Does generating examples aid proof production?

Many mathematics education researchers have suggested that asking learners to generate examples of mathematical concepts is an effective way of learning about novel concepts. To date, however, this suggestion has limited empirical support. We asked undergraduate students to study a novel concept by either tackling example generation tasks or reading worked solutions to these tasks. Contrary to suggestions in the literature, we found no advantage for the example generation group on subsequent proof production tasks. From a second study, we found that undergraduate students overwhelmingly adopt a trial and error approach to example generation and suggest that different example generation strategies may result in different learning gains. We conclude by arguing that the teaching strategy of example generation is not yet understood well enough to be a viable pedagogical recommendation.     

Fragmentation and Interrogation as an Approach to Integration

This article tracks the generative role of research and fragmentation as a means for integrating technology and form within an architecture technology lecture class and a co‐requisite design studio. The complexity of teaching building systems integration within a design studio context is achieved by removing any expectation of building design completion on a comprehensive scale. Typically, in a comprehensive studio, students will design an entire building at a general scale, but at the expense of detailed technical design. However, with use of building fragments, students will design a building corner or a structural bay in great detail while leaving the rest of the building less developed. With our approach, integration occurs through interrogation of case‐study buildings and student projects in the technical course which is complemented by a series of fragmental design studies in the studio. We propose that designing fragments encourages constructive thinking at multiple scales rather than design as a singular problem solving process. As a result, design is not seen as the creation of objects, but as the guidance of multiple, simultaneously acting forces into an integrated assembly. The co‐requisite technical course also embraces fragmentation for research purposes: three professors provide three different technical (structures, environment and construction) and conceptual viewpoints for three distinct building pairs. Various forces within those building pairs are compared to illuminate strategic thinking for comprehensive building design. The intense focus on selective technical systems within these building pairs is intended to support the same development of integrative strategic thinking in the studio.     

Toward Integration: From Quantitative Biology to Mathbio-Biomath?

In response to the call of BIO2010 for integrating quantitative skills into undergraduate biology education, 30 Howard Hughes Medical Institute (HHMI) Program Directors at the 2006 HHMI Program Directors Meeting established a consortium to investigate, implement, develop, and disseminate best practices resulting from the integration of math and biology. With the assistance of an HHMI-funded mini-grant, led by Karl Joplin of East Tennessee State University, and support in institutional HHMI grants at Emory and University of Delaware, these institutions held a series of summer institutes and workshops to document progress toward and address the challenges of implementing a more quantitative approach to undergraduate biology education. This report summarizes the results of the four summer institutes (2007–2010). The group developed four draft white papers, a wiki site, and a listserv. One major outcome of these meetings is this issue of CBE—Life Sciences Education, which resulted from proposals at our 2008 meeting and a January 2009 planning session. Many of the papers in this issue emerged from or were influenced by these meetings.     

Training on the project: a quantifying approach to competence development

In the project ‘Competence-Driven Project Portfolio Analysis’ (CDPPA), an integrated system for supporting R&D project selection, staff assignment and activity scheduling with special consideration of the strategic development of competencies has been designed and implemented prototypically. The system has been field-tested at the Electronic Commerce Competence Center (EC3), a public–private partnership R&D enterprise. Experiences from this trial application are summarised and discussed, particularly concerning data collection and competence measurement, the benefits and limits of the chosen multi-criteria decision analysis approach, the evaluation of introduced changes to the decision-making processes, and the transparency of the formal planning model and its components.     

The physiological cost of velocity coupling during tennis groundstrokes

Velocity coupling denotes a perceptual motor behaviour known to occur during coincidence timing tasks. Individuals have been shown to increase their effector limb speed with increases in stimulus speed during interceptive tasks. However, little is known about the physiological effects of velocity coupling. The aim of this study was to determine the physiological cost of velocity coupling during tennis groundstrokes. Eight male and eight female competitive tennis players volunteered to perform three 4-min bouts of continuous groundstrokes against balls projected from a tennis ball machine at speeds of 18, 22, and 27 m x s(-1) (65, 79, and 97 km x h(-1)) and a frequency of 14 balls per minute, the order of which was counterbalanced. Breath-by-breath pulmonary gas exchange, heart rate, locomotion time, and limb acceleration were measured throughout each of the 4-min bouts. Capillary blood samples (for blood lactate analysis), rating of perceived exertion, and difficulty rating were taken at the end of each bout. Increasing ball speed did not influence the locomotion time between groundstrokes but did result in a bilateral increase in both the mean upper- and lower-limb acceleration (all P < 0.05). Velocity coupling behaviour increased oxygen uptake, blood lactate concentration, heart rate, rating of perceived exertion, and perceived task difficulty (all P < 0.05). It would appear, therefore, that velocity coupling influenced tennis groundstroke behaviour and indirectly modified the concurrent cardiopulmonary and metabolic responses.     

How persistent and general is the contextual interference effect?

The persistence and generality of the contextual interference (CI) effect was tested using a rapid sequential aiming task. Participants (N=48) practiced three movement patterns for three blocks of 18 trials under a blocked (BL) or random (RA) schedule. Movement patterns were displayed and KR provided throughout practice and testing. A 24-hr delayed knowledge of results (KR) retention test included three blocks of 18 trials, followed by a transfer test of a single new movement pattern. In contradiction of the CI effect, RA practice provided an advantage for RA retention only, not BL retention. Furthermore, group differences at transfer were not persistent. Hence, RA practice does not necessarily provide enhanced, context-free learning, but it is essential training for task switching. Overall the findings reveal limited persistence and generality of the CI effect.