Game Building with Complex-Valued Functions

Abstract

In this paper, we describe how we integrated complex analysis into the second semester of a geometry course designed for preservice secondary mathematics teachers. As part of this inquiry-based course, the preservice teachers incorporated their geometric understanding of the arithmetic of complex numbers and complex-valued functions to create a game using Geometer’s Sketchpad. We detail a game created by a pair of preservice teachers that exemplifies their creativity and knowledge of complex-valued functions. Given inquiry-based courses have inherent challenges we also present projects that were not as exemplary.     

The complex development of student-teachers' thinking

Studies of student-teacher development have tended to suggest a three-stage model of development in which the novices' concerns shift outwards from an initial preoccupation with self, to a focus on tasks and teaching situations, and finally to consideration of pupil learning. This paper, based on sequence of post-lesson interviews conducted with 25 student teachers following 1-year postgraduate courses within school-based partnership schemes of initial teacher education, questions the adequacy of such a model. Analysis of the reasons that the student-teachers offered for their teaching decisions, and of their lesson evaluations suggests a high level of concern for pupils' learning and an awareness of the complexity of teaching from very early in their training. The implications of these findings are explored; in particular, the challenges that they pose to teacher educators in terms of course structure and curricula, and the need to be responsive to individual learners.     

Are sports club members big spenders?: Findings from sport specific analyses in Germany

This paper analyses the sport expenditures of people who are members of non-profit sports clubs (N = 10,013) in Germany. Adult members, active in 21 sports, were asked about their sport expenditure relating to several defined categories. The results show that members spend an average of €1610 per year on their chosen sport. Sport specific analyses reveal big differences in expenditure between sports, ranging from badminton (€338) to equestrian (€7902). According to sport-specific regression analyses, personal income, level of performance, and weekly time of participation are the main predictors of sport-specific expenditures. Compared to other studies, these results show that the financial status of members of non-profit sports clubs is very strong.     

The effect of westward travel across five time zones on sleep and subjective jet-lag ratings in athletes before and during the 2015’s World Rowing Junior Championships

This study examined sleep-wake habits and subjective jet-lag ratings of 55 German junior rowers (n = 30 male, 17.8 ± 0.5 years) before and during the World Rowing Junior Championships 2015 in Rio de Janeiro, Brazil. Athletes answered sleep logs every morning, and Liverpool John Moore’s University Jet-Lag Questionnaires each evening and morning. Following an 11-h westward flight with 5-h time shift, advanced bedtimes (?1 h, P < .001, η_p² = 0.68), reduced sleep onset latency (P = .002, η_p² = 0.53) and increased sleep duration (P < .001, η_p² = 0.60) were reported for the first two nights. Jet-lag symptoms peaked upon arrival but were still present after 6 days. Sleep quality improved (P < .001, η_p² = 0.31) as well as some scales of the Recovery-Stress Questionnaire for Athletes. Participation was successful as indicated by 11 of 13 top 3 placings. Overall, the initial desynchronisation did not indicate negative impacts on competition performance. As travel fatigue probably had a major effect on perceptual decrements, sleep during travel and time to recover upon arrival should be emphasised. Coaches and practitioners should consider higher sleep propensity in the early evening by scheduling training sessions and meetings until the late afternoon.     

Testing the validity of value‐added measures of educational progress with genetic data

Value‐added measures of educational progress have been used by education researchers and policy‐makers to assess the performance of teachers and schools, contributing to performance‐related pay and position in school league tables. They are designed to control for all underlying differences between pupils and should therefore provide unbiased measures of school and teacher influence on pupil progress, however, their effectiveness has been questioned. We exploit genetic data from a UK birth cohort to investigate how successfully value‐added measures control for genetic differences between pupils. We use raw value‐added, contextual value‐added (which additionally controls for background characteristics) and teacher‐reported value‐added measures built from data at ages 11, 14 and 16. Sample sizes for analyses range from 4,600 to 6,518. Our findings demonstrate that genetic differences between pupils explain little variation in raw value‐added measures but explain up to 20% of the variation in contextual value‐added measures (95% CI = 6.06% to 35.71%). Value‐added measures built from teacher‐rated ability have a greater proportion of variance explained by genetic differences between pupils, with 36.3% of their cross‐sectional variation being statistically accounted for by genetics (95% CI = 22.8% to 49.8%). By contrast, a far greater proportion of variance is explained by genetic differences for raw test scores at each age of at least 47.3% (95% CI: 35.9 to 58.7). These findings provide evidence that value‐added measures of educational progress can be influenced by genetic differences between pupils, and therefore may provide a biased measure of school and teacher performance. We include a glossary of genetic terms for educational researchers interested in the use of genetic data in educational research.     

