Boys and girls as social support theorists

Interviews were conducted with 36 children (6 girls and 6 boys at each of three age levels: 7, 10, and 13) to explore gender differences in the perceived costs and benefits of seeking social support from the social network. Each child was asked why children in five hypothetical situations would or would not turn to others. Content analysis of the interview protocols revealed that boys and girls did speak about the goals and concerns of children in distinctive ways. Girls were more likely than boys to describe children as seeking practical help from others, but were also more likely to envision children who were too overcome with emotion to confide in others or who desired to be alone to work out their own responses to the situation. The findings are discussed in light of gender role norms concerning interpersonal connection and emotional expression.     

Voicing conflict: preferred conflict strategies among incremental and entity theorists

The way individuals choose to handle their feelings during interpersonal conflicts has important consequences for relationship outcomes. In this article, the authors predict and find evidence that people's implicit theory of personality is an important predictor of conflict behavior following a relationship transgression. Incremental theorists, who believe personality can change and improve, were likely to voice their displeasure with others openly and constructively during conflicts. Entity theorists, who believe personality is fundamentally fixed, were less likely to voice their dissatisfactions directly. These patterns were observed in both a retrospective study of conflict in dating relationships (Study 1) and a prospective study of daily conflict experiences (Study 2). Study 2 revealed that the divergence between incremental and entity theorists was increasingly pronounced as conflicts increased in severity: the higher the stakes the stronger the effect.     

The educational theorists, the teachers, and their history of education

The following contribution expands the current discussion on the status and function of the history of education at the methodological, or epistemological, level by introducing the perspective of a history of educational knowledge. This opens up a theoretical option for educational historiography that avoids the identification of history of education with history of a discipline, or the institutionalized knowledge of education and teaching. As a consequence, some history of education topoi – as the history of a discipline – can be called into question and practiced historically rather than educationally or morally.     

The educational theorists, the teachers, and their history of education

The following contribution expands the current discussion on the status and function of the history of education at the methodological, or epistemological, level by introducing the perspective of a history of educational knowledge. This opens up a theoretical option for educational historiography that avoids the identification of history of education with history of a discipline, or the institutionalized knowledge of education and teaching. As a consequence, some history of education topoi – as the history of a discipline – can be called into question and practiced historically rather than educationally or morally.     

Proof-theoretic Semantics for Classical Mathematics

We discuss the semantical categories of base and object implicit in the Curry-Howard theory of types and we derive derive logic and, in particular, the comprehension principle in the classical version of the theory. Two results that apply to both the classical and the constructive theory are discussed. First, compositional semantics for the theory does not demand ‘incomplete objects’ in the sense of Frege: bound variables are in principle eliminable. Secondly, the relation of extensional equality for each type is definable in the Curry-Howard theory.     

Multimedia-Supported Metaphors for Meaning Making in Mathematics

We examined a number-line metaphor presented using interactive multimedia as a means of helping students build connections between an arithmetic procedure and their existing conceptual knowledge. Elementary school children learned to add and subtract signed numbers through a computer-based multimedia program over 4 training sessions. Participants received 64 example problems presented only in symbolic form (single-representation [SR] group) or in symbolic, visual, and verbal forms (multiple-representation [MR] group). In Experiment 1, compared to the SR group, the MR group (a) showed a larger pretest-to-posttest gain for high-achieving students but not for low-achieving students, (b) showed a greater gain on difficult problems but not easy problems, (c) learned faster during training, and (d) showed a greater pretest-to-posttest reduction in the use of conceptual bugs reflecting conceptually confusion between negative signs and subtraction operators. In Experiment 2, high spatial ability students in the MR group outperformed low spatial ability students on pretest-to-posttest gain. Productive learning with MRs is strongest when working memory is not overloaded, so cognitive load and MR theories can be reconciled.     

Experimental Mathematics

The rise of the field of “experimental mathematics” poses an apparent challenge to traditional philosophical accounts of mathematics as an a priori, non-empirical endeavor. This paper surveys different attempts to characterize experimental mathematics. One suggestion is that experimental mathematics makes essential use of electronic computers. A second suggestion is that experimental mathematics involves support being gathered for an hypothesis which is inductive rather than deductive. Each of these options turns out to be inadequate, and instead a third suggestion is considered according to which experimental mathematics involves calculating instances of some general hypothesis. The paper concludes with the examination of some philosophical implications of this characterization.

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An in depth, astute, comprehensive, and erudite attempt at categorization of stuttering theorists

The purpose of this paper is to make the reader aware of the various theoretical categories into which people who have been productive in the area of stuttering can be “slotted.” Readers are encouraged to read the characteristics, as I conceive of them, of each group of people and then see where their favorite “authorities” (which in many cases will undoubtedly include themselves) fit.     

A Role for Mathematics in the Physical Sciences

Conflicting accounts of the role of mathematics in our physical theories can be traced to two principles. Mathematics appears to be both (1) theoretically indispensable, as we have no acceptable non‐mathematical versions of our theories, and (2) metaphysically dispensable, as mathematical entities, if they existed, would lack a relevant causal role in the physical world. I offer a new account of a role for mathematics in the physical sciences that emphasizes the epistemic benefits of having mathematics around when we do science. This account successfully reconciles theoretical indispensability and metaphysical dispensability and has important consequences for both advocates and critics of indispensability arguments for platonism about mathematics.     

The Indispensability Argument and Multiple Foundations for Mathematics

One recent trend in the philosophy of mathematics has been to approach the central epistemological and metaphysical issues concerning mathematics from the perspective of the applications of mathematics to describing the world, especially within the context of empirical science. A second area of activity is where philosophy of mathematics intersects with foundational issues in mathematics, including debates over the choice of set–theoretic axioms, and over whether category theory, for example, may provide an alternative foundation for mathematics. My central claim is that these latter issues are of direct relevance to philosophical arguments connected to the applicability of mathematics. In particular, the possibility of there being distinct alternative foundations for mathematics blocks the standard argument from the indispensable role of mathematics in science to the existence of specific mathematical objects.     

Theism and Mathematics

The author investigates the connection between God and mathematics, and argues (1) that the “unreasonable effectiveness of mathematics” makes much better sense from the perspective of theism than from that of naturalism, (2) that the accessibility (to us human beings) of advanced mathematics is much more likely given theism than given naturalism, (3) that the existence of sets, numbers, functions and the like fits in much better with theism than with naturalism, and (4) that the alleged epistemological obstacles to knowledge of mathematics offered by the abstract character of numbers, sets, etc., disappear from the point of view of theism.