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.     

Predicting who will major in a science discipline: Expectancy–value theory as part of an ecological model for studying academic communities

Research on factors that shape recruitment and retention in undergraduate science majors currently is highly fragmented and in need of an integrative research framework. Such a framework should incorporate analyses of the various levels of organization that characterize academic communities (i.e., the broad institutional level, the departmental level, and the student level), and should also provide ways to study the interactions occurring within and between these structural levels. We propose that academic communities are analogous to ecosystems, and that the research paradigms of modern community ecology can provide the necessary framework, as well as new and innovative approaches to a very complex area. This article also presents the results of a pilot study that demonstrates the promise of this approach at the student level. We administered a questionnaire based on expectancy-value theory to undergraduates enrolled in introductory biology courses. Itself an integrative approach, expectancy-value theory views achievement-related behavior as a joint function of the person's expectancy of success in the behavior and the subjective value placed on such success. Our results indicated: (a) significant gender differences in the underlying factor structures of expectations and values related to the discipline of biology, (b) expectancy-value factors significantly distinguished biology majors from nonmajors, and (c) expectancy-value factors significantly predicted students' intent to enroll in future biology courses. We explore the expectancy-value framework as an operationally integrative framework in our ecological model for studying academic communities, especially in the context of assessing the underrepresentation of women and minorities in the sciences. Future research directions as well as practical implications are also discussed.     

Further Reflections on an Evolutionary Theory of Socialization

In response to Maccoby's and Hinde's thoughtful commentaries, we highlight points of concurrence and disagreement. In particular, we note that mating and reproduction are affected by many factors beyond those to which our theory draws immediate attention; that the data linking socialization experiences and social structural conditions with pubertal timing are not restricted to either correlational studies or investigations of contemporaneous associations; that there may be more reason to question the theory's applicability to males than to females; that the question of whether male behave and develop the way we propose and Maccoby doubts is an empirically testable one; and that the data on relations between antecedent socialization conditions and pubertal timing and on variation in parental investment in the case of females run counter to Maccoby's doubts about the theory's applicability to females. Attention is drawn to the potential benefits of asking questions about proximal and ultimate causation simultaneously, and thus the need for child developmentalists to think both about the how and why of development.     

Childhood Experience, Interpersonal Development, and Reproductive Strategy: An Evolutionary Theory of Socialization

The concept of "reproductive strategy" drawn from the field of behavioral ecology is applied to the study of childhood experience and interpersonal development in order to develop an evolutionary theory of socialization. The theory is presented in terms of 2 divergent development pathways considered to promote reproductive success in the contexts in which they have arisen. One is characterized, in childhood, by a stressful rearing environment and the development of insecure attachments to parents and subsequent behavior problems; in adolescence by early pubertal development and precocious sexuality; and, in adulthood, by unstable pair bonds and limited investment in child rearing, whereas the other is characterized by the opposite. The relation between this theory and prevailing theories of socialization, specifically, attachment, social-learning, and discrete-emotions theory, is considered and research consistent with our evolutionary theory is reviewed. Finally, directions for future research are discussed.