Describing the plastic deformation of aluminium softball bats

Hollow aluminium bats were introduced over 30 years ago to provide improved durability over wooden bats. Since their introduction, however, interest in hollow bats has focused almost exclusively around their hitting performance. The aim of this study was to take advantage of the progress that has been made in predicting bat performance using finite elements and apply it to describe bat durability. Accordingly, the plastic deformation from a ball impact of a single-wall aluminum bat was numerically modelled. The bat deformation from the finite-element analysis was then compared with experiment using a high-speed bat test machine. The ball was modelled as an isotropic, homogeneous, viscoelastic sphere. The viscoelastic parameters of the ball model were found from instrumented, high-speed, rigid-wall ball impacts. The rigid-wall ball impacts were modelled numerically and showed good agreement with the experimentally obtained response. The strain response of the combined bat-ball model was verified with a strain-gauged bat at intermediate ball impact speeds in the elastic range. The strain response of the bat-ball model exhibited positive correlation with the experimental measurements. High-speed bat-ball impacts were performed experimentally and simulated numerically at increasing impact speeds which induced correspondingly increased dent sizes in the bat. The plastic deformation from the numerical model found good agreement with experiment provided the aluminium work hardening and strain rate effects were appropriately described. The inclusion of strain rate effects was shown to have a significant effect on the bat deformations produced in the finite-element simulations. They also helped explain the existence of high bat stresses found in many performance models.     

Understanding a High School Physics Teacher’s Pedagogical Content Knowledge of Argumentation

Scientific argumentation is an important learning objective in science education. It is also an effective instructional approach to constructivist science learning. The implementation of argumentation in school settings requires science teachers, who are pivotal agents of transforming classroom practices, to develop sophisticated knowledge of argumentation. However, there is a lack of understanding about science teachers’ knowledge of argumentation, especially the dialogic meaning of argumentation. In this case study, we closely examine a high school physics teacher’s argumentation-related pedagogic content knowledge (PCK) in the context of dialogic argumentation. We synthesize the teacher’s performed PCK from his argumentation practices and narrated PCK from his reflection on the argumentation practices, from which we summarize his PCK of argumentation from the perspectives of orientation, instructional strategies, students, curriculum, and assessment. Finally, we describe the teacher’s perception and adaption of argumentation in his class. We also identity the barriers to argumentation implementation in this particular case and suggest solutions to overcome these barriers.     

Socio-economic status,cultural diversity and the aspirations of secondary students in the Western Suburbs of Melbourne,Australia

Using data from a recent survey of Australian secondary students, we find that those from higher socio-economic backgrounds are more likely to aspire to attend university. The same can be said for students who do not speak English at home. We find that students with an ethnic minority background are more likely to perceive higher levels of support from parents. However, we find that all students believe they receive encouragement from their parents to do well at school (rather than discouragement or disinterest), and that there is little difference in the level of importance placed on the views of parents between students from English and non-English speaking background. While interest in university education is strong across all socio-economic groups, particularly for students who do not speak English at home, there is a considerable gap between aspirations and enrolment levels. We suggest that this ‘aspirations gap’ is larger for students from low socio-economic backgrounds. This analysis also supports growing evidence that the postcode methodology for allocating socio-economic status to individuals is unreliable.     

Types of reasoning in 3D geometry thinking and their relation with spatial ability

The aim of this study is to describe and analyse the structure of 3D geometry thinking by identifying different types of reasoning and to examine their relation with spatial ability. To achieve this goal, two tests were administered to students in grades 5 to 9. The results of the study showed that 3D geometry thinking could be described by four distinct types of reasoning which refer to the representation of 3D objects, spatial structuring, conceptualisation of mathematical properties and measurement. The analysis of the study also showed that 3D geometry types of reasoning and spatial abilities should be modelled as different constructs. Finally, it was concluded that students’ spatial abilities, which consist of spatial visualisation, spatial orientation and spatial relations factors, are a strong predictive factor of the four types of reasoning in 3D geometry thinking.     

An empirical study of using history as a ‘goal’

This article discusses an empirical study on the use of history as a goal. A historical module is designed and implemented in a Danish upper secondary class in order to study the students’ capabilities at engaging in meta-issue discussions and reflections on mathematics and its history. Based on videos of the implementation, students’ hand-in essay assignments, questionnaires, and follow-up interviews, the conditions, sense, and extent to which the students are able to perform such discussions and reflections are analyzed using a described theoretical framework.