Book Vignettes

Book reviewed in this article: Northeastern Forest Experiment Station, Forest Service, U.S. Department of Agriculture, A Tree Hurts, Too. National Coordinating Council on Drug Education, Special Action Office for Drug Abuse Prevention and Multi-Cultural Resource Center for Drug Abuse Prevention, Super Me/Super Yo. Simon, Seymour, Pets in a Jar: Collecting and Caring for Small Wild Animals. Stopfer, Janet Y. (ed.), Science Fair Project Index 1960–1972.     

The landscape: Through a Different Lens A New Angle on the Price Spiral in Higher Education

Abstract

“Academic institutions now find themselves confronting hard questions about whether their spending patterns match their priorities and about how to communicate the choices they have made to the public.”

The College Cost Crisis: A Congressional Analysis of College Costs and Implications for America's Higher Education System     

Conceptions of Science Achievement in Major Reform Documents

The construct of science achievement—what K‐12 students should know and be able to do in science—is central to science education reform. This paper examines current conceptions of science achievement in major reform documents in the context of standards‐based and systemic reform. The paper reviews documents on (a) science content standards, including the National Science Education Standards ( National Research Council, 1996 ) and Project 2061 ( American Association for the Advancement of Science, 1989, 1993 ); (b) performance standards in the New Standards Project ( National Center on Education and the Economy, 1997a, 1997b, 1997c, 1998 ); and (c) assessment frameworks, including the 1996 National Assessment of Educational Progress ( National Assessment Governing Board, 1994, 1996 ) and the Third International Mathematics and Science Study ( Martin & Kelly, 1996 ; McKnight, Schmidt, & Raizen, 1993 ; Robitallie et al., 1993 ). Although there is an overall agreement on the conceptions of science achievement among the documents, there are also noticeable differences. Based on the analysis of the five sets of documents, an aggregated view of science achievement is presented in terms of science content and process. Implications for promoting science achievement in standards‐based and systemic reform are discussed.     

Collecting Their Thoughts: The Future in the Making edited by Dyckman Vermilye and Education and the Endangered Individual: A Critique of Ten Modern Thinkers by Brian V. Hill

Abstract

Higher Education and the Law by Henry T. Edwards and Virginia Davis Nordin, Cambridge: Institute for Educational Management, Harvard University, 1979, xl + 844 pages, $25.00.     

A New Inequality for Weakly （K1, K2）-Quasiregular Mappings

We obtain a new inequality for weakly （K1,K2）-quasiregular mappings by using the McShane extension method. This inequality can be used to derive the self-improving regularity of （K1, K2）-Quasiregular Mappings.     

Linear-size nonobtuse triangulation of polygons

We give an algorithm for triangulatingn-vertex polygonal regions (with holes) so that no angle in the final triangulation measures more than π/2. The number of triangles in the triangulation is onlyO(n), improving a previous bound ofO(n ²), and the running time isO(n log² n). The basic technique used in the algorithm, recursive subdivision by disks, is new and may have wider application in mesh generation. We also report on an implementation of our algorithm. The research of S. Mitchell was supported by the Applied Mathematical Sciences program, U.S. Department of Energy Research and by the U.S. Department of Energy under Contract DE-AC04-76DP00789. J. Ruppert's work was performed while he was at the NASA Ames Research Center as an employee of Computer Sciences Corporation, under NASA Contrast NAS 2-12961.     

Teachers' ways of listening and responding to students' emerging mathematical models

In this paper, I present the results of a case study of the practices of four experienced secondary teachers as they engaged their students in the initial development of mathematical models for exponential growth. The study focuses on two related aspects of their practices: (a) when, how and to what extent they saw and interpreted students' ways of thinking about exponential functions and (b) how they responded to the students' thinking in their classroom practice. Through an analysis of the teachers' actions in the classroom, I describe the teachers' developing knowledge when using modeling tasks with secondary students. The analysis suggests that there is considerable variation in the approaches that teachers take in listening to and responding to students' emerging mathematical models. Having a well-developed schema for how students might approach the task enabled one teacher to press students to express, evaluate, and revise their emerging models of exponential growth. Implications for the knowledge needed to teach mathematics through modeling are discussed.     

