No abstract

In this study, 140 fourth graders were asked to solve proportion problems about juice-mixing situations both before and after an intervention that used a manipulative model or other materials in 3 experiments. Using a manipulative model based on children's prior knowledge about crowdedness and equal distribution was effective in letting children discover a unit strategy, which was useful for solving proportion problems. The model was more effective for those who had an appropriate representation but could not correctly compare juice concentrations than it was for those who didn't have the representation. On the basis of this study, different approaches appear to be necessary to facilitate children's proportional reasoning, depending on the reasoning process (representation or comparison) with which children are having difficulty. Interventions on the basis of the process model and learning that builds on intuitive knowledge are discussed.

An evaluation method for the energy level of the valence band (VB) top from the vacuum level (VL) for metals, dielectrics, and semiconductors from the results of X-ray photoelectron spectroscopy (XPS) is presented for the accurate determination of the energy band diagram for materials of interest. In this method, the VB top can be determined by the energy difference between the onset of VB signals and the cut-off energy for secondary photoelectrons by considering the X-ray excitation energy (hν). The energy level of the VB top for three kinds of Si-based materials (H-terminated Si, wet-cleaned 4H-SiC, and thermally grown SiO2) has been investigated by XPS under monochromatized Al Kα radiation (hν = 1486.6 eV). We have also demonstrated the determination of the electron affinity for the samples by this measurement technique in combination with the measured and reported energy bandgaps (E g).

The energy distribution of the electronic state density of wet-cleaned epitaxial GaN surfaces and SiO 2 /GaN structures has been studied by total photoelectron yield spectroscopy (PYS). By X-ray photoelectron spectroscopy (XPS) analysis, the energy band diagram for a wet-cleaned epitaxial GaN surface such as the energy level of the valence band top and electron affinity has been determined to obtain a better understanding of the measured PYS signals. The electronic state density of GaN surface with different carrier concentrations in the energy region corresponding to the GaN bandgap has been evaluated. Also, the interface defect state density of SiO 2 /GaN structures was also estimated by not only PYS analysis but also capacitance-voltage (C-V) characteristics. We have demonstrated that PYS analysis enables the evaluation of defect state density filled with electrons at the SiO 2 /GaN interface in the energy region corresponding to the GaN midgap, which is difficult to estimate by C-V measurement of MOS capacitors.

The electrical dipole moment at an ultrathin high-k (HfO 2 , Al 2 O 3 , TiO 2 , Y 2 O 3 , and SrO)/SiO 2 interface and its correlation with the oxygen density ratio at the interface have been directly evaluated by X-ray photoelectron spectroscopy (XPS) under monochromatized Al Kα radiation. The electrical dipole moment at the high-k/SiO 2 interface has been measured from the change in the cut-off energy of secondary photoelectrons. Moreover, the oxygen density ratio at the interface between high-k and SiO 2 has been estimated from cation core-line signals, such as Hf 4f, Al 2p, Y 3d, Ti 2p, Sr 3d, and Si 2p. We have experimentally clarified the relationship between the measured electrical dipole moment and the oxygen density ratio at the high-k/SiO 2 interface.