Key Ideas: What are they and how can they help us understand how people view proof?

This paper examines the views of proof held by university level mathematics students and teachers. A framework is developed for characterizing people's views of proof, based on a distinction between public and private aspects of proof and the key ideas which link these two domains. This revised version was published online in August 2006 with corrections to the Cover Date.     

Vibrotactile feedback for correcting aerodynamic position of a cyclist

ABSTRACT

Guidance to maintain an optimal aerodynamic position is currently unavailable during cycling. This study used real-time vibrotactile feedback to guide cyclists to a reference position with minimal projected frontal area as an indicator of aerodynamic drag, by optimizing torso, shoulder, head and elbow position without compromising comfort when sitting still on the bike. The difference in recapturing the aerodynamic reference position during cycling after predefined deviations from the reference position at different intensities was analysed for 14 participants between three interventions, consisting of 1) vibrotactile feedback with a margin of error of 1.5% above the calibrated reference projected frontal area, 2) vibrotactile feedback with a margin of 3%, and 3) no feedback. The reference position is significantly more accurately achieved using vibrotactile feedback compared to no feedback (p < 0.001), but there is no significant difference between the 1.5% and 3% margin (p = 0.11) in terms of relative projected frontal area during cycling compared to the calibrated reference position (1.5% margin ?0.46 ± 1.76%, 3% margin ?0.01 ± 2.01%, no feedback 2.59 ± 3.29%). The results demonstrate that vibrotactile feedback can have an added value in assisting and correcting cyclists in recapturing their aerodynamic reference position.     

Observer-based exponential stabilization for time-delay systems via augmented weighted integral inequality

In this paper, we design observer-based feedback control for a class of linear systems. The novelty of the paper comes from the consideration of an augmented weighted based integral inequality involving quadratic functions with an exponential term which is less conservative than the celebrated weighted integral inequality employed in the context of time-delay systems. By using appropriately chosen Lyapunov–Krasovskii functional (LKF), together with the derived integral inequality, a new sufficient condition for exponential stability in terms of linear matrix inequalities (LMIs) is proposed for the delayed linear systems with state feedback control. Finally, the applicability and superiority of the proposed theoretical results over the existing ones are analyzed in virtue of numerical examples.     

Teacher opinions on performance pay: Evidence from India

The practical viability of performance-based pay programs for teachers depends critically on the extent of support the idea will receive from teachers. We present evidence on teacher opinions with regard to performance-based pay from teacher interviews conducted in the context of an experimental evaluation of a program that provided performance-based bonuses to teachers in the Indian state of Andhra Pradesh. We report four main findings in this paper: (1) over 80% of teachers had a favorable opinion about the idea of linking a component of pay to measures of performance, (2) exposure to an actual incentive program increased teacher support for the idea, (3) teacher support declines with age, experience, training, and base pay, and (4) the extent of teachers’ stated ex ante support for performance-linked pay (over a series of mean-preserving spreads of pay) is positively correlated with their ex post performance as measured by estimates of teacher value addition. This suggests that teachers are aware of their own effectiveness and that implementing a performance-linked pay program could not only have broad-based support among teachers but also attract more effective teachers into the teaching profession.     

Nature watch

Fascinating and grand, with curious beaks and breeding habits, hornbills are a naturalist’s delight. In forest types ranging from open savannah to rainforest across Africa and Asia, they occupy the pride of place among birds and play a pivotal role as mutualistic frugivores and seed dispersers of various trees. Due to the impact of humans on hornbills and their habitats, most species are now endangered. Fortunately, there has been some success in recent conservation efforts to save these magnificent forest flagships.