Children's Judgments of Durations: A Modified Replication of Piaget's Study

One hundred students, 25 each in grades 2, 4, 6, and 8, were individually interviewed. A cylindrical beaker with five equidistant levels marked on it was presented first, and a pear‐shaped separation funnel was also presented. The funnel had a “faucet” at the bottom that allowed water to start and stop running into the beaker. The interviewer asked the child to mark the water levels on the funnel when the water had run to the first level in the beaker, to the second level, to the third level, and so on. The levels on the funnel thus varied a great deal depending on its diameter. The interviewer then asked, “Did the water take the same amount of time to go down from this level to the next in the funnel as it did to go up from this level to the next in the beaker?” It was found that correct judgments about durations were not made before eighth grade (the criterion being 75% of the eighth graders giving correct answers). This grade level was considerably later than the age of 7 or 8 (second grade) that Piaget reported.     

Latinos In Higher Education: Today and Tomorrow

Abstract

Several dozen faculty and staff members went off-campus to reflect for a day about the quality of their institution's undergraduate program. To frame the discussion, participants read in advance Willimon and Naylor's, The Abandoned Generation (see box), a critical examination of the contemporary undergraduate experience. The English professor leading the retreat claimed to lack experience in facilitating such events. Nevertheless, he deftly brought the group to consensus on more than a few points, using a decision rule borrowed from his Shakespeare class: “We assume consensus unless two or more people disagree with an observation.”     

Categorical Abstract Algebraic Logic: Ordered Equational Logic and Algebraizable PoVarieties

A syntactic apparatus is introduced for the study of the algebraic properties of classes of partially ordered algebraic systems (a.k.a. partially ordered functors (pofunctors)). A Birkhoff-style order HSP theorem and a Mal’cev-style order SLP theorem are proved for partially ordered varieties and partially ordered quasivarieties, respectively, of partially ordered algebraic systems based on this syntactic apparatus. Finally, the notion of a finitely algebraizable partially-ordered quasi-variety, in the spirit of Pałasińska and Pigozzi, is introduced and some of the properties of these quasi-povarieties are explored in the categorical framework.      

The Future of Logic: Foundation-Independence

Throughout the twentieth century, the automation of formal logics in computers has created unprecedented potential for practical applications of logic—most prominently the mechanical verification of mathematics and software. But the high cost of these applications makes them infeasible but for a few flagship projects, and even those are negligible compared to the ever-rising needs for verification. One of the biggest challenges in the future of logic will be to enable applications at much larger scales and simultaneously at much lower costs. This will require a far more efficient allocation of resources. Wherever possible, theoretical and practical results must be formulated generically so that they can be instantiated to arbitrary logics; this will allow reusing results in the face of today’s multitude of application-oriented and therefore diverging logical systems. Moreover, the software engineering problems concerning automation support must be decoupled from the theoretical problems of designing logics and calculi; this will allow researchers outside or at the fringe of logic to contribute scalable logic-independent tools. Anticipating these needs, the author has developed the Mmt framework. It offers a modern approach towards defining, analyzing, implementing, and applying logics that focuses on modular design and logic-independent results. This paper summarizes the ideas behind and the results about Mmt. It focuses on showing how Mmt. provides a theoretical and practical framework for the future of logic.     

2n-布尔值逻辑:2-值命题逻辑的自然推广

将2-值命题逻辑的语义理论推广到了有限布尔代数,得到了2n-布尔值命题逻辑.同时本文给出了2n-布尔值命题逻辑应用的一些例子.     

Universal Logic: Evolution of a Project

We discuss the origin and development of the universal logic project. We describe in particular the structure of UNILOG, a series of events created for promoting the universal logic project, with a school, a congress, a secret speaker and a contest. We explain how the contest has evolved into a session of logic prizes.     

A Comparison of Sentential Logic Skills: Are Teachers Sufficiently Prepared to Teach Logic?

