A determination of the dynamic response of softballs

An apparatus is described for measuring the stiffness and coefficient of restitution (COR) of balls with application to softballs. While standardized test methods currently exist to measure these properties, they do not represent the displacement rate and magnitude that occur in play. The apparatus described herein involves impacting a fixed, solid cylindrical surface (matched to the diameter of the bat) with a ball and measuring the impact force during impact and speed of the ball before and after impact. The ratio of the ball speeds determines the COR, while the impact force is used to derive a ball stiffness. For an example of the contribution of the new ball test, the performance of hollow bats, which is sensitive to ball stiffness, was compared. Bat performance showed a much stronger dependence on the proposed ball stiffness than the traditional measure. Finally, it was shown that to achieve similar conditions between impacts with fixed and recoiling objects, the impact speed should be chosen so that the centre of mass energy was the same in the two cases. The method has application to associations wishing an improved method to regulate ball and bat performance.     

Two Teachers' Conceptions of a Reform-Oriented Curriculum: Implications for Mathematics Teacher Development

This paper describes two high school teachers' conceptions of the cooperation and exploration components of a reform-oriented mathematics curriculum. Although the teachers appreciated the themes of cooperation and exploration in theory, their conceptions of these themes with respect to their implementations of the curriculum differed. One teacher viewed the curriculum's problems as open-ended and challenging for students, whereas the other teacher claimed that the problems were overly structured. Each teacher attributed difficulties with students' cooperative work to the amount of structure and direction (too little or too much) offered by the problems. Discussion of such similarities and differences in the teachers' conceptions emphasizes the dynamic, humanistic nature of curriculum implementation and gives rise to important implications for mathematics teacher development in the context of reform. This revised version was published online in July 2006 with corrections to the Cover Date.