An Expanded Taxonomy of Sorting Algorithms

I present an expanded taxonomy of sorting algorithms that is based upon Merritt's inverted taxonomy [1] and Lau's logic‐based derivations [2, 3]. The inverted taxonomy was based on a higher level, more abstract, and conceptually simple top‐down approach to sorting than the traditional taxonomy such as that given by Knuth [4], Work done in automatic program synthesis suggested the approach. Sorts were divided into two categories, hardsplit/easyjoin and easysplit/hardjoin, of which quicksort and mergesort are the canonical examples, respectively. Lau's [2, 3] logic‐based derivations strengthen the inverted taxonomy by deriving comparison‐based sorting algorithms that fall into the two categories of hardsplit/easyjoin and easysplit/hardjoin. Moreover, they expand the taxonomy by deriving distributive algorithms in a symmetric way.     

Discovering Functional Programming Through Imperative Languages

The pedagogical desirability of functional programming is effectively swamped by an overwhelmingly imperative‐language‐oriented culture. Because a meaningful subset of the functional paradigm is accessible within imperative languages, it is possible to identify a subset of Modula‐2 that characterizes the functional paradigm subset. A series of list‐processing problems and their solutions in the Modula‐2 subset provides students with ample exposure to the practice and theory of functional programming. Extension to the full functional paradigm and migration to specialized functional languages are managed, in the worst case by initial pseudo‐Modula‐2 programming involving hypothetical extensions supporting higher‐order functions and polymorphism. More powerful solutions to this problem are foreshadowed, in the form of preprocessor implementations of Modula‐2‐ and Ada‐derivative functional languages.     

A Data‐Parallel Programming Library for Education (DAPPLE)

In the context of our goal to bring parallel computing into the undergraduate curriculum, we needed a parallel‐programming language that was accessible to students and independent of any particular hardware platform. Finding nothing appropriate, we chose to design our own language. The result, DAPPLE, is a C++ class library designed to provide the illusion of a data‐parallel programming language on conventional hardware and with conventional compilers. DAPPLE defines Vectorand Matrixclasses, with most C++ operators overloaded to provide elementwise arithmetic, and supports data‐parallel operations like scans, permutations, and reductions. DAPPLE also provides a parallel if‐then‐else statement to restrict the scope of the above operations to partial vectors or matrices. In this article we describe the DAPPLE language, the pedagogical decisions that went into its design, and our experience using DAPPLE in the classroom. DAPPLE is freely available on the Internet.     

Career‐span education for the chemistry teacher

This paper considers the implications of the Cognitive Acceleration through Science Education (case) project results for science teaching methods. Results are summarized briefly and then the peculiar features of the case methodology and subject‐matter are described and consideration given to how they could be incorporated into any science curriculum. In particular, the use of cognitive conflict, metacognition, and bridging are described, and set in the context of the development of formal operational thinking. Finally, the potential roles of printed materials and INSET are reviewed for introducing such features into the professional repertoire of science teachers.     

Case‐Based Teaching: Four Experiences in Educational Software Design

Abstract

Good teaching is good story telling. Case‐based teaching exploits the basic capacity for students to learn from stories and the basic desire of teachers to tell stories that are indicative of their experiences. The premise of software that used case‐based teaching would be to place a student in a situation that the student found interesting and where the telling of a story would be appreciated. First, case‐based teachers teach the student what he or she needs to know at precisely the point of becoming interested in knowing the information. This information should be presented in the form of stories. Law schools and business schools have been teaching this way for years. They teach cases rather than rules because, by and large, they don't have rules to teach. The second critical part of learning in a case‐based environment is teaching a student to abstract from what the student has been told, and adapting it to situations for which the student was not specifically trained.

At the Institute, we have, to date, built four examples of case‐based teaching software. The programs are:

VICTOR — a voice and image courtesy tutor — built for Ameritech

DUSTIN — a language experience — built for Andersen Consulting

CREANIMATE — a biology experience‐built for schools and supported by IBM

TAXOPS — a tax opportunity advisor and cross seller — built for the Tax division of Arthur Andersen     

Enterprise,Economic and Industrial Awareness: making the links in initial teacher education ‐‐ two case studies

Abstract

Two case studies of work in initial teacher education provide the stimulus for a discussion of the incorporation of enterprise, economic and industrial issues within student programmes’. The first case study describes a seminar at Manchester University where these issues are introduced to students within the constraints of a 36‐week PGCE course. The second describes IT‐INSET activities undertaken by primary BEd students from Edge Hill College of Higher Ecucation.