A sentential logic test consisting of 30 items was administered to advanced 7th grade, 8th grade, and 12th grade students and preservice secondary mathematics teachers in 1986 and 1992. The resulting data were compared with data obtained in a similar study conducted in 1976. An examination of the changes in scores by age level according to item type and semantic form was made over the three data collection periods. The results indicate that the impact of maturation and/or education has decreased in its effect on the development of logic skills. Concern is raised over preservice teachers' level of understanding of sentential logic.     

Literacy, Matheracy, and Technocracy: A Trivium for Today

This article focuses on the relations between mathematics and mathematics education on the one hand and human behavior, societal models, and power on the other. Based on a critical analysis of school systems and of mathematical thinking, its history and its sociopolitical implications, anew concept of curriculum is suggested, organized in 3 strands: literacy, matheracy, and technoracy. This new concept sees education and scholarship as pursuing a major, comprehensive goal of building up a new civilization that rejects arrogance, inequity, and bigotry. Because the development of mathematics has been intertwined with all forms of human behavior in the history of human- kind, it is relevant to discuss mathematics and mathematics education with this major goal in mind.     

Resource Review: Supporting the New Students in Higher Education Today

Abstract

It would be nice if there were a demonstrable relationship between the price that a college or university charges and the product that it delivers. Institutions with superior market positions most often make that claim, whether true or not, when defending their higher prices—stating that what the student pays for is both a better and a different educational experience. Those vaunted differences ought to include what faculty do before a course begins, how they prepare for the daily challenge of the classroom, how they administer their courses and assess their students' progress, and how frequently they interact with students outside of the classroom.

The National Center for Postsecondary Improvement (NCPI) is supported under the Educational Research and Development Center program, agreement number R309A60001, CFDA 84.309A, as administered by the Office of Educational Research and Improvement (OERI), U.S. Department of Education. The findings and opinions expressed by NCPI do not necessarily reflect the position or policies of OERI or the U.S. Department of Education. The Institute for Research on Higher Education retains the copyright for this column.     

Efficiency and Cross-efficiency in DEA: Derivations,Meanings and Uses

In this paper we examine a neglected aspect of Data Envelopment Analysis: cross-efficiency. We develop the concept of cross-efficiency in a number of new directions. We ground an intuitive understanding of cross-efficiency in the concept of peer-appraisal, as opposed to self-appraisal implied by simple efficiency, and discuss the relative merits of each. We also present mathematical formulations of, and intuitive meanings for three possible implementations of aggressive and benevolent cross-efficiency. We have implemented two of these formulations in computer programs; their performance is compared empirically on a real data set. Finally, we suggest practical uses for cross-efficiency, illustrated with reference to the same data set.     

Categorical Abstract Algebraic Logic: Algebraizable Institutions

The framework developed by Blok and Pigozzi for the algebraizability of deductive systems is extended to cover the algebraizability of multisignature logics with quantifiers. Institutions are used as the supporting structure in place of deductive systems. In particular, the concept of an algebraic institution and that of an algebraizable institution are made precise using the theory of monads from categorical algebra and the notion of equivalence of institutions introduced by Voutsadakis. Several examples of algebraic and algebraizable institutions are provided.     

Attributing Meanings to Representations of Data: The Case of Statistical Process Control

This article is concerned with the meanings that employees in industry attribute to representations of data and the contingencies of these meanings in context. Our primary concern is to more precisely characterize how the context of the industrial process is constitutive of the meaning of graphs of data derived from this process. We draw on data from a variety of sources, including ethnographic studies of workplaces and reflections on the design of prototype learning activities, supplemented by insights obtained from trying out these activities with a range of employees. The core of this article addresses how different groups of employees react to graphs used as part of statistical process control, focusing on the meanings they ascribe to mean, variation, target, specification, trend, and scale as depicted in the graphs. Using the notion of boundary crossing, we try to characterize a method that helps employees to communicate about graphs and come to data-informed decisions.     

从事实逻辑到任务逻辑

在经典命题逻辑语言中引入附加算子几,较系统地研究近几年刚刚被提出的任务逻辑。这里把公式理解为“任务”,介绍了“任务逻辑”的语义理论,并从语构上定义形式系统L与之对应,证明该系统的可靠性、完备性及可判定性定理．最后建立系统L中的一系列基本定理。