Learning and teaching axiomatic geometry

Summary To sum up, we have examined the various difficulties-mathematical, conceptual, and logical-involved in learning and teaching axiomatic geometry. Taking as a typical axiomatic approach one that couples Emil Artin's treatment of affine geometry with Choquet's handling of the basic order and orthogonality phenomena of Euclidean geometry, we have tried to identify these difficulties in some detail. We have noted that this particular approach isolates the graver difficulties, separating them from one another in such a way that they can be mastered by comparatively simple techniques. For both student and teacher the burden is shifted to the fuller understanding of certain fundamental concepts, such as that of a geometrical transformation, which permit making an early contact with algebra-specifically, with group theory-in the spirit of Descartes and Felix Klein. We have proposed an organization of the school program in geometry from grade K or grade 1 through grade 12 aimed at gradually acquainting the student with these basic concepts and their technical uses as they emerge from the persistent contemplation of the physical, mathematical, and logical facts. We have stated our conviction that by the 10th grade students should be prepared to understand the strategy and the significance of the axiomatic approach, and by the 11th and 12th grades to carry through that approach in adequate detail. We have taken explicitly into account the need to arrange the school geometry program in such a way that students can reach terminal points appropriate to their capacities, needs, and interests. We must emphasize that what has been presented here is no more than a rough outline, to be filled out on the basis of further psychological, mathematical and curricular investigations. I am confident that these suggestions can mature into a school geometry program not only far more significant intellectually and technically than those now commonly offered but also one easier to learn and to teach. This is not just a matter of personal belief, because many elements of the proposed program have actually been tried out in one form or another with success. What is now needed is a grand effort to assemble the tested and untested parts into an experimental whole.     

Anthropometric and physical abilities profiles: US National Skeleton Team

The aim of this study was to characterize sprint ability, anthropometry, and lower extremity power in the US National Team Skeleton athletes. Fourteen athletes (male n = 7; mean +/- SD: height 1.794 +/- 0.063 m, body mass 81.2 +/- 3.7 kg, age 26.9 +/- 4.1 years; female n = 7; 1.642 +/- 0.055 m, 60.1 +/- 5.9 kg, 27.3 +/- 6.9 years) volunteered to participate. Sprinting ability was measured over multiple intervals using custom infrared timing gates in both an upright and a crouched sprint. The crouched sprint was performed while pushing a wheeled-simulated skeleton sled on rails on an outdoor skeleton and bobsleigh start track. Crouched skeleton sprint starts were able to achieve about 70% to 85% of the upright sprint times. The mean somatotype ratings for females were: 3.5-3.5-2.1, and males: 3.6-4.9-1.9. Lower extremity strength and power were measured via vertical jumps on a portable force platform using squat and countermovement jumps, and jumps with added mass. Jump height, power, rate offorce development and peak force were determined from force-time data. Lower extremity strength and power were strongly correlated with both upright and crouched sprint times. The results indicated that these athletes are strong sprinters with varying body structures, mostly mesomorphic, and that stronger and more powerful athletes tend to be better starters.     

Opportunities for faculty‐librarian collaboration in an expanded dentistry curriculum

With the increased emphasis on evidence based practice, developing information literacy skills earlier in health care education programmes is widely accepted. However finding opportunities for relevant teaching can present challenges, often leading to a lack of integration. In this paper, guest writers Sean Stone and colleagues from Indiana University discuss their involvement with an expanded dental hygiene curriculum in the University School of Dentistry. This expansion has provided the opportunity to plan integration of information and oral health literacy instruction and evidence based practice across the new curriculum, and provide transferable skills for any major. In particular, the paper addresses the developmental work the health librarian team engaged in from course design, delivery and assessment to improve student preparedness for evidence based practice. H.S.     

Capabilities of traditional quantitative admissions criteria in predicting performance of off‐campus engineering graduate students enrolled in videotaped courses

This paper examines many of the traditional measures used to admit students to tertiary study and tests their efficacy against subsequent performance. The groups involved were on‐campus and off‐campus engineering students. The conclusions were that traditional admissions criteria offer little in their ability to predict student performance in the different modes of study.     

Sleep,anxiety and electronic device use by athletes in the training and competition environments

This study subjectively assessed sleep quality and quantity, state anxiety and electronic device use during a 7-day training week (TRAIN) and a 7-day competitive tournament (COMP). Eight state-level netball players used wrist-watch actigraphy to provide indirect sleep measures of bedtime, wake time, sleep duration, sleep onset latency, sleep efficiency, wake after sleep onset and fragmentation index. State anxiety was reported using the anxiety sub-scale in the Profile of Mood States-Adolescents. Before bed duration of electronic device use and the estimated time to sleep after finishing electronic device use was also recorded. Significant main effects showed that sleep efficiency (p = 0.03) was greater in COMP as compared to TRAIN. Furthermore, the bedtime and wake time were earlier (p = 0.01) during COMP. No further differences existed between conditions (p > 0.05). However, strong negative associations were seen between state anxiety and the sleep quality rating. Here, sleep efficiency was likely greater in COMP due to the homeostatic need for recovery sleep, resulting from the change in environment from training to competition. Furthermore, an increased anxiety before bed seems to influence sleep quality and should be considered in athletes portraying poor sleep habits.     

The accuracy of academic self-evaluations in adolescents with learning disabilities

The purpose of this study was to document the degree of overestimation of academic skills among students with learning disabilities (LD) and to evaluate the role of reference group and metacognitive awareness in such overestimation. High school students with (n = 52) and without (n = 49) LD in Grades 9 through 12 completed a self-concept scale and a survey requiring them to rate their own academic skills in 17 specific skill areas. Students were further asked to predict their performance on two academic tasks prior to actually performing the tasks. The students' mothers or fathers, their English teachers or academic advisors, and (in the case of the students with LD) their special education case managers also completed the skill rating inventory and predicted student performance on the two tests. Despite reporting significantly lower academic self-concepts, students with LD overestimated their academic skills relative to the ratings of others and to their actual test performance. Such overestimation was less pronounced among the students without LD. All participants reported using similar reference groups in making their judgments. Analyses of item-by-item accuracy judgments from the two tests revealed evidence of group differences in metacognitive awareness that may be related to the overestimation. These findings have implications for realistic goal setting and effective self-advocacy.