A number of issues are raised, not least of which is the need to overcome student concerns about the incorporation of the National Curriculum cross‐curricular themes into teaching. The conclusion reached is that much work remains to be done and some possible future developments are examined.     

Triple‐X and passivity — barriers to learning

Abstract

Triple‐X Syndrome is a little‐known condition that is found in approximately one‐in‐a‐thousand girls. The effects are not readily observable and are variable, particularly in the area of academic achievement. However, passivity and delayed expressive language skills are generally noted as characteristics of the syndrome and are very likely to have implications for the child's learning. The extremely passive nature of the child may mean that explicit and direct teaching is required if learning is to keep pace with peers. This paper presents a single case study involving a seventeen‐year‐old girl with Triple‐X. It describes and explains a ’later’ intervention program based on sight recognition of common words, use of controlled text, short‐term auditory memory training, and development of semantic skills and working memory. The program proved successful in improving reading, short‐term memory, and spoken language skills.     

A Visualization System for Correctness Proofs of Graph Algorithms

In this paper we describe a system for visualizing correctness proofs of graph algorithms. The system has been demonstrated for a greedy algorithm, Prim's algorithm for finding a minimum spanning tree of an undirected, weighted graph. We believe that our system is particularly appropriate for greedy algorithms, though much of what we discuss can guide visualization of proofs in other contexts. While an example is not a proof, our system provides concrete examples to illustrate the operation of the algorithm. These examples can be referred to by the user interactively and alternatively with the visualization of the proof where the general case is portrayed abstractly.     

Structural Zeros and Their Implications With Log‐Linear Bivariate Presmoothing Under the Internal‐Anchor Design

In equating, when common items are internal and scoring is conducted in terms of the number of correct items, some pairs of total scores (X) and common‐item scores (V) can never be observed in a bivariate distribution of X and V; these pairs are called structural zeros. This simulation study examines how equating results compare for different approaches to handling structural zeros. The study considers four approaches: the no‐smoothing, unique‐common, total‐common, and adjusted total‐common approaches. This study led to four main findings: (1) the total‐common approach generally had the worst results; (2) for relatively small effect sizes, the unique‐common approach generally had the smallest overall error; (3) for relatively large effect sizes, the adjusted total‐common approach generally had the smallest overall error; and, (4) if sole interest focuses on reducing bias only, the adjusted total‐common approach was generally preferable. These results suggest that, when common items are internal and log‐linear bivariate presmoothing is performed, structural zeros should be maintained, even if there is some loss in the moment preservation property.     

The Development of Individualized Audio‐Visual Learning Units in Junior High School Biology and the Students’ Achievements

Summaries

English

The development of series of audio‐tutorial units for biological education at junior high school level is described. The effectiveness of these units was tested with students from a Kibbutz school and found to produce higher achievement than a ‘normal’ teaching approach, based on the BSCS Yellow Version (Israeli adaptation) materials. The audio‐tutorial method led to a particularly high achievement gain in the case of girls. The achievement gains resulting from the audio‐tutorial approach are explained in terms of the motivational effect of this method on students.     

Does socioeconomic sorting of teacher qualifications exacerbate mathematics achievement inequity? Panel data estimates from 20 years of TIMSS

Recent and older studies have reported either a persistence or a widening of the socioeconomic achievement gap—the difference in performance between students in top and bottom socioeconomic groups. Using a panel data technique with country fixed effects for 32 education systems and six waves of data from the Trends in International Mathematics and Science Study, we examine whether the sorting of teachers by specialization level in mathematics education and novice status across students of different socioeconomic backgrounds exacerbates mathematics achievement inequity despite the presence of a time-varying control for socioeconomic school segregation. We find modest evidence that sorting by mathematics education is associated with achievement inequity, but no evidence supporting the importance of sorting based on teacher experience. Socioeconomic school segregation, on the other hand, clearly and persistently exacerbates achievement inequity. The results have policy implications regarding the effective distribution of educational resources.Availability of data and materialsThe data are freely available via the TIMSS data repository.     

