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.     

On 'The Myth of the Learning Society'

A recent critique by Hughes and Tight (1995) argued that the 'Learning Society' and related notions of productivity and change are 'myths'. In response, it is argued here that myth should not be confused with ideological distortion. The rhetorical dimension of current initiatives is a necessary feature of theoretical formulation, intended to influence public discussion and policy-making. The concepts of productivity and change are reconsidered in a wider historical dimension and the communitarian aspects of the project are shown to have a more positive significance in the light of, for example, recent work by Beck and Giddens on 'reflexivity' and 'risk'. It is acknowledged that faith in the application of technological solutions to societal learning challenges is frequently misplaced. But fear that the project's aims might be subverted by interests hostile to humane educational values is insufficient reason for such scepticism, which is too narrowly grounded and is misdirected.     

Job satisfaction: perceptions of a national sample of teachers of students who are deaf or hard of hearing

The study examined the perceptions of a national sample of teachers of students who are deaf or hard or hearing to assess their level of job satisfaction. A questionnaire was developed and distributed; 610 completed surveys were analyzed. Overall, respondents appeared satisfied with their jobs. Of the 59 items in the survey, 51 were scored as positive for the group as a whole. Participants reported that their relationships with colleagues were the most enjoyable aspect of the job. Paperwork, state assessment tests, and lack of family involvement were identified as the least satisfying aspects. Data were also analyzed by comparing the responses of teachers across groups--itinerant, elementary, secondary, and resource room. Generally, this group-by-group analysis produced findings similar to those for the overall sample. Recommendations on addressing the specific factors that teachers responded to negatively are provided.     

Financing desegregation in the Yonkers public schools

The Yonkers public school district is under a federal court order to desegregate its schools. Accordingly, the district has developed and implemented a detailed desegregation plan that will cost up to $170 million over a five-year period. However, there are various constraints on school district financing that could affect the plan. The Board of Education in Yonkers, which is appointed by the mayor, is fiscally dependent on the city. Thus, the school district budget must be approved by city officials. Also, because Yonkers appears to be a wealthy district, it receives less wealth-equalized state aid than other large-city districts. Given these circumstances, in addition to increase in state and federal aid, other measures to assist the district should be explored. Note: The opinions expressed in this paper are my own and do not necessarily reflect the official views of the New York State Education Department.     

Cognitive load theory and educational technology

Educational technology research and development - Cognitive load theory provides instructional recommendations based on our knowledge of human cognition. Evolutionary psychology is used to assume...     

Attenuation of blocking by a change in US locus

A classical conditioning procedure was instituted in which the locus of the US was changed coincidentally with the onset of the compound conditioning phase of the Kamin blocking design. The nictitating membrane of the rabbit served as the conditioning preparation. Three groups of nine rabbits each were employed: a conventional blocking group in which the US was unchanged during the simple and compound conditioning phases, a control group that received only the compound conditioning phase, and an experimental group given both simple and compound conditioning but in which the US was administered to the contralateral paraorbital region during the compound conditioning phase. Postconditioning presentations of the elements of the compound CS indicated that, relative to the control group, responding during the new element was markedly reduced in the conventional blocking group but was strongly conditioned in the group in which the US locus was changed. Implications of these findings for theoretical analyses of conditioning are discussed.     

What is Lesson Study?

This article addresses the conceptual question “what is lesson study?” as an issue that arises in the context of the globalisation of lesson study as a method for improving teaching and learning beyond its presumed origins in the Japanese education system. To what extent can adaptations of the method in different national settings be interpreted as faithful representations of its practically significant “critical features” in the country of origin? In order to address this question, the article begins by examining the comparative classroom research by Stigler and Hiebert that culminated in the publication of The Teaching Gap. This work is generally acknowledged to have been seminal for the global development of lesson study as a method for improving teaching and learning. Sponsored by the 1997 TIMMS testing programme, the research sought to explain pronounced differences in measured educational attainment between students of all ages in Japan, and the US and Germany. In the process Stigler and Hiebert discovered the extensive use of lesson study in Japanese primary schools as a school‐based research method for securing consistency between learning goals and teaching methods. In doing so, they identified six principles which underpinned the method and pinpointed its practical significance. In this article, the author claims that the principles identified by Stigler and Hiebert can be used as a framework for assessing adaptations of lesson study in the context of globalisation, and connecting it to related methodological ideas that are internationally circulating. In particular, the author stresses links between lesson study, the tradition of classroom action research forged by Lawrence Stenhouse and his colleagues at the University of East Anglia, UK and the theory of variation developed in Sweden and Hong Kong by Ference Marton, Lo Mun Ling and others. Such links can deepen a theoretical understanding of “lesson study” and safe‐guard it against a “cherry‐picking” approach to its implementation in a context of globalisation. The article particularly highlights the importance of understanding the ways in which the organisational cultures of schooling in many countries shape and distort the implementation of lesson study. It argues for the greater involvement of school leaders and administrators in a form of second‐order action research aimed at transforming the organisational context of teachers’ work in classrooms and creating more space for them to spend less time as test data managers and more time as lesson researchers in accordance with the six principles outlined.