A stability problem for holonomic systems

Sunto Si studia il problema della stabilità di una posizione di equilibrio di un sistema meccanico olonomo soggetto ad una sollecitazione derivante da un potenziale del tipo U(q, t)=f(t) U*(q), conf funzione periodica, e ad una sollecitazione dissipativa. I risultati ottenuti estendono a sistemi con un numero finito qualsiasi di gradi di libertà risultati noti per sistemi ad un solo grado di libertà.

---

---

Work performed under the auspices of the Italian Council of Research (C.N.R.): National Group of Mathematical Physics (G.N.F.M.), and Italian Ministry of Public Education (M.P.I.).

---

The author wishes to thank professors S.Busenberg and L.Salvadori for many useful discussions.     

Secondary teachers’ meanings for function notation in the United States and South Korea

This study investigates what teachers in U.S. reveal about their meanings for function notation in their written responses to the Mathematical Meanings for Teaching secondary mathematics (MMTsm) items, with particular attention to how productive those meanings would be if conveyed to students in a classroom setting. We then report South Korean teachers’ responses to see whether the meanings U.S. teachers demonstrated are shared with South Korean teachers. The results show that many U.S. teachers use function notation to name rules instead of to represent relationships. The data from South Korean teachers indicates that the problematic meanings in U.S. teachers’ responses are shared with a minority of South Korean teachers. The results suggest a need for attention to ideas regarding function notation in teacher education for pre-service teachers and professional development programs for in-service teachers.     

Outsourcing in Higher Education: A Business Officer and Business Partner Discuss a Controversial Management Strategy

Abstract

It's common knowledge that major changes have taken place in the college literature classroom. We hear that English departments across the nation have remade their curricula. The English faculty, which until recently concentrated on the well-known works and authors of the literary canon, now focuses on works by women and minorities, and also on products of popular culture and the mass media. Old distinctions of aesthetic quality have given way. The investigations of critical theory, deconstruction, feminism, and Marxism dominate the field. Educational goals for the classroom, which once centered on aesthetic appreciation, have altered accordingly. (For an account of literary study that takes these conclusions for granted, see Edward Jayne, “Academic Jeremiad,” Change, May/June, 1991, page 32.)     

Making Connections in Math and Science: Identifying Student Outcomes

A three-phase Collaborative Science Education Research Project (CSERP) has been established between the AIMS Education Foundation and The National Center for Science Teaching and Learning. The goal of Phase I is to identify student outcomes as perceived by classroom teachers to be related to participation in a hands-on, integrated mathematics science program called AIMS, Activities Integrating Math and Science. The raw data were then summarized and interpreted by the principal investigators. Data collection procedures involved seven Research Team Leaders; 45 teacher-researchers; and 2,025 students in Grades 4, 5, and 6 located in six states. The teacher-researchers identified 423 cognitive, 234 affective, and 188 social outcomes that were coded and classified by the principal investigators. An unanticipated teacher outcome also emerged. Teacher involvement in the research project greatly contributed to their own sense of professionalism. These outcomes will be used to develop, pilot (Phase II), and field test (Phase III) prototypic assessment items in the subsequent phases of the CSERP.     

Extension of a crack by a shear wave

Zusammenfassung Eine ebene, unstetige, horizontal polarisierte Schubwelle breitet sich in einem brüchigen elastischen Material aus, das einen Riss enthält. In dieser Arbeit werden die Bedingungen für den Rissfortschritt untersucht, nachdem die ankommende Welle durch den Riss gebeugt wurde. Die Untersuchung besteht aus zwei Teilen. Im ersten Teil werden die Teilchengeschwindigkeiten und Schubspannungen in der Ebene des Risses infolge Beugung der Schubwelle bestimmt. Es wird dabei angenommen, dass der Riss sich sofort, oder kurz nachdem die Wellenfront die Risskante getroffen hat, mit beliebiger Geschwindigkeit ausbreitet. Im zweiten Teil wird die Energiegleichung als Kriterium für den Rissfortschritt benützt. Es wird gezeigt, dass in einem ursprünglich ungestörten Material der Riss sich nur dann sofort ausbreitet, wenn die Schubspannung eine Quadratwurzelsingularität an der Wellenfront zeigt. Wenn die Schubspannung an der Wellenfront kontinuierlich ist, dann beginnt der Rissfortschritt, kurz nachdem die Risskante getroffen wird. In einem statisch vorgespannten Material, das einen Riss enthält, kann der Rissfortschritt sofort einsetzen, wenn der Spannungsfaktor gross genug ist.

