Ten Myths of Science: Reexamining What We Think We Know About the Nature of Science

This article addresses and attempts to refute several of the most widespread and enduring misconceptions held by students regarding the enterprise of science. The ten myths discussed include the common notions that theories become laws, that hypotheses are best characterized as educated guesses, and that there is a commonly-applied scientific method. In addition, the article includes discussion of other incorrect ideas such as the view that evidence leads to sure knowledge, that science and its methods provide absolute proof, and that science is not a creative endeavor. Finally, the myths that scientists are objective, that experiments are the sole route to scientific knowledge and that scientific conclusions are continually reviewed conclude this presentation. The paper ends with a plea that instruction in and opportunities to experience the nature of science are vital in preservice and inservice teacher education programs to help unseat the myths of science.     

Management,Operational Research and the Micro: A Critical Review of What is Available

This paper reviews the state of the microcomputer market as at January 1981. The authors have been involved in computer systems for many years and began working with microcomputers towards the end of 1978. Since then, they have had experience of nearly 20 varied microcomputer installations. A version of the paper was first given at the two-day seminar. ‘Management, Operational Resarch and the Micro’, held in London during November 1980.     

From solving equations to the meaning of life: mathematics, rationality and values

An attempt is made to suggest some ultimate goals for education beyond the narrow framework of the mathematics curriculum. In addition, there is an attempt to link mathematics education to these goals by pointing at some principles which direct mathematical behavior as well as educated behavior. The main claim is that both mathematical behavior and educated behavior are supposed to be directed by rational thinking.     

Time-reversal symmetry,Poincaré recurrence,irreversibility, and the entropic arrow of time: From mechanics to system thermodynamics

In this paper, we use a large-scale dynamical systems perspective to provide a system-theoretic foundation for thermodynamics. Specifically, using a state space formulation, we develop a nonlinear compartmental dynamical system model characterized by energy conservation laws that is consistent with basic thermodynamic principles. In addition, we establish the existence of a unique, continuously differentiable global entropy function for our large-scale dynamical system, and using Lyapunov stability theory we show that the proposed thermodynamic model has convergent trajectories to Lyapunov stable equilibria determined by the system initial energies. Finally, using the system entropy, we establish the absence of Poincaré recurrence for our thermodynamic model and develop a clear connection between irreversibility, the second law of thermodynamics, and the entropic arrow of time.     

From convergence to divergence: the development of mathematical problem solving in research, curriculum, and classroom practice in Singapore

Following the movement of problem solving in the US and other parts of the world in the 1980s, problem solving became the central focus of Singapore’s national school mathematics curriculum in 1990 and thereafter the key theme in research and practice. Different from some other countries, this situation has largely not changed in Singapore mathematics education since then. However, within the domain of problem solving, mathematics educators in Singapore focused more on the fundamental knowledge, basic skills, and heuristics for problem solving till the mid 1990s. In particular, problem solving heuristics, especially the so-called “model method”, a term most widely used for problem solving, received much attention in syllabus, research, and classroom instruction. Since the late 1990s, following the national vision of “Thinking Schools, Learning Nation” and nurturing modern citizens with independent, critical, and creative thinking, Singapore mathematics educators’ attention has greatly expanded to the development of students’ higher-order thinking, self-reflection and self-regulation, alternative ways of assessment and instruction, among other aspects concerning problem solving. Researchers have also looked into the advantages and disadvantages of Singapore’s textbooks in representing problem solving, and the findings of these investigations have influenced the development of the latest school mathematics textbooks.     

Visibility graphs of staircase polygons and the weak Bruhat order,I: From visibility graphs to maximal chains

The recognition problem for visibility graphs of simple polygons is not known to be in NP, nor is it known to be NP-hard. It is, however, known to be inPSPACE. Further, every such visibility graph can be dismantled as a sequence of visibility graphs of convex fans. Any nondegenerated configuration ofn points can be associated with amaximal chain in the weak Bruhat order of the symmetric groupS _n . The visibility graph ofany simple polygon defined on this configuration is completely determined by this maximal chain via a one-to-one correspondence between maximal chains andbalanced tableaux of a certain shape. In the case of staircase polygons (special convex fans), we define a class of graphs calledpersistent graphs and show that the visibility graph of a staircase polygon is persistent. We then describe a polynomial-time algorithm that recovers a representative maximal chain in the weak Bruhat order from a given persistent graph, thus characterizing the class of persistent graphs. The question of recovering a staircase polygon from a given persistent graph, via a maximal chain, is studied in the companion paper [4]. The overall goal of both papers is to offer a characterization of visibility graphs, of convex fans. The research of J. Abello was supported by NSF Grants Nos. DCR 8603722 and DCR 8896281. This research was done while K. Kumar was at the Department of Computer Science, Texas A & M University.     

Contemporary Metaphysics: Review of David J. Chalmers, Constructing the World, Oxford: Oxford University Press 2012, 494 Pages; John Heil, The Universe as We Find It, Oxford: Oxford University Press 2012, 311 Pages; and Theodore R. Sider, Writing the Book of the World, Oxford: Oxford University Press 2011, 318 Pages

Metaphysics is definitely back on the agenda of contemporary philosophy. It is a metaphysics in the full traditional sense, seeking to provide the means to gain knowledge that covers being as a whole, not just parts of it (such as the metaphysics of mind, the metaphysics of values, etc.). Oxford University Press published three books in 2011 and 2012 each of which spells out that ambition. The present review sums up the main topics covered in these books and offers some comments.     

A Comparison of Calculator Use in Eighth‐Grade Mathematics Classrooms in the United States,Japan, and Portugal: Results From the Third International Mathematics and Science Study

The study used data from the Third International Mathematics and Science Study to determine trends in calculator use among Population 2 (13‐year‐olds) students in Japan, the United States, and Portugal. While relatively high levels of calculator use were observed for the US and Portugal, virtually no calculator use was found for the Japanese sample. Hierarchical Linear Model analysis determined a statistically significant negative relationship between students' frequency of calculator use and student performance in Japan; no statistically significant relationship was detected for the US and Portuguese samples. US student achievement was positively associated with each of the five reported ways in which calculators are used; however, a statistically significant negative relationship was found between student performance and Japanese students' use of calculators on tests. Plausible explanations are explored.