Educational opportunities for adult disabled persons

Abstract

Educational opportunities for adult disabled persons are limited, despite the growing consensus on their importance. Unesco has assembled case studies of provision for disabled adults from eight countries. These are analysed here in terms of five aspects: disabled and non‐disabled adults studying together; facilitating the study situation; training for independent living; sociocultural and creative stimulation; and increasing public awareness of disability. Guidelines for future action are set out.     

Web‐enhanced alternative teacher licensure

Abstract

College and university teacher education programs are increasingly required to integrate technology into teacher preparation in response to the requirements of national accreditation groups like the International Society for Technology in Education (ISTE) and the National Council for Accreditation of Teacher Education (NCATE). Delivery of teacher education programs through pure distance education methodologies still has critics. A Web‐enhanced approach, with on‐campus courses and Web‐based information and/or testing as a supplement, is suggested as a compromise. An alternative teacher licensure program in career and technical education at Ohio State University uses this approach extensively, with positive results. This case study explores the use of an alternative teacher licensure program, defines the components of a Web‐based curriculum, and illustrates the benefits and challenges of a Web‐enhanced teacher education program. Student and faculty issues and reactions are outlined, along with strategies for integrating Web‐based activities into courses. Suggested future plans for continuing to infuse technology into teacher education are also discussed.     

Computer Toolkits in Special Education

Abstract

Modular software tools and common user‐interfaces have much to offer special education, especially in reducing the problems a child (and sometimes a teacher) has in understanding complex modes. Examples are given of mode‐free toolkits used in the design of a Smart Wheelchair, and in an assessment kit for tailoring communication aids. Toolkit metaphors are outlined. The multiple control and learning tasks for a handicapped user of computers is related to potential toolkit metaphors available to designers. The case is made for common operating systems powerful enough to support those metaphors requiring advanced features like multi‐tasking.     

A Case Study in ADT Implementation Verification

This article proposes a unit on program verification that could be included in are intermediate‐level undergraduate course. A linked cursor implementation within an array for the binary search tree abstract data type (ADT) is used ASA case study. The proofs of correctness for the ADT operations are given in a careful, but informal style consistent with the level of formality common in discrete mathematics and calculus courses.     

Enhancing the Executive Functions of 3‐Year‐Olds in the Dimensional Change Card Sort Task

Executive functions enable flexible thinking, something young children are notoriously bad at. For instance, in the dimensional change card sort (DCCS) task, 3‐year‐olds can sort cards by one dimension (shape), but continue to sort by this dimension when asked to switch (to color). This study tests a prediction of a dynamic neural field model that prior experience with the postswitch dimension can enhance 3‐year‐olds' performance in the DCCS. In Experiment 1A, a matching game was used to preexpose 3‐year‐olds (n = 36) to color. This facilitated switching from sorting by shape to color. In 3 , 3‐year‐olds (n = 18) were preexposed to shape. This did not facilitate switching from sorting by color to shape. The model was used to explain this asymmetry.     

“元语言”与“字本位”理论的结合研究

以“字本位”理论为指导,研究释义元语言：首先,选定研究对象,整理出常用字和通用字;然后,通过单字的排列组合来生成新词,并对新词进行分类、筛选、优化,构建基本的释义元词;最后,参照其他的相关材料,整理出释义元词的核心词汇。     

Effectively integrating the computer to teach children with literacy difficulties

Abstract

Two case studies (a 6–8 year old girl and a 10–12 year old boy) are discussed. These will show structured, sustained multi‐sensory teaching, integrated where appropriate with a range of good educational software, for reading, writing and spelling, can enhance and optimize literacy learning as well as improving self‐esteem.

The importance of such students using software in the classroom is shown. If they are provided with this kind of programme they can look positively towards the future but without it (and currently too many do not have it) life is likely to be very hard indeed for them.     

Interdisciplinary In‐service at the University: a participatory case‐based model for professional development

Abstract

The Participatory Case‐Based Model for Professional Development is an in‐service model which is useful across the human service disciplines (social work, occupational therapy, public health, special education, early childhood and family education). In the model, participants enrolled in a graduate course engage in dialogue and perspective‐taking, through case analysis and case writing. Using grounded theory and inductive data analyses, the major effects of this professional development model were studied. These effects included: (1) gaining new knowledge; (2) ‘really seeing’ from multiple perspectives; and (3) developing a sense of support, renewal and networking across various professions. Connections to the selected professional development literature —; problem‐based learning, case process and effects, and the practical argument model — offered affirmations and challenges to the Participatory Case‐Based Model for Professional Development