Domain Coloring and the Argument Principle

Abstract

The domain-coloring algorithm allows us to visualize complex-valued functions on the plane in a single image—an alternative to before-and-after mapping diagrams. It helps us see when a function is analytic and aids in understanding contour integrals. The culmination of this article is a visual discovery and subsequent proof of the Argument Principle, which relates the count of poles and zeros of a meromorphic function inside a contour to the accumulated change in argument of the function around the contour. Throughout, I offer connections to standard learning goals of courses in complex variables.     

Supplemental instruction in introductory biology I: enhancing the performance and retention of underrepresented minority students

Supplemental instruction classes have been shown in many studies to enhance performance in the supported courses and even to improve graduation rates. Generally, there has been little evidence of a differential impact on students from different ethnic/racial backgrounds. At San Francisco State University, however, supplemental instruction in the Introductory Biology I class is associated with even more dramatic gains among students from underrepresented minority populations than the gains found among their peers. These gains do not seem to be the product of better students availing themselves of supplemental instruction or other outside factors. The Introductory Biology I class consists of a team-taught lecture component, taught in a large lecture classroom, and a laboratory component where students participate in smaller lab sections. Students are expected to master an understanding of basic concepts, content, and vocabulary in biology as well as gain laboratory investigation skills and experience applying scientific methodology. In this context, supplemental instruction classes are cooperative learning environments where students participate in learning activities that complement the course material, focusing on student misconceptions and difficulties, construction of a scaffolded knowledge base, applications involving problem solving, and articulation of constructs with peers.     

The dyadic nature of bullying and victimization: testing a dual-perspective theory

For this study, information on Who Bullies Who was collected from 54 school classes with 918 children (M age = 11) and 13,606 dyadic relations. Bullying and victimization were viewed separately from the point of view of the bully and the victim. The two perspectives were highly complementary. The probability of a bully-victim relationship was higher if the bully was more dominant than the victim, and if the victim was more vulnerable than the bully and more rejected by the class. In a bully-victim dyad, boys were more often the bullies. There was no finding of sex effect for victimization. Liking reduced and disliking increased the probability of a bully-victim relationship.     

Socio-scientific reasoning and environmental literacy in a field-based ecology class

The complex environmental challenges humanity faces require citizens who are scientifically and environmentally literate. Many environmental education programs are situated in the field where students are immersed in their learning. These field-based activities are engaging but may lack opportunities for students to develop critical thinking and reasoning skills necessary to be environmentally literate. We suggest a socio-scientific issue (SSI) based teaching approach can increase epistemic engagement and lead to student gains in scientific and environmental literacy. This study describes how we modified an existing field-based ecology course, framing the learning around a local environmental socio-scientific issue. We used a convergent parallel mixed-methods approach to examine the changes in socio-scientific reasoning (SSR) over time for high school students in this course as a measure of scientific and environmental literacy. Results indicate that a focused SSI field-based environmental education curriculum can support development of socio-scientific reasoning and environmental literacy competencies among high school students.     

Bridging Research and Practice: How Sales Training Can Contribute to New Product Launch Success

This study demonstrates how academicians and practitioners can work together on an important topic that matters to organizational performance: the pivotal role played by salespeople during new product launches. In particular, the authors present three potential interventions that training and sales managers may use to sell a new product to salespeople. The results legitimatize the critical contribution of sales training to new product sales performance and highlight the value of the partnership between training professionals and sales managers.     

Computer support in a rural setting: A comparison of computer-assisted and handwritten evaluation reports

The present blind study compared the quality of psychoeducational reports generated under two conditions. On the average, reports written with computer assistance were rated to be of higher quality than those prepared by hand. Also presented are data validating the large expenditure of staff time on report preparation, along with estimates of the time saving that may be realized with computer assistance. The relevance of computer support to relatively isolated, rural-based clinical staff is discussed.     

Helsen, Gilis and Weston (2006) err in testing the optical error hypothesis

In this commentary, we react to the recent study by Helsen, Gilis and Weston (2006) on judging offside in football. Helsen et al. claim that their data falsify the optical error hypothesis presented by Oudejans et al. (2000). However, as we will elucidate here, they misinterpret this hypothesis and present a data set that is seriously flawed, and hence not suited to test it. Therefore, their conclusions regarding the optical error hypothesis are in error.