An Objectivist Critique of Relativism in Mathematics Education

Many constructivists tag as `absolutist' references to mathematics as an abstract body of knowledge, and stake-out the moral high-ground with the argument that mathematics is not only utilised oppressively but that mathematics is, in-itself, oppressive. With much reference to Ernest's (1991) Philosophy of Mathematics Education this tag has been justified on the grounds that if mathematics is a social-cultural creation that is mutable and fallible then it must be social acceptance that confers the objectivity of mathematics. This paper argues that mathematics, albeit a social-cultural creation that is mutable and fallible, is a body of knowledge the objectivity of which is independent of origin or social acceptance. Recently, Ernest (1998) has attempted to express social constructivism as a philosophy of mathematics and has included the category of logical necessity in his elaboration of the objectivity of mathematics. We argue that this inclusion of logical necessity not only represents a U-turn, but that the way in which Ernest has included this category is an attempt to maintain his earlier position that it is social acceptance that confers the objectivity of mathematics.     

Prevalence,School Progress and Referral of Mildly Retarded Children in Regular Classes

This study sought to determine the prevalence of mildly retarded children in a sample of 312 primary school classes (N (pupils) = 8,967). Schools were chosen at random from each of the eight Psychological Service districts of metropolitan Auckland; all Grade 2‐5 classes in the sample schools were included in the investigation. Eighty percent of the teachers surveyed believed they had one or more mildly retarded children in their classes, yielding an overall prevalence rate of 8.04 percent (N = 721). Approximately one‐third of the children designated as mildly retarded were considered by their teachers to be not coping academically as well as socially, but of these 75 percent had not been referred for special educational consideration. Comparisons among the eight districts revealed that prevalence/referral rates and characteristics of identified/referred children did not differ significantly across districts. Results are discussed in terms of their policy implications for the identification and referral of mildly retarded children in need of special educational services.     

Students' ability to visualize set expressions: An initial investigation

Visualization is a powerful tool for understanding and solving mathematical problems. The use of Venn diagrams to visualize set expressions, however, is problematic for many students and may actually hinder their problem-solving efforts. In this study, 92 university students construct visual representations of eight set expressions. Through the use of a production system model and detailed analyses of students' work and verbal protocols, it is discovered that (1) competent and error-prone students construct and use procedures to complete set translation tasks, and (2) two-thirds of the observed errors arise from the consistent implementation of ill-formed procedures. The procedural origins of students' errors are identified and conjectures are offered regarding the perceptions and experiences that lead to the development of erroneous translation procedures.NotesThis article is based on the author's doctoral dissertation completed in 1992 at Indiana University under the direction of Frank K. Lester.     

The impact of relational markers on expository text comprehension in L1 and L2

This article reports on an experimentinvestigating the impact of causal discoursemarkers (connectives and signaling phrases) onthe comprehension of expository texts in L1 andL2. Although several psycholinguistic studieshave investigated the impact of connectives andlexical markers of text structure oncomprehension (i.e. off-line), there is noconsensus on the exact effect of explicitdiscourse markers on text understanding; threedifferent findings are reported in theliterature: markers would have a facilitatingeffect, an interfering effect or no effect atall. The first goal of this article is toclarify this problem of contradicting resultsby limiting the scope of the study to causalrelations, and to one specific text type:expository texts. Furthermore, the naturalnessof the experimental texts was controlled,readers did not need specific backgroundknowledge to understand the texts and theexperimental method consisted of open answerquestioning. Our second goal is to investigateto what extent a supposed effect of linguisticmarking depends on readers proficiency in afirst or second language.The experiment consisted in the reading of short expository texts in two languages, Dutchand French, which both functioned as L1 and L2.The results indicate that readers benefit fromthe presence of causal relational markers bothin L1 and in L2. Implications for (theoriesof) text processing are discussed, as well asfor the further insights in readingcomprehension in L1 and L2.     

The influence of activity-based elementary science programs on classroom practices: A quantitative synthesis

The results of 11 studies of classroom practices used with the activity-based elementary science programs, ESS, SCIS, and SAPA, were combined quantitatively. All studies included control groups and employed techniques for coding lesson events. A composite category system was developed for combining study results. It was found that teachers using activity-based programs spent about 10% more time on student activity and 10% less time on talk than teachers using traditional methods. More direction giving, more higher level questions, and less lecturing were also reported. Teachers trained in program use spent less time giving directions, more time on activities, and less time on talk than untrained teachers using the programs. On the average, researchers coded slightly less student talk and slightly less student-initiated talk in activity-based classrooms.     

A new approach to assessing the technological complexity of different categories of R&D (with examples from Singapore)

This paper attempts to develop a set of generic questions the answers to which allow any given R&D activity to be correctly classified in one or another conventional R&D box—basic, applied, development, etc. Such systematic pigeon-holing allows latecomer countries to gauge the distance of their R&D activity from the world frontier, and how policies may be designed to overcome the hurdle that divides applied research and developmental research.     

COLLABORATION FOR EXCELLENCE: ENGAGED SCHOLARSHIP AT COLLIN COUNTY COMMUNITY COLLEGE

American democracy depends on civic involvement. However, many Americans are increasingly withdrawing from civic responsibility and community involvement. In his best-selling book Bowling Alone , Harvard sociologist Robert D. Putnam presents data showing that Americans have become increasingly unwilling to engage in ways that make American democracy successful. Collin County Community College (CCCC) is addressing civic disengagement through engaged scholarship collaboration between service learning and learning communities programs. Although college students are politically disengaged, most report being or having been involved in some form of community service in the previous year and say they are motivated by giving back to the community and making a difference. Engaged scholarship at CCCC draws on this interest in community service to enhance learning communities, create deeper learning for students, and instill values of citizenship and civic engagement. Learning communities classes blend courses from 2 or more disciplines into a single course with a common theme, enabling students to understand the connection between disciplines. Most integrate a service learning component into that theme, often in the form of a class project promoting civic involvement. Institutional research data reflect increased student retention and success in these classes and a climate of increased communication and objectivity, practical experience in community organizations, and a deeper understanding of democratic ideals. Faculty member focus groups indicate increased satisfaction with teaching, enhanced interdisciplinary knowledge, and feelings of being innovative in the classroom. Engaged scholarship at CCCC enhances student learning, helps develop a unified vision among faculty members, and benefits the community.