Complex Variables Throughout the Curriculum

Abstract

We offer many specific detailed examples, several of which are new, that instructors can use (in lecture or as student projects) to revitalize the role of complex variables throughout the curriculum. We conclude with three primary recommendations: revise the syllabus of Calculus II to allow early introductions of complex numbers and linear algebra, include complex variables and some infinite-dimensional linear maps in linear algebra courses, and spice up complex variable courses by better connecting them with the mathematics used in engineering in physics.     

How Many Libraries Do We Need?

ABSTRACT

According to the American Library Association, there are 119,000 libraries in the United States. But how many do we need? In this vision session report, Arizona State University Librarian James J. O’Donnell addresses this question through the lenses of discovery tools, usability, and marketing strategy. He also addresses the need for a more global and collaborative approach to collection building in libraries. This deliberately provocative talk provides several different ways to think about the answer to the title question—and several answers.     

Tune discrimination in monkeys (Cebus apella) and in rats

Monkeys and rats were trained on an operant discrimination employing structured auditory stimuli (tunes). The rats acquired the tune discrimination very rapidly and considerably faster than the monkeys. Both species generalized the discrimination across intensity and octave transformations. Discriminative performance remained at a high level when only the first halves of the tunes were presented, but substantially less generalization occurred to the second halves. Rats trained with tones (broken or steady) required three to four times more training to reach criterion than did the rats trained with tunes. The potential of structured auditory stimuli for investigations of information-processing mechanisms in animals is pointed out.     

Boyz in the ‘Burbs: Parental Negotiation of Race and Class in Raising Black Males in Suburbia

This paper explores the outlooks of black parents raising sons in a suburban school setting in a town that I call Rolling Acres. Dominant narratives about black males center on urban environments where hazards of violence, failing schools, and socially disorganized neighborhoods are prevalent. However, black parents in suburban settings are not immune to racial hazards when raising black boys. This article engages two domains of distinct concern for the parents of black boys: academics and social life. Through a series of in-depth interviews and participant observations with 18 families in a suburban context, I argue parents of black boys, though sometimes divided along gender lines, were concerned with a host of race-related challenges such as social promotion, special education classification, dating preferences, the stereotyping of black boys, and the strain between being cool and academically successful. These concerns demonstrate the importance of understanding how black families, and boys in particular, wrestle with the racialized and gendered power structures even in well-resourced settings. This paper adds to the emerging body on suburbia by highlighting the continued significance of race and gender for black residential families sending their children to suburban schools.     

Northeast wisconsin science forum,an example of cooperative effort in upgrading science education

Conclusions In view of growing national concern over the decline in scientific literacy among students and the need to attract more students to science and engineering, it is incumbent upon college and precollege science faculties to work together to find ways to help solve these problems. To this end, college and precollege science teachers and administrators established the NEW Science Forum and its dinner-and-lecture series and Science Teacher Day field trips. These activities stimulate teacher interest in science, upgrade scientific understanding, and provide new insights and information for classroom use. In addition, the Forum is an opportunity for discussion among techers and between teachers and university science faculty members. The continued high level of participation by teachers and professors during the seven years since the founding of the NEW Science Forum attests to its value to area educators. Our experience prompts us to encourage our colleagues at other colleges and universities to explore the feasibility of establishing a similar program in their regions. The rewards of strengthening ties with area school science teachers far outweigh lost time from research and the trepidation of operating with a zero budget.     

Examining the Exam: A Critical Look at The California Critical Thinking Skills Test

This paper examines the content of The California Critical Thinking Skills Test (1990). This report is not a statistical review. Instead it brings under scrutiny the content of the exam. This content will be of interest to the general reader, because the issues range from logic to ethics to pedagogy, and to questions of evidential and epistemological support. Anyone interested in clear thought and expression will find these issues of significance. Although the exam has a number of strengths and has the clearest instructions of all the presently available Critical Thinking exams, the content of 9 of the exams 34 questions is defective, namely the content of questions 6, 7, 8, 19, 21, 23, 24, 29, and 33. These questions make errors in critical thinking. Hence, no statistical results pertaining to the administration of these questions to students can be acceptable. The remaining questions are acceptable as to content. But until the problems are corrected, those who may use the exam should remove the defective questions from test administration or from data collection and reporting.The scope of the exam also is quite limited, but this may be unavoidable for any instrument designed to be completed in about an hour. Further, the scores resulting from any such testing can be understood only as a measure of minimal competency (below which remediation likely is needed) for the skills tested, but not as an adequate measure of critical thinking.Disclosure: Three of the authors are engaged in producing and marketing a critical thinking test. Though this paper was written before any of us considered developing such a test, the reader should be informed. Each of the writers has exercised considerable care to avoid any bias, and we thank our independent reviewers for helping us in this regard as well.     

