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The purpose of this paper is to examine how lesson study can lead to teacher learning and improvement of instruction by developing teachers’ mathematical-task knowledge and by supporting teachers’ selection, modification, and implementation of mathematical tasks. Mathematical-task knowledge includes knowledge needed to use tasks that require a high level of thinking and reasoning.

A qualitative case study design was used to explore the learning and instruction of three teachers as they went through the process of lesson study, developed knowledge around mathematics tasks, and made changes to their instruction. Methods included direct observation of lessons, semi-structured interviews, and participant observation.

This lesson study project supported teachers in developing mathematical-task knowledge and in making change to instructional practice. The teachers discussed in this paper added to their understanding of mathematical tasks and changed how they implemented tasks after lesson study. The teachers began to challenge students to go beyond memorizing or executing procedures to deepen the students’ understanding of mathematical concepts. Teachers developed key insights and understandings of mathematical tasks, triggering shifts in their thinking, and changes to instruction. Collaboration and reflection altered the selection, modification, and implementation of mathematical tasks.

This study reveals the connections between features of lesson study and the pathways that lead to learning and improvements to instruction. Limitations included the demands of the school district’s pacing guide and curriculum, and a limited number of interviews and observations were conducted after lesson study.

There are many different ways lesson study has been implemented in the USA, yet the effectiveness of many lesson study projects is still unclear. This study reveals more about the lesson study process, what features are important, and how these features lead to development of knowledge and practice. This study examines how teachers within the same lesson study group added to their knowledge and practice and how different features of lesson study prompt them to make changes.

This study was intended to determine the effects of self-instructional training on algebra problem solving performance of students with learning disabilities, students for whom English is a second language and students who were at risk of failing algebra. Four high school algebra classes consisting of 74 students, of whom 17 were classified as having learning disabilities, 37 had English as a second language, and 20 were considered at-risk for math failure, were assigned randomly to either a self-instructional training condition or a traditional instructional condition. All students were administered pretests, immediate posttests, and delayed posttests of algebra problem solving, pre and post strategy usage questionnaires, and attitude measures. After training, results indicated that both groups’ performance increased from pretest to immediate posttest and pretest to delayed posttest, but no statistical difference was found between groups. The self-instruction group significantly outperformed the traditional instruction group on independent strategy use. Significant correlations were obtained between strategy usage and immediate and delayed posttest scores, indicating that students who successfully learned the strategy had better performance on the math problem solving tests. No significant differences were found across groups in attitude change. Future research issues are discussed with respect to strategy instruction for at risk learners.

This paper is devoted to the topic of how mathematics might be more efficiently used in educational administration. The position taken here is that mathematics is a branch of philosophy whose subject matter is a set of abstract entities and identified operational rules. It is a vocabulary of symbols that can be used to label objects and, more importantly, a set of grammatical rules for using the vocabulary. The paper begins with a review of some recent developments reported in the social science literature on the uses of mathematics in political science, sociology and economics, and ends with some illustrations of how these developments could lead to similar applications in both the practice and theory domains of educational administration.

The objective of this paper is to show the modernity of the approach developed by Carl Menger. The author argues that the Mengerian approach is part of a conceptual pattern composed of four interdependent, hierarchical and coherent parts (ontology, epistemology, methodology and key concepts) and that this conceptual pattern in all its originality and consistency fits perfectly within the approach of complexity. Ontologically (Section 1), the starting point is different from that of Léon Walras and William Stanley Jevons, the economy being apprehended as an open system; from an epistemological point of view (Section 2), Menger adopts a distinct conception of what constitutes a good scientific explanation, which contrasts with the Walrasian conception; methodologically (Section 3), his rejection of mathematics can therefore be understood as a consequence of his ontological and epistemological position: it is not mathematics as such that the author rejects but the functionalist tools then available, which are not adapted to his conception of economic reality; and finally the key concept (Section 4) of the author’s analysis is not that of equilibrium but an analysis of the process of exchange and production, with the emphasis placed on the emergence of organic phenomena.