Stabilizing Conditional Standard Errors of Measurement in Scale Score Transformations

The focus of this article is on scale score transformations that can be used to stabilize conditional standard errors of measurement (CSEMs). Three transformations for stabilizing the estimated CSEMs are reviewed, including the traditional arcsine transformation, a recently developed general variance stabilization transformation, and a new method proposed in this article involving cubic transformations. Two examples are provided and the three scale score transformations are compared in terms of how well they stabilize CSEMs estimated from compound binomial and item response theory (IRT) models. Advantages of the cubic transformation are demonstrated with respect to CSEM stabilization and other scaling criteria (e.g., scale score distributions that are more symmetric).     

Rethinking Assessment Design: Evidence-Informed Strategies to Boost Educational Impact in the Anatomical Sciences

University assessment is in the midst of transformation. Assessments are no longer designed solely to determine that students can remember and regurgitate lecture content, nor in order to rank students to aid with some future selection process. Instead, assessments are expected to drive, support, and enhance learning and to contribute to student self-assessment and development of skills and attributes for a lifetime of learning. While traditional purposes of certifying achievement and determining readiness to progress remain important, these new expectations for assessment can create tensions in assessment design, selection, and deployment. With the recognition of these tensions, three contemporary approaches to assessment in medical education are described. These approaches include careful consideration of the educational impact of assessment—before, during (test or recall enhanced learning) and after assessments; development of student (and staff) assessment literacy; and planning of cohesive systems of assessment (with a range of assessment tools) designed to assess the various competencies demanded of future graduates. These approaches purposefully straddle the cross purposes of assessment in modern health professions education. The implications of these models are explored within the context of medical education and then linked with contemporary work in the anatomical sciences in order to highlight current synergies and potential future innovations when using evidence-informed strategies to boost the educational impact of assessments.     

The evolving nature of Taiwan's national innovation system: The case of biotechnology innovation networks

The dynamics of national innovation systems (NISs) are a source of considerable academic and policy interest, especially when to address new competitive challenges they involve changing institutions and relationships within successful systems. This paper examines the case of Taiwan which is embarking on a new phase in its approach to building its national innovative capacity through creating the infrastructure for a biotechnology industry. By examining the process and mechanisms by which new biotechnology innovation networks are being created, and contrasting their development with existing networks, we analyse the dynamics of Taiwan's NIS. The paper reviews the prospects for this new phase in Taiwan's transition from ‘imitation’ to ‘innovation’. The paper aims to add to the understanding of how innovation systems evolve. It is concerned with the contributors, processes and challenges of NIS evolution and the form and meaning of its dynamic changes.     

Comparison of the One‐ and Bi‐Direction Chained Equipercentile Equating

This study investigated differences between two approaches to chained equipercentile (CE) equating (one‐ and bi‐direction CE equating) in nearly equal groups and relatively unequal groups. In one‐direction CE equating, the new form is linked to the anchor in one sample of examinees and the anchor is linked to the reference form in the other sample. In bi‐direction CE equating, the anchor is linked to the new form in one sample of examinees and to the reference form in the other sample. The two approaches were evaluated in comparison to a criterion equating function (i.e., equivalent groups equating) using indexes such as root expected squared difference, bias, standard error of equating, root mean squared error, and number of gaps and bumps. The overall results across the equating situations suggested that the two CE equating approaches produced very similar results, whereas the bi‐direction results were slightly less erratic, smoother (i.e., fewer gaps and bumps), usually closer to the criterion function, and also less variable.