A LONGITUDINAL STUDY OF THE DEVELOPMENT OF MATHEMATICS STRATEGIES AND UNDERLYING COUNTING SCHEMES

The purpose of this study was to determine whether patterns of strategy use in second, third and fourth grade children’s arithmetic supported Steffe’s model of numerical development. In addition to student-generated strategies, we looked at commonly taught algorithms not considered in Steffe’s model to determine whether these algorithms reflected underlying schemes. 206 children were assessed on their strategy use while solving arithmetic problems in the second grade, the third grade and again in the fourth grade. Factor analyses indicated some support for Steffe’s model, but there were exceptions. Not all children progressed in their number knowledge and strategies as a function of schooling and schooling appeared to affect the types of strategies children use independent of underlying schemes.     

正义、美德与教育（英文）

如果说正义是人类道德交往的基本法则或者维度,那么这也似乎适用于一些教育问题。简而言之,我们需要教育孩子和年轻人正义和公平。然而,这并不是可以仅通过教授正义的理论就能够实现的。因为,正如这篇文章所揭示的那样,这些理论通常涉及到维护正义的准则,即在有些情况下,公民个体不能总是做到如其所期待的那样正义与公平。所以,正义教育更多的是培养正义的美德。从这点出发,本文致力于探究如何借助富有想象力的文学作品来培养正义的美德。     

The dynamic impact characteristics of tennis balls with tennis rackets

Abstract

The dynamic properties of six types of tennis balls were measured using a force platform and high-speed digital video images of ball impacts on rigidly clamped tennis rackets. It was found that the coefficient of restitution reduced with velocity for impacts on a rigid surface or with a rigidly clamped tennis racket. Pressurized balls had the highest coefficient of restitution, which decreased by 20% when punctured. Pressureless balls had a coefficient of restitution approaching that of a punctured ball at high speeds. The dynamic stiffness of the ball or the ball-racket system increased with velocity and pressurized balls had the highest stiffness, which decreased by 35% when punctured. The characteristics of pressureless balls were shown to be similar to those of punctured balls at high velocity and it was found that lowering the string tension produced a smaller range of stiffness or coefficient of restitution. It was hypothesized that players might consider high ball stiffness to imply a high coefficient of restitution. Plots of coefficient of restitution versus stiffness confirmed the relationship and it was found that, generally, pressurized balls had a higher coefficient of restitution and stiffness than pressureless balls. The players might perceive these parameters through a combination of sound, vibration and perception of ball speed off the racket.     

Amplitude-modulated sinusoidal microchannels for observing adaptability in C. elegans locomotion

In this paper, we present a movement-based assay to observe adaptability in Caenorhabditis elegans locomotion behavior. The assay comprises a series of sinusoidal microchannels with a fixed wavelength and modulating (increasing or decreasing) amplitude. The channel width is comparable to the body diameter of the organism. Worms are allowed to enter the channel from the input port and migrate toward the output port. Within channel sections that closely match the worm's natural undulations, the worm movement is relatively quick and steady. As the channel amplitude increases or decreases along the device, the worm faces difficulty in generating the propulsive thrust, begins to slow down and eventually fails to move forward. A set of locomotion parameters (i.e., average forward velocity, number and duration of stops, range of contact angle, and cut-off region) is defined for worm locomotion in modulated sinusoidal channels and extracted from the recorded videos. The device is tested on wild-type C. elegans (N2) and two mutants (lev-8 and unc-38). We anticipate this passive, movement-based assay can be used to screen nematodes showing difference in locomotion phenotype.