---

---

This work was supported by the Advanced Research Project Agency of the U.S. Department of Defense through the Northwestern University Materials Research Center.     

Reconstructing the Adjusted Census for Florida: A Case Study in Data Examination

Abstract

This article is a case study in the value of close examination of available data when one is attempting to make inferences. The article is also an example of what can be done to reconstruct government files when data have been concealed, whether for administrative or political reasons, as here, or to preserve confidentiality. The various methods currently used are under review by a panel under the aegis of the Committee on National Statistics of the National Research Council. The upshot of our work is that even suppressing half of the microlevel data in a file need not daunt a determined and reasonably adroit reconstructor equipped with modern computers. The particular problem discussed here arose due to a bizarre set of political and legal circumstances, explained in Section 1, whereby the U.S. Department of Commerce released a tape consisting of the adjusted population (cross-classified by age, race, and gender) of half the Census Blocks in the nation, together with certain summary adjusted information. This article concerns techniques used to fill in the other half of the adjusted block data for possible use in reapportionment.     

Optimization problems involving collections of dependent objects

We describe a class of problems motivated by numerous real-world applications where there is a collection of objects that have both a cost and a value, but where some of those objects depend upon other objects to obtain their full value. Applications include finding an optimal order for transferring files under threat of system failure, ordering sequences of actions by a heterogeneous team of agents or robots, picking an optimal set of products to store in a warehouse, selecting courses to take at a university, or picking what products to cut from production. We formalize the problem of representing objects and their dependence relationships as a directed acyclic graph (DAG). We define simple formulae for calculating the utility of both sets and sequences of graph vertices. We motivate, using real-world examples, a taxonomy of problems associated with the model we present. We also prove that two variants of problems associated with our formalism are NP-hard, and present an efficient algorithm for solving a restricted version of a third problem. Part of this research was performed while on appointment as a U.S. Department of Homeland Security (DHS) Fellow under the DHS Scholarship and Fellowship Program, a program administered by the Oak Ridge Institute for Science and Education (ORISE) for DHS through an interagency agreement with the U.S. Department of Energy (DOE). ORISE is managed by Oak Ridge Associated Universities under DOE contract number DE-AC05-00OR22750. All opinions expressed in this paper are the author’s and do not necessarily reflect the policies and views of DHS, DOE, or ORISE.     

The MIME project at Loughborough — a first report†

This paper describes the experiences of the first months of the MIME Project (Micros In Mathematics Education) at Loughborough. The early difficulties and setbacks are mentioned as well as the initial successes.

The first part of the paper examines the educational philosophy behind the establishment of the project and details its aims, objectives and scope. Consideration is given to how these aims were put into practice and what revisions to them were necessitated by experience.

The second part traces the story of the production of a unit from the author's early ideas, through the program development, to the finished product. Emphasis is given to the way the educational objectives are achieved by careful design of the program. The testing and evaluation of a unit is outlined.

The third part reviews the practical programming difficulties that have been encountered; the strengths and weaknesses of the BBC micro are discussed and problems of the speed of display and of storage limitation are highlighted. The need for assembly language is shown and the case is put for hardware/software independence.

The fourth part looks at the different modes of use of the units. Demonstrations are given of use as a teacher aid in the classroom and as self‐paced instruction.

Finally, conclusions are drawn from the early experiences of the MIME team and the lessons they have learned, and future developments are outlined.     

