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191.
This paper concerns proof presentation at the university level. We report on a study in which we observed ten mathematicians constructing or revising proofs for pedagogical purposes. We highlight the factors that they claimed to consider when completing these tasks. We found that intended audience and medium (lecture or textbook) influenced proof presentation. We also found that, although mathematicians generally valued pedagogical proofs featuring diagrams and emphasizing main ideas, these mathematicians did not always incorporate these aspects in the proofs they constructed or revised. 相似文献
192.
In a recent paper (Weber & Mejia-Ramos, Educational Studies in Mathematics, 76, 329–344, 2011), we reported findings from two small-scale interview studies on the reasons why and the ways in which mathematicians read proofs. Based on these findings, we designed an Internet-based survey that we distributed to practicing mathematicians working in top mathematics departments in the USA. Surveyed mathematicians (N?=?118) agreed to a great extent with the interviewed mathematicians in the exploratory studies. First, the mathematicians reported that they commonly read published proofs to gain different types of insight, not to check the correctness of the proofs. Second, they stated that when reading these proofs, they commonly: (a) appeal to the reputation of the author and the journal, (b) study how certain steps in the proof apply to specific examples, and (c) focus on the overarching ideas and methods in the proofs. In this paper, we also report findings from another section of the survey that focused on how participants reviewed proofs submitted for publication. The comparison of participant responses to questions in these two sections of the survey suggests that reading a published proof of a colleague and refereeing a proof for publication are substantially different activities for mathematicians. 相似文献
193.
Demands for female handball players are not yet sufficiently specified, especially not with respect to position-specific performance. For optimal match preparation, individual training based on specific demands of each position is necessary. Consequently, the aim of the study was to gain insight into position-specific differences in female handball players in order to establish position-specific training recommendations. Data from 652 female players from German leagues of all levels were analyzed using a test-battery assessing handball-relevant physical performance factors. Players were tested during their usual training in their regular training locations for running, throwing speed, jumping height, reaction-speed, basic running endurance, arm and abdominal muscle strength and hamstrings and lower back flexibility. Significant differences between positions were found for several parameters, while the differences were pronounced variably at the different performance levels. For example, goalkeepers performed worst in the Half-Cooper test (p?<?0.001) at elite level with wings displaying the best values. Halfbacks had the highest throwing speed (p?<?0.001) and jumping heights (p?<?0.002) at elite level. Goalkeepers were slowest for best and mean value out of five attempts (p?<?0.001; p?<?0.010) in 20?m sprint but, together with wings outperformed half and centre backs at elite level in 30?m sprint (best out of two attempts, p?<?0.001). Goalkeepers also did fewer chin ups than wing and back players at elite level (p?<?0.003). The present study demonstrated positional differences regarding physical performance parameters, thus suggesting the need to intensify position-specific training, especially for goalkeepers during preparation and in-season. Also, position-specific testing during selection-processes might be indicated. 相似文献