The role of reflection in mathematics learning

Reflective abstraction is central to the theory of constructivism as put forth by von Glasersfeld. In coming to know, persons make major cognitive advances by taking their actions as objects of thought. Leamers move beyond being in the action when they engage in reflection. There are serious limitations in the explain-practice method of instruction and active learning. Performing even self-generated mathematical operations does not have the power which results from reflecting on the activity. Problem-centered learning, an instructional strategy which has been shown to provide rich opportunities for reflection, is examined. The nature of reflection in mathematical activity is also considered.     

The Frontier of Web-based Instruction

In spite of advances in course design software and experience with online offerings, the question of how web-based education affects teaching and learning remains largely unanswered, and the terrain of online learning remains largely unmapped. In this paper, through the stories of 10 faculties of education and one computer science instructor in Ontario, we map out a small piece of the frontier of web-based course delivery and plot a course for future exploration. We argue that most existing offerings take the form of a Lone Ranger or Greenhorn approach but that there is a need to move toward a strategic institutional Wagon Train approach that consolidates and integrates support for online teaching and learning. We argue, as well, that failures in online instruction cannot simply be attributed to improper instruction or inappropriate course design. Rather, at least part of the problem locates in the ways in which conversation is structured in the online environment.     

Connecting Teacher Beliefs to the Use of Children’s Literature in the Teaching of Mathematics

This article presents examples that illustrate how teachers use childrens literature in the teaching of mathematics. The examples are related to four curriculum ideologies that have influenced mathematics education in the USA for the last 75 years. It discusses why it is relevant to help teachers understand the ideological positions that influence their use of childrens literature during mathematics instruction, summarizes the four ideological positions, and presents results of a study of how teachers ideological positions relate to their use of childrens literature in the teaching of mathematics. The study examines two research questionsCan an instructional tool be developed that will highlight for teachers the different ways in which they and others use childrens literature to teach mathematics? and Can that instructional tool stimulate teacher discussion and reflection about their own beliefs and the ideological nature of the instructional environment in which they learned (as students) and teach (as teachers)? Study results indicate that both questions can be answered in the affirmative.     

Enhancing teaching through constructive alignment

Two lines of thinking are becoming increasingly important in higher educational practice. The first derives from constructivist learning theory, and the second from the instructional design literature. Constructivism comprises a family of theories but all have in common the centrality of the learner's activities in creating meaning. These and related ideas have important implications for teaching and assessment. Instructional designers for their part have emphasised alignment between the objectives of a course or unit and the targets for assessing student performance. Constructive alignment represents a marriage of the two thrusts, constructivism being used as a framework to guide decision-making at all stages in instructional design: in deriving curriculum objectives in terms of performances that represent a suitably high cognitive level, in deciding teaching/learning activities judged to elicit those performances, and to assess and summatively report student performance. The performances of understanding nominated in the objectives are thus used to systematically align the teaching methods and the assessment. The process is illustrated with reference to a professional development unit in educational psychology for teachers, but the model may be generalized to most units or programs in higher education.     

A Textbook Case of the Nature of Science: Laws and Theories in the Science of Biology

The two concepts law and theory are among the most important elements of the nature of science. They represent both the tools and products of science itself. Unfortunately, the variable meanings and use of these terms in general discourse and in other school disciplines results in much confusion with respect to their proper application in a science context. The project included the design of a six-part model definition for law and theory based on a review of the literature of the philosophy of science with special reference to biology. These model definitions were then compared with those provided in a range of U.S. secondary school biology textbooks. The majority of all current major U.S. secondary school biology texts were reviewed and analyzed with respect to how the concepts of law and theory were defined and applied, in an attempt to determine whether students and teachers using such texts would gain an accurate impression of these terms and the distinction between them. This study focuses on biology instruction since a life science course is completed as a graduation requirement by virtually all U.S. high school students and as such serves as a widely shared educational experience across the nation. The term law is rarely defined in any text but various laws such as those found in genetics are frequently included as examples. The term theory is frequently defined but with a wide range of completeness of the definitions. Only rarely are theories in biology included as examples.     

Alternative frameworks,conceptual conflict and accommodation: Toward a principled teaching strategy

Students' alternative frameworks (frequently regarded as misconceptions) play a crucial role in science concept learning. Accumulated research findings indicate that alternative frameworks are resistant to extinction despite formal instruction.This paper presents an instructional strategy based on the thesis that science concept learning involves cognitive accommodation of an initially held alternative framework. The strategy consists of three phases: (1) exposing alternative frameworks, (2) creating conceptual conflict, (3) encouraging cognitive accommodation. The first phase is facilitated through an exposing event, while the second and third focus on a discrepant event.The authors have used previous research findings about student alternative frame-works for the structure of a gas to create exposing and discrepant events for an introduction to the particle model of gases. The paper presents a case study of two lessons in a sequence on the particle model, accompanied by an analysis of the phases of the instructional strategy employed for cognitive accommodation.Based on a paper presented at the AERA convention, Los Angeles, California, April, 1981.This paper was prepared while the first author was a visiting professor at Cornell University, Ithaca, New York.     

