This study investigated K‐12 teachers' beliefs and reported teaching practices regarding calculator use in their mathematics instruction. A survey was administered to more than 800 elementary, middle and high school teachers in a large metropolitan area to address the following questions: (a) what are the beliefs and practices of mathematics teachers regarding calculator use? and (b) how do these beliefs and practices differ among teachers in three grade bands? Factor analysis of 20 Likert scale items revealed four factors that accounted for 54% of the variance in the ratings. These factors were named Catalyst Beliefs, Teacher Knowledge, Crutch Beliefs, and Teacher Practices. Compared to elementary teachers, high school teachers were significantly higher in their perception of calculator use as a catalyst in mathematics instruction. However, the higher the grade level of the teacher, the higher the mean score on the perception that calculator use may be a way of getting answers without understanding mathematical processes. The mean scores for teachers in all three grade bands indicated agreement that students can learn mathematics through calculator use and using calculators in instruction will lead to better student understanding and make mathematics more interesting. The survey results shed light on teachers' self reported beliefs, knowledge, and practices in regard to consistency with elements of the National Council of Teachers of Mathematics Principles and Standards for School Mathematics (2000) technology principle and the NCTM use of technology position paper (2003). This study extended previous research on teachers' beliefs regarding calculator use in classrooms by examining and comparing the results of teacher surveys across three grade bands. 相似文献
We present a soft lithographic method to fabricate multiphenotype cell arrays by capturing cells within an array of reversibly sealed microfluidic channels. The technique uses reversible sealing of elastomeric polydimethylsiloxane (PDMS) molds on surfaces to sequentially deliver various fluids or cells onto specific locations on a substrate. Microwells on the substrate were used to capture and immobilize cells within low shear stress regions inside channels. By using an array of channels it was possible to deposit multiple cell types, such as hepatocytes, fibroblasts, and embryonic stem cells, on the substrates. Upon formation of the cell arrays on the substrate, the PDMS mold could be removed, generating a multiphenotype array of cells. In addition, the orthogonal alignment and subsequent attachment of a secondary array of channels on the patterned substrates could be used to deliver fluids to the patterned cells. The ability to position many cell types on particular regions within a two dimensional substrate could potentially lead to improved high-throughput methods applicable to drug screening and tissue engineering. 相似文献
The extraction of Al(III) and Zn(II) from an aqueous solution with two water-in-oil microemulsions, one containing di(2-ethylhexyl)phosphoric acid (DEHPA), was investigated to aid the understanding of the role of the extractant and the metal specific characteristics in the mechanism of microemulsion extraction. The extraction of Al with the DEHPA microemulsion increased by a factor of about 10 with respect to that in the conventional DEHPA system, whereas the extraction of Zn was lower than that in the single DEHPA system. Extraction with the DEHPA-free microemulsion was very low, showing that metal ion solubilization was not important in the mechanism of microemulsion extraction. It is proposed that the effect of the mixed microemulsion on the metal distribution coefficient is the result of the balance between a decrease in the complexation reaction yield due to the interaction between butanol and DEHPA, and the adsorption of the metal complex at the macro- and microinterfaces. The former leads to a decrease in Zn(II) extraction and the latter to Al(III) extraction synergism. Copyright 2000 Academic Press. 相似文献
Although , (Fp η-C5H5Fe(CO)2) (I) is stable and characterizable, the lower homologue FpCH2CH(CO2CH3)2 (II) is not; this we attribute to a facile elimination reaction resulting from the relatively acidic β-hydrogen of II. Formation of I from Fp? and XCH2CE2CH3 (X Br, Cl; E CO2CH2CH3) and cleavage of its FeC bonds (using H+, Br2, CeIV and HgII) occur without major amounts of ester group migrations, even though ·CH2CE2CH3 radicals are involved in some of these reactions. 相似文献
The dynamic response of an elastic, semi-infinite strip with sliding surfaces, subjected to various forms of end excitations, was solved analytically employing the property of bi-orthogonality of wave modes. An explicit relation between the amplitudes of evanescent waves and the form of the excitation was obtained. Quantitative measure for dynamic end effects was suggested, termed Saint-Venant ratio (SVR). It was shown that two qualities of that ratio are useful for monitoring the health of structural joints (SHM): being that ratio not affected by the intensity of the end excitation and its high sensitivity to small variations in the form of the excitation. The axial behavior of the strip subjected to several forms of end excitations was further used to demonstrate the validity of a previously suggested dynamic version of Saint-Venant’s principle. 相似文献