Evidence for the Phase Transition from Rule I to Rule II on the Balance Scale Task

A central and recurrent theme in developmental psychology is the question whether development proceeds continuously or discontinuously. This question is difficult to answer because the two types of development may be hard to distinguish. To investigate whether change is discontinuous, one requires a formal model for discontinuous development. Such a model should provide operational, empirical criteria to investigate the nature of development. The cusp model, which is derived from catastrophe theory, is a formal model of discontinuity that provides such criteria. Eight criteria, so-called catastrophe flags, can be derived from the model. Some of these flags are predicted in other models of discontinuity, but others, notably hysteresis, are unique to catastrophe theory. In the present research, it is tested whether the transition from Rule I to Rule II on the balance scale task proceeds discontinuously. The present research centers around five catastrophe flags: bimodality, inaccessible region, sudden jump, divergence, and hysteresis. Two experiments are reported. In Experiment 1, a paper-and-pencil version of the balance scale task was administered to 314 children who were 6 to 10 years old. In Experiment 2, an adapted version of the test was administered to 302 children who were 6 to 10 years old. Bimodality, inaccessible region, hysteresis, and sudden jump were clearly observed. Divergence was not observed. The presence of four of the five flags strongly supports the hypothesis that the transition from Rule I to Rule II is discontinuous.     

Comprehension of algebraic expressions by experienced users of mathematics

Little is known about how people comprehend mathematical expressions. In the present study we investigate the internal representations used by experienced users of mathematics to encode algebraic expressions. Initially, a memory recognition task was conducted that examined the role of mathematical syntax in the encoding of algebraic expressions. The results indicate that participants could more readily identify those parts of a previously seen expression that were syntactically well formed than those that were not well formed, suggesting that syntax plays an important role. To determine the level of syntactic structure involved, a second recognition task was conducted. The results indicate that algebraic expressions are encoded into components that represent the phrasal constituents of the expression. However, the results of these experiments did not rule out the possibility that the visual processes of perceptual organization were used to encode the expressions, or that the data were a consequence of a mathematical “lexicon” of common mathematical “phrases”. Three further experiments were conducted to examine this, the results of which indicate that the encoding of algebraic expressions is based primarily on processes that occur beyond the level of visual or “lexical” processing. This is consistent with our finding that syntactic structure plays a key role.     

"On my bed at night I sought him whom my heart loves"" reflections on trust, horror, G*d, and the queer body in vowed religious life

What can the multifaceted bouquet of queer love reveal about G*d? In this paper I wish to answer this question by reflecting on the queer body of the male vowed religious. I will argue that, since gendering is a key feature in our attempts to create epistemic order, the performance of gender instability in turn destabilizes our attempts to create epistemic order. In short: gender trouble leads to epistemic trouble. Far from being only a passive sign for these troubles, the male religious body, which is stylized by renouncing penetration, is also a field for the active experience of the horror and the need for trust implied in our fragile epistemic situation. Both trust and horror can be interpreted as an experience of the Dark Night, as the experiential side of Negative Theology. I will argue that the grace that we as queer men and women in general contribute to the Church is that we are pointing to and living out the fundamental reality of epistemic uncertainty and the troubling necessity of trust.