Hierarchies in children's learning: A symposium

There has been a continuing increase in the application of hierarchy theory to the problems of instruction and evaluation, since Gagné first used the term hierarchy in his theory of how human beings acquire complex skills and knowledge. This article, based on a 1970 symposium of the American Educational Research Association, presents an overview and analysis of the use of learning hierarchies in instruction and research, examines some current research on learning hierarchies, and considers the implications of this research for instructional psychology and for theories of cognitive development.Lauren B. Resnick is with the University of Pittsburgh, Pittsburgh, Pennsylvania     

CHEMMAT: Adaptive Multimedia Courseware For Chemistry

The trend towards Multimedia technology in Education is exemplified by the growing number of multimedia ready classrooms. Besides using the conventional computer-based training techniques, courseware has included multimedia capabilities, such as graphics, sound, animation, and video clips. This paper illustrates the development of such multimedia courseware. Additionally, this courseware employs sound instructional and learning strategies; thereby making the courseware not only educational, but also captivating. The other unique feature of the courseware is its adaptability. Teachers who are not computer experts can use the Teacher module to modify and add content to the courseware. By selecting the predefined objects, and/or filling in a form, the teachers can create simple animation by using the module. Another good feature is the ease of customizing the content in different languages. This is illustrated by the translation of a module in CHEMMAT into Chinese.     

Integrated learning systems: An application linking technology with human factors and pedagogical principles

The development of integrated learning systems (ILSs) holds great promise for enhancing the instructional process and for improving student learning. This article describes an application of an ILS that takes into account learning theory research, principles of instructional design, and other factors related to human learning. The application presented utilizes IBM's Advanced Technology Classroom to verify the efficacy of integrated learning systems from both a student-user perspective and the perspective of instructors in a university setting.She has also been the Research Director for the IBM Advanced Technology Classroom at the university.     

Education of the refugee in the United States

Conclusion This historical survey of the educational goals developed on behalf of the immigrant and refugee in America indicates that there has been a complete cycle. The first systematic educational efforts, as we have shown, were aimed at teaching the immigrant the English language so that he would be useful for his tasks in American industry. Then came the period which extended this educational goal by offering instruction in several aspects of acculturation (officially, assimilation, but a concept which has never been put into effect in the history of America's minorities). The post-war period saw the stress on the academic level on the cultural democracy concept; but this ideal has been more academic than practical, and World War II saw no definite evidences of the popular interest in any Americanization program. The recent waves of refugees, bringing in more or less well-educatedindividuals, saw a revival of educational efforts on their behalf; but they differ from the former endeavors in their emphasis on individual education and on instruction in English. The social aspects of acculturation — featuring, in general, the period between World War I and II — have been entirely ignored 1).     

Theoretical Eclecticism in the College Classroom

In this article we argue that student learning is enhanced by theoretical eclecticism, which we define as intentionally drawing on different theories of learning when making instructional decisions to provide students with the instructional support they need to be successful. We briefly review the literature on four views of learning and on learner-centered approaches to instruction and then integrate this literature with Barr and Taggs (1995) distinction between the instruction paradigm and the learning paradigm. Finally, we present examples from a teacher education course to illustrate how theoretical eclecticism can be used to support student learning.Anastasia S. Morrone is the Executive Director of the Center for Teaching and Learning and an Associate Professor of Educational Psychology in the School of Education at Indiana University-Purdue University Indianapolis. She received her B.S. degree in Technical Communication from the University of Minnesota and her Ph.D. degree in Educational Psychology from the University of Texas at Austin. Her research interests center around instructional practices that promote college student motivation and learning. Terri A. Tarr is the Director of the Instructional Design and Development unit of the Center for Teaching and Learning and the Director of Associate Faculty Development at Indiana University-Purdue University Indianapolis. She is also an adjunct assistant professor in the Department of Psychology. She earned the Ph.D. in Developmental Psychology from Purdue University as well as an M.A. in School Psychology and a B.A. in Psychology from Ball State University. Her special interests are individual differences in learning and effective practices in faculty development     

Towards minimizing social,cultural, and intellectual disruptions embedded in literacy instruction

A personal attempt to make sense of the diverse array of information, both practical and theoretical, about the complex concept called literacy is articulated through the development of the Integrative Systems Model of literacy. The model illustrates how understanding literacy has direct applications to both instruction and research. As well, the model's utility in reconciling opposing concepts of literacy is shown. Finally, some practical suggestions for literacy instruction consistent with the model and which appear to minimize social, cultural, and intellectual disruption are presented.     

Student learning work: Grounds for anin situ analysis

The ethnomethodological programme of studies of work is drawn on to provide a general framework within which we might develop ways to undertake thein situ analysis of the competencies which constitute student learning activities. The objective of such research is to describe the locally managed and temporally organised nature of student learning work. Emphasis is placed on the development of methods of investigation which will enable us to describe the whatness of the work from within the setting of that work's accomplishment. The twin conceptions of the visibility and sequential order of student activities are discussed in detail. The implications of this approach for the notion of student learning are also examined.     