Addresses the standardization of the measurements and the labels for concepts commonly used in the study of work organizations. As a reference handbook and research tool, seeks to improve measurement in the study of work organizations and to facilitate the teaching of introductory courses in this subject. Focuses solely on work organizations, that is, social systems in which members work for money. Defines measurement and distinguishes four levels: nominal, ordinal, interval and ratio. Selects specific measures on the basis of quality, diversity, simplicity and availability and evaluates each measure for its validity and reliability. Employs a set of 38 concepts ‐ ranging from “absenteeism” to “turnover” as the handbook’s frame of reference. Concludes by reviewing organizational measurement over the past 30 years and recommending future measurement reseach.

In this article recommendations are made on departmentalization in an institute of technology based on the research findings drawn from the field of organization theory. In the first place, it seems that the critical factor so far as organizational objectives is concerned is the conversion of the high level goal of the organization into operational sub‐goals for the various sub‐groups. Secondly, a consideration of motivational factors indicates that structuring each of the sub‐organizations around a “whole task” has important advantages. In the light of the discussion of the objectives of an institute of technology it seems appropriate that the departments should be goal‐oriented and should do their own teaching in the central and peripheral disciplines rather than use service departments. Care would have to be taken to ensure that these disciplines were taught by competent staff. It is likely that this would result in a coincidence of the departments' goals with those of the institute as a whole, a reduction of conflict within the organization, and the development of sound teaching by a multi‐disciplinary staff committed to the goals of the task‐oriented departments.

America’s patent rate (per 100,000 population) rose steeply to 34 from 1820‐1885, hovered between 28‐36 for the next 40 years then started its plunge to the present 18. This article examines the numerous possible causes often found in the literature ‐ expenditures on R&D, poor patent protection, high fees and pendency delays, decline in education in sciences and engineering, etc. While there is some evidence to support each of these, none is as important as the decline in our immigrants from Europe. Projections of possible improvements in our creativity and innovation in sciences and technology are bound in the characteristics of our present and future immigrant streams, and these are not expected to replace the role played by our previous immigrant streams.

Studies of inequality in higher education on both undergraduate and graduate levels have rarely examined experiences of Asians and Pacific Islanders (APIs). In this study, we focus on the experiences and outcomes of API students in doctoral education. More specifically, we examine socialization experiences and research productivity of three groups of students: domestic API, international API, and domestic white students. The results, based on a national cohort of PhD students in biology, reveal notable differences in experiences and outcomes of domestic and international API students. Although variation in socialization experiences explains differences in research productivity in the first year, that is not the case in the second year of doctoral study. In the second year, international API students have publication productivity comparable to their white peers, despite less favorable socialization experiences. Domestic API students, however, have lower research productivity than their white peers, even though they have comparable socialization experiences. Given the presumption of APIs’ success, especially in the STEM fields, findings for domestic API students are surprising and not aligned with the model minority stereotype. Contributions to research on API students, doctoral education, and socialization theory are discussed.

The first Principia Mathematica (1686) by Sir Isaac Newton with reference to natural philosophy and his system of the world has largely contributed to the first revolution in scientific thinking in modern times. It has created the conceptual basis of modern science in the classical tradition by providing the tools of analysis and the technique of reasoning in terms of stability—from—within or, as we would say today, the model of stable equilibrium conditions.

This paper takes as its starting point the apparent chaotic nature of a great deal of social life in the final years of the twentieth century. The breakdown of many nation states in Eastern Europe, uncontrolled urban growth and the expanding number of homeless refugees all suggest reasons why “chaos theory” has been attractive to social scientists. Providing its metaphoric nature is realized it may be helpful in providing an organizing principle for research. The concept of social polarization on the other hand, while addressing a number of the same issues, has the advantage perhaps of being more empirically grounded.