Factors mathematicians profess to consider when presenting pedagogical proofs

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.     

Why and how mathematicians read proofs: further evidence from a survey study

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.     

Entrepreneurial orientation in turbulent environments: The moderating role of absorptive capacity

The literature on entrepreneurial orientation (EO) has confirmed the positive relationship between EO and firm performance and that relationship's dependence on several contingencies. The present study connects the resource-based view and its dynamic capability extension to introduce absorptive capacity (ACAP) as a moderator of the relationship between EO and firm performance. This theoretically derived research model is empirically validated using survey data from 219 small and medium-sized enterprises in Germany. Our empirical findings are that ACAP strengthens the EO–performance relationship in turbulent markets.     

The use of heuristics during route planning by expert and novice orienteers

Expert orienteers have reported using two heuristics when planning routes to points in the environment that must be located, known as 'controls'. These heuristics constitute attending to the start first and subsequently planning forward to a given control, and attending to the control first and planning backwards to the start. The aim of this study was to establish which heuristic experts use predominantly and whether novices' use of these heuristics differs from that of experts. Two methods for tracing attention were used while 20 expert and 20 novice orienteers planned routes in the laboratory. The results were used to infer the use of heuristics. The orienteers were also interviewed about planning. We found that, when planning, experts generally attend to the control first and novices to the start first. There was also some evidence that novices work forwards from the start to the control and that experts work backwards from the control to the start. From the interviews, it would appear that experts regard the location of the control as the crux of the problem and prioritize this area during planning. These results have implications for an understanding of expertise and problem-solving in sport.     

Physical activity, nutrition, screen time and sleep associated with body weight and physical condition in young children

The aim of this cross-sectional study was to explore the possible relationship between (un)healthy behaviour and (over)weight and physical condition in families with young children (4–7 years), in a village (30,000 inhabitants) in the eastern part of the Netherlands, close to Germany. It is one of two pilot studies as a precursor of a cross-border project including six Dutch and six German villages, to counteract physical inactivity and possible future metabolic problems. In total, 459 children of five elementary schools and their parents were included. Parents were requested to fill in a questionnaire on the nutritional, physical, sedentary, and sleeping behaviour of their child. Relevant background characteristics were obtained and lifestyle classifications were made. At school, the children's height and weight (body mass index (BMI)) were measured, as well as their physical condition (two tests) and basic motor abilities (four physical exercise tests). The relationship between the standardized BMI z-scores and physical condition test scores, and nutritional, physical, sedentary and sleeping habits was analysed using independent sample t-test, bivariate correlation analysis and multiple regression analysis. Latent class analysis was used to identify clusters of people based on their nutritional, physical and sleep habits. Of the parents, 376 (82?%) were willing to fill out the questionnaire. High birth weight and a high BMI of the mother and/or father correlated with a higher BMI of the child (ρ?=?0.28, p?<?0.001; ρ?=?0.13, p?=?0.016; and ρ?=?0.23, p?<?0.001, respectively). Daily playing outside, eating small cookies (compared with large cookies) and no sleeping problems (no waking up during the night) were related to low BMI levels (no overweight) [ρ?=???0.14, p?=?0.005; ρ?=???0.12, p?=?.020; t(364)?=?1.81, p?=?0.072 (trend), respectively]. Daily playing outside (frequency and duration) and being a member of a sports club were related to positive scores on the physical condition tests [ρ?=?0.20, p?<?0.001; t(365)?=???2.99, p?=?0.003, respectively]. High levels of television (TV) watching and general sleeping problems were related to a less optimal physical condition [ρ?=???0.09, p?=?0.076 (trend); and ρ?=???0.10, p?=?0.059 (trend), respectively]. A latent class analysis revealed three clusters: 46?% of the sample belonged to the ‘healthy group’ concerning nutrition, sedentary lifestyle and TV/personal computer (PC) use; 17?% to the ‘less healthy’ group and 37?% to a group with nutrition and physical activity habits close to the healthy group, but with low conditional probabilities for the sleeping items. Conducting a pilot study before the start of a binational intervention study gives a blueprint for the final questionnaire, and clues for tailored interventions in the schools, as proposed in the approach of ‘Gesunde Kinder in gesunden Kommunen’ (GKGK). The results of a latent class analysis underscore that interventions should exist of a multi-component strategy, focusing on promoting physical activity, healthy nutrition habits and appropriate sleep.     

Computer‐based scaffolding to facilitate students' development of expertise in academic writing

Research on expert performance suggests that deliberate practice provides optimal opportunities for expertise development. This study examined whether the provision of computer‐based scaffolding (CBS) guiding deliberate practice facilitates students' development of writing expertise. A CBS environment escribo was designed to externally support expert writing activities, generate feedback and offer opportunities to practise corrected performance in academic writing. There were two testing times. First, the effects of practising writing with escribo were compared with the effects of a practice‐only situation without support. Second, a post‐test comprised composing an essay discussing an academic position without scaffolding. Results revealed that the escribo group at both testing times wrote essays of better comprehensibility than students in the practice‐only group. Furthermore, at both testing times the escribo group expended significantly more time on prewriting. These findings suggest that CBS guiding deliberate practice may be a promising means to facilitate the development of writing expertise.     

The specific relationship between disgust and interest: Relevance during biology class dissections and gender differences

This investigation examined trajectories of interest and disgust related to a biology dissection class. Three hundred and two secondary students completed ratings of disgust sensitivity and individual interest in the topic of the heart approximately one week before a dissection class. States of disgust and interest were recorded before, during, and after the dissection, and again four weeks later. Overall, girls expressed higher disgust sensitivity than boys, but showed similar levels of individual interest in the heart topic. Individual interest was negatively related to feelings of disgust prior to and during the dissection while feelings of disgust at the beginning of the class negatively predicted students’ interest during the dissection. These findings extend knowledge of the interactive influences of students’ affective experiences during a specific curriculum task and provide a complementary perspective to research findings on emotions relating to achievement outcomes.     

E-Book Collection Development: Formalizing a Policy for Smaller Libraries

Three librarians from two similar but unaffiliated state colleges—both members of larger university systems—discuss how they confronted similar e-book acquisition concerns. In this session, presenters described how they took two different approaches toward revising their collection development policies, economizing their processes and streamlining their workflows. The presenters discussed patron-driven acquisition e-book programs, as well as the importance of communication and collaboration among library personnel. By formalizing the purchasing decisions of electronic formats, libraries can provide the structure needed to support changing staff roles and shrinking resources, as well as address important related issues such as accessibility and timeliness.     

Developmental associations between risk-taking and anxiety symptoms across ages 8–12 years

This study explored the transactional association between anxiety symptoms and risk-avoidance in Dutch elementary schoolchildren (N = 1200; 50% girls) across ages 8–12. Anxiety symptoms were obtained using self-, peer-, and teacher-reports. Risk-avoidance was measured using the Balloon Analogue Risk Task—Youth Version. Random-intercept cross-lagged panel models showed that, across informants, increases in anxiety symptoms predicted decreases in risk-taking. Apart from minor exceptions, this effect was similar across sexes. For peer-reports, the reverse path from decreases in risk-taking to increased anxiety was also found. Overall, this study gives insight into the developmental link between symptoms of anxiety and risk-avoidance which is important for early signaling and prevention as well as for our understanding of the consequences of childhood anxiety symptoms.     

Why flipping the classroom is not enough: Digital curriculum making after the pandemic

PROSPECTS - To slow down the proliferation of Covid-19, governments virtually shut down public life, temporarily closed schools, and forced teaching to be done exclusively on a remote basis. These...