Two improved algorithms for envelope and wavefront reduction

Two algorithms for reordering sparse, symmetric matrices or undirected graphs to reduce envelope and wavefront are considered. The first is a combinatorial algorithm introduced by Sloan and further developed by Duff, Reid, and Scott; we describe enhancements to the Sloan algorithm that improve its quality and reduce its run time. Our test problems fall into two classes with differing asymptotic behavior of their envelope parameters as a function of the weights in the Sloan algorithm. We describe an efficientO(nlogn+m) time implementation of the Sloan algorithm, wheren is the number of rows (vertices), andm is the number of nonzeros (edges). On a collection of test problems, the improved Sloan algorithm required, on the average, only twice the time required by the simpler RCM algorithm while improving the mean square wavefront by a factor of three. The second algorithm is a hybrid that combines a spectral algorithm for envelope and wavefront reduction with a refinement step that uses a modified Sloan algorithm. The hybrid algorithm reduces the envelope size and mean square wavefront obtained from the Sloan algorithm at the cost of greater running times. We illustrate how these reductions translate into tangible benefits for frontal Cholesky factorization and incomplete factorization preconditioning. This work was partially supported by the U. S. National Science Foundation grants CCR-9412698, DMS-9505110, and ECS-9527169, by U. S. Department of Energy grant DE-FG05-94ER25216, and by the National Aeronautics and Space Administration under NASA Contract NAS1-19480 while the second author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA.     

What Is STEM? A Discussion About Conceptions of STEM in Education and Partnerships

Educational reformation has proceeded slowly despite the many calls to improve science and mathematics for our students. The acronym STEM (science, technology, engineering, and mathematics) has been adopted by numerous programs as an important focus for renewed global competitiveness for the United States, but conceptions of what STEM entails often vary among stakeholders. This paper examines the conceptions of STEM held by faculty members from a public Research I institution in the middle of a regional “STEM movement.” Faculty members responded to two open‐ended questions: (1) What is STEM? and (2) How does STEM influence and/or impact your life? Although 72% of these faculty members possessed a relevant conception of STEM, the results suggest that they do not share a common conceptualization of STEM. Their conception is most likely based on their academic discipline or how STEM impacts their daily lives. STEM faculty members were likely to have a neutral or positive conception where non‐STEM faculty members often had negative feelings about STEM.     

Optimal preconditioners of a given sparsity pattern

We consider the problem of finding the symmetric positive definite preconditionerM of a given form- e.g., having nonzero elements only in specified positions — which minimizes the ratio of the largest to smallest eigenvalue ofM ^–1 A, for a given symmetric positive definitive matrixA. We show how this problem can be expressed as one of minimizing a convex function and how an optimization code can be used to solve the problem numerically. Results are presented showing optimal preconditioners of various sparsity patterns and comparing these to preconditioners that have been proposed in the literature. Several conjectures are made, based on results from the optimization code.This work was supported by the Advanced Research Projects Agency of the Department of Defense under contract F49620-87-C-0065 and by the Applied Mathematical Sciences Program of the U.S. Department of Energy under contract DE-AC02-76ER03077.     

Steady state thermal stresses in an elastic solid bounded by two cones

Zusammenfassung Es wird für das Problem der Wärmespannungen in einem kegelförmig begrenzten elastischen Körper eine Ähnlichkeitstransformation entwickelt. Ist die Temperatur an der freien Oberfläche als Potenz des Abstandes von der Spitze vorgeschrieben, so lässt sich ein Satz von Ähnlichkeitsvariablen angeben, welcher die thermoelastischen Beziehungen auf Legendre-Gleichungen reduziert und damit der Lösung leicht zugänglich macht. Die Rechnung ist für den Sonderfall konstant gehaltener Oberflächentemperatur im einzelnen durchgeführt.

---

---

This work has been done at the Mathematics Research Center, University of Wisconsin, under the U.S. Army Contract DA-11-022-ORD-2059.     

On the Lower Bound of the Hausdorff Measure of the Koch Curve

This paper gives a lower bound of the Hausdorff measure of the Koch curve by means of the mass distribution principle.