Mathematics education as a ‘design science’

Mathematics education (didactics of mathematics) cannot grow without close relationships to mathematics, psychology, pedagogy and other areas. However, there is the risk that by adopting standards, methods and research contexts from other well-established disciplines, the applied nature of mathematics education may be undermined. In order to preserve the specific status and the relative autonomy of mathematics education, the suggestion to conceive of mathematics education as a design science is made.Revised and extended version of the paper Mathematikdidaktik als design science, published inJournal für Mathematikdidaktik 13 (1992), 55–70. I am indebted to Jerry P. Becker, P. Bender, H. Besuden, W. Blum, E. Cohors-Fresenborg, Th.J. Cooney, L. Führer, H.N. Jahnke, A. Kirsch, G.N. Müller, H._Chr. Reichel, H. Schupp, Ch. Selter, H.-J. Vollrath, J. Voigt, G. Walther and H. Winter for critical remarks to earlier drafts.     

In search of Samoan research approaches to education: Tofā’a’anolasi and the Foucauldian tool box

Abstract

This article introduces Tofā’a’anolasi, a novel Samoan research framework created by drawing on the work of other Samoan and Pacific education researchers, in combination with adapting the ‘Foucauldian tool box’ to use for research carried out from a Samoan perspective. The article starts with an account and explanation of the process of developing and of naming Tofā’a’anolasi as a Samoan form of Critical Discourse Analysis. Following this is a discussion of the features of Tofā’a’anolasi and the theoretical underpinnings that explain the understandings and processes of this research framework. The article concludes with a story from assessment practice that acts as an example of applying this approach to educational research centred on Samoan students in Auckland, New Zealand.     

Parents,quality, and school choice: why parents in Nairobi choose low-cost private schools over public schools in Kenya’s free primary education era

Low-cost private schools (LCPS) are widespread in Kenya, particularly in urban areas. This study examines the reasons that parents send children to fee-charging schools in a context of free public primary education. Drawing on parent survey and interview data, as well as interviews with national policy makers, we found that parents who chose LCPS for their children were more driven by quality concerns than were public school parents. We also present data on the costs of the school types, compared to household income. Despite being termed ‘low cost’, the fees charged by schools primarily serving the poor were often a heavy burden on families. We conclude with recommendations for maximising the impact of LCPS on educational access and quality.     

Behind and Beyond Self-Mastery: Risk,Vulnerability, and Becoming Through Dewey and Heidegger

In the last two decades, a decisive anti-foundationalist turn has emerged in educational philosophy and theory. With such a shift, both the possibility and the desirability to conceive of educational processes and practices in terms of mastery and predictability has been challenged. In this paper, by locating my work on such an anti-foundationalist horizon and by staging a comparison between Dewey and Heidegger, I wish to frame the issue in terms of what is behind and what is beyond the detached and self-assured subject that is supposed to found the kind of managerial frameworks that dominate educational practice worldwide. Specifically, it is my contention that for both Heidegger and Dewey, we are, on the one hand, vulnerable from the very beginning, delivered to an uncanny and uncertain condition; even knowledge is dependent upon a wider, non-discursive context. On the other hand, such an uncanniness and dependency, rather than flowing in some nihilistic defeat of educational purposes, puts radical responsibility on the side of the subject. For both Dewey and Heidegger, being a subject means being-with-others while transcending and advancing one’s boundaries. The notion of education that will emerge through the comparison between Dewey and Heidegger is a type of both subtraction and overstepping, a type of event that we cannot manage, and yet requires our attention, our educational effort in dealing with it, in loading it upon ourselves, thus reconsidering our existence.