 5f series, in particular, longer than expected Eu-E and Am-E bond lengths, smaller reductions in charge difference between M and E down group 16, and larger f populations. The latter are interpreted not as evidence of f-based metal-ligand covalency but rather as being indicative of ionic metal centers closer to M (II) than M (III). The Cm complexes are found to be very ionic, with very metal-localized f orbitals and Cm (III) centers. The implications of the results for the separation of the minor actinides from nuclear wastes are discussed, as is the validity of using La (III)/U (III) comparisons as models for minor actinide/Eu systems.     

Assessing the Impact of a Statewide STEM Investment on K–12, Higher Education,and Business/Community STEM Awareness Over Time

Despite monetary and educational investments in science, technology, engineering, and mathematics (STEM) being at record high levels, little attention has been devoted to generating a common understanding of STEM. In addition, working with business, K–12 schools, and/or institutions of higher education to establish a grassroots effort to help community members understand the importance of STEM regarding the future prosperity of the United States in general, and specifically the preparedness of children for careers of now and the future, has been nonexistent. The purpose of our study is to assess the impact of a statewide STEM professional development program implemented for two years on STEM awareness over time among various community stakeholders (i.e., K–12 teachers, higher education faculty, and business members). STEM awareness and beliefs about STEM engagement, resources, student preparation, and careers all improved over time for all groups. However, business members had the greatest growth over time and held significantly higher awareness compared with the other groups in most areas. Our findings suggest that a statewide STEM partnership/network model is a viable option for growing collective impact and sustainability of STEM K–12 education.     

Unusual substituent effects on the bonding of iminoboranes

Substituent effects on iminoboranes XBNH, HBNX and XBNX (X = H, CH3, NH2, OH, F) have been analyzed in the framework of the NBO, AIM and ELF approaches, using B3LYP/6-311++G(d,p) optimized geometries and electron densities. Boron-substituted derivatives, XBNH, are more stable than the corresponding nitrogen-substituted isomers HBNX, with the energy difference increasing as the electron withdrawing character of the substituent increases. The BN linkage is not much affected by N-substitution, but it is significantly altered when the substituent is attached to the boron atom in both XBNH and XBNX series of compounds. Moreover, substituent effects on the structures of iminoboranes are opposite those observed for the corresponding isoelectronic acetylene derivatives. The ELF analysis indicates that electron-withdrawing substituents enhance the localization of electrons in a torus around the CC or the BN axis. As a result, although electron density is depleted at the bcp, the bond does not necessarily become weaker, since density increases around the periphery, a phenomenon named the "hole" effect. The dissimilarities between acetylene and iminoborane derivatives are primarily a consequence of the significant distortion of this torus in the latter, due to the large difference between the electronegativities of B and N, which leads to a large contribution of the X-B=:N-Y resonance structure in some cases. The "hole" effect is reflected in a reasonable correlation between the Laplacian of the electron density at the bcp and the BN bond length.