Influence of problem familiarity on learning in a problem-based course

The results of an experimental study investigating the influence of problem familiarity on learning in a problem-based psychology course are presented. Participants worked with either a familiar or an unfamiliar version of the same problem. The following measurements were taken (1) a measure of problem quality as perceived by students, (2) number of explanations of the problem put forward by the students while discussing it, (3) quality of learning issues derived from the discussion, (4) amount of time spent on self-study, and (5) the amount of knowledge acquired as indicated by a test. The results demonstrate that participants in the familiar problem condition perceived the problem to be of higher quality than the participants in the unfamiliar problem condition. No significant differences in learning were found. The findings do suggest, however, that problems may be improved by making them more relevant to the everyday experience of students.     

Higher education's role in educating the older worker

Educational programs for mature adults have become widespread in the past few years but still attract only a small minority of the potential older population. One approach to increasing enrollment is to gain access to older people through their place of employment. This offers the advantages of a captive group, clear objectives for the instructional experience, a supportive environment, and a substantial experience base on which to plan the instruction. European industrial training of older workers offers substantial insight and application to the U.S. and may prove a boon to both educators and employers.     

Do transitional classrooms really provide transitional time?

In the United States, kindergarten marks the beginning of formal schooling for more than 3 million children each year (Shepard & Smith, 1986). At the end of the kindergarten year, most of these children demonstrate expected levels of achievement and are promoted to traditional first-grade classrooms. Others are labeled unready or immature for successful performance in today's academically rigorous first grade. In most elementary schools, the placement for these at-risk children is either retention in kindergarten or social promotion to first grade. An alternative in approximately 17% of the nation's elementary schools is assignment to a transitional classroom between kindergarten and first grade (Educational Research Service, in press). This additional year of instruction is often viewed as a gift of time — time for children to mature and make a gradual transition from kindergarten to first grade.Judith E. Stroud is Assistant Professor of Elementary Education, Ball State University, Munice, IN. R. Ann Williams is Professor of Elementary Education, Ball State University, Muncie, IN.     

Fostering Distributed Science Learning Through Collaborative Technologies

TACTICS (French and Spanish acronym standing for Collaborative Work and Learning in Science with Information and Communications Technologies) is an ongoing project aimed at investigating a distributed community of learning and practice in which information and communications technologies (ICT) take the role of collaborative tools to support social construction of knowledge. This community is composed of researchers, graduate students, and high-school teachers and their students, from six schools and four universities in Canada and Mexico. It set out in fall 2000 to develop a community around the general topic of integrating concepts in science school subjects. Once a prototype community is established, it can become a terrain where different aspects could be studied. Subsequently, researchers could gradually take a back seat allowing as well as ensuring the autonomy of the school members involved and, thereby, the viability of the learning community. The set up of the proposed prototype distributed science learning community was therefore an essential yet far from trivial first step. This paper discusses the process of setting up the community and the lessons learned.     

Transactive Peer Tutoring: Distributing Cognition and Metacognition

ASK to THINK—TEL WHY®© is an inquiry-based model of mutual peer tutoring in which tutoring partners mediate each others' learning in a transactive manner. This tutorial model is designed as a person-plus cognitive partnership that supports the distribution of cognition and metacognition in order to promote complex, higher-level learning. This article focuses on what is being distributed during ASK to THINK—TEL WHY®© (i.e., the cognitive tasks of questioning, explaining, thinking, problem solving, as well as monitoring and regulation of learning) and how these cognitions are distributed across the tutoring pair and various aspects of their learning environment. Results of research on the effectiveness of using this model in classroom contexts has shown that the model promotes students' construction of new knowledge.     

The relationship between attributes of a children's radio program and its appeal to listeners

An approach was developed to investigate the link between attributes of a children's radio program and children's judgments of appeal. Program tapes were divided into 28 segments and were rated for the presence of 30 attributes. Through multidimensional scaling analysis, attributes were organized into six clusters of Superattributes on the basis of their co-occurrence across the 28 segments. Superattributes were labeled and assigned scores that reflected the degree to which each was present in the 28 segments. A sample of 42 children 8–12 years old listened to the test tapes and provided a written judgment of their interest in the program at each segment. Results revealed that the Superattributes Instruction, Intro Talk, and Jokes were negatively associated with children's interest, while Popular Music was positively correlated with interest. In planning programs and understanding the effects of radio on children, designers and researchers should pay special attention to those formats in radio programming that are familiar to children, especially popular music and instructional material.     

The marginal costs of instruction

This is a study of the costs of instruction in a large public research university. It departs from other work on instructional costs in its attempt to draw inferences about the economic costs of incremental or marginal enrollments. Focusing on graduate education, we examine how the costs directly facing faculty differ from those incurred by the institution's administration and legislature as reflected in the budgetary rewards for instruction. These cost differences provide the wherewithal for a university to carry out basic research and other important functions that lack a paying clientele. The study also explores the roles of economic costs in the institution's pricing of graduate education.