Interest in science and math plays an important role in encouraging STEM motivation and career aspirations. This interest decreases for girls between late childhood and adolescence. Relatedly, positive mentoring experiences with female teachers can protect girls against losing interest. The present study examines whether visitors to informal science learning sites differ in their expressed science and math interest, as well as their science and math stereotypes following an interaction with either a male or female educator. Participants were (...) visitors to one of four ISLS in the United States and United Kingdom. Following an interaction with a male or female educator, they reported their math and science interest and responded to math and science gender stereotype measures. Female participants reported greater interest in math following an interaction with a female educator, compared to when they interacted with a male educator. In turn, female participants who interacted with a female educator were less likely to report male-biased math gender stereotypes. Self-reported science interest did not differ as a function of educator gender. Together these findings suggest that, when aiming to encourage STEM interest and challenge gender stereotypes in informal settings, we must consider the importance of the gender of educators and learners. (shrink)

This study examined the relationship of intelligence mindsets to math achievement for primary school students in the Chinese educational context, as well as the mediating function of math self-efficacy and failure beliefs in this relationship. Participants included 466 fifth graders (231 boys and 235 girls) from two Chinese primary schools. Results indicated that boys had significantly higher mean levels of growth mindsets and math self-efficacy than girls, whereas boys had no statistically significant differences to girls on failure (...) beliefs and math grade. Further, intelligence mindsets had a significant positive effect on math achievement, and failure beliefs and math self-efficacy played a full mediating role in the relationship between intelligence mindsets and math achievement. Moreover, intelligence mindsets affected math achievement through the chain mediating role of failure beliefs and math self-efficacy. These above findings contribute to advance our knowledge about the underlying mechanisms through which intelligence mindsets affect math achievement, which are of great significance to students' growth and current educational practice. (shrink)

It is well established that math anxiety has a negative relationship with math performance. A few theories have provided explanations for this relationship. One of them, the Attentional Control Theory, suggests that anxiety can negatively impact the attentional control system and increase one's attention to threat-related stimuli. Within the ACT framework, the math anxiety —working memory relationship is argued to be critical for math performance. The present meta-analyses provides insights into the mechanisms of the MA—MP relation (...) and the mediating role of WM. Through database searches with pre-determined search strings, 1,346 unique articles were identified. After excluding non-relevant studies, data from 57 studies and 150 effect sizes were used for investigating the MA—MP correlation using a random-effects model. This resulted in a mean correlation of r = −0.168. The database search of WM as a mediator for the MA—MP relation revealed 15 effects sizes leading to a descriptive rather than a generalizable statistic, with a mean indirect effect size of −0.092. Overall, the results confirm the ACT theory, WM does play a significant role in the MA—MP relationship. (shrink)

LEGO and math are both about what one do with the objects. In LEGO, he/she can build sets following the instructions, or alternatively dump a whole bunch of LEGO on the floor and build whatever he/she like. In math, he/she have a similar freedom to create new things, solve problems, and play around. Geometry makes far greater use of pictures and diagrams than tends to be the case for other areas of mathematics. This chapter focuses on diagrammatic (...) proofs as a key case where proofs guide him/her through a series of actions. If one accepts the LEGO account of diagrammatic proofs then he/she has strongly sided with the geometers against Plato. The main principle of departure from Plato is to focus on mathematical activities. The same thought is meant to apply to LEGO: the particular bricks are only important insofar as they facilitate the things we can practically do with them. (shrink)

This study examined individual differences in mathematics learning by combining antecedent (A), opportunity (O), and propensity (P) indicators within the Opportunity-Propensity model. Although there is already some evidence for this model based on secondary datasets, there currently is no primary data available that simultaneously takes into account A,O and P factors in children with and without Mathematical Learning Disabilities (MLD). Therefore the mathematical abilities of 114 school-aged children (grade 3 till 6) with and without MLD were analyzed and combined with (...) information retrieved from standardized tests and questionnaires. Results indicated significant differences in personality, motivation, temperament, subjective well-being, self-esteem, self-perceived competence and parental aspirations when comparing children with and without MLD. In addition, A, O and P factors were found to underlie mathematical abilities and disabilities. For the A factors, parental aspirations explained about half of the variance in fact retrieval speed in children without MLD, and SES was especially involved in the prediction of procedural accuracy in general. Teachers’ experience contributed as O factor and explained about 6% of the variance in mathematical abilities. P indicators explained between 52 and 69% of the variance, with especially intelligence as overall significant predictor. Indirect effects pointed towards the interrelatedness of the predictors and the value of including A, O and P indicators in a comprehensive model. The role parental aspirations played in fact retrieval speed was partially mediated through the self-perceived competence of the children, whereas the effect of SES on procedural accuracy was partially mediated through intelligence in children of both groups and through working memory capacity in children with MLD. Moreover, in line with the componential structure of mathematics, our findings were dependent on the math task used. Different A, O and P indicators seemed to be important for fact retrieval speed compared to procedural accuracy. Also, mathematical development type (MLD or typical development) mattered since some A, O and P factors were predictive for MLD only and the other way around. Practical implications of these findings and recommendations for future research on MLD and on individual differences in mathematical abilities are provided. (shrink)

Stereotype threat is a possible reason for difficulties faced by girls and women in the fields of science, technology, engineering, and mathematics. The threat experienced due to gender can cause elevated worry during performance situations. That is, if the stereotype that women are not as good as men in math becomes salient, this stereotype activation draws women’s attention to task-irrelevant worry caused by the fear of conforming to the negative stereotype. Increased worry can reduce cognitive resources, potentially leading to (...) performance decrements. We argue that such worry is more pronounced immediately after an unrelated self-control demand, which is assumed to temporarily decrease people’s self-control exertion over their attention and stream of thought. This prediction was examined in an experiment conducted with 102 participating university students enrolled in courses in which math plays a crucial role. After the manipulation of self-control capacity, stereotype threat was induced for the female students, but not the male students. Then, the students were asked to report their thoughts during a math performance situation three times. Multiple-group autoregressive path models revealed that when self-control capacity was relatively low, female compared with male students reported more intense worry in the initial two thought protocols. In contrast, in the relatively high self-control capacity condition, female and male students did not differ significantly in their reported worry at any time. These results expand on previous findings, suggesting that threat effects depend on definable situational self-control conditions. (shrink)

Gestures—hand movements that accompany speech and express ideas—can help children learn how to solve problems, flexibly generalize learning to novel problem‐solving contexts, and retain what they have learned. But does it matter who is doing the gesturing? We know that producing gesture leads to better comprehension of a message than watching someone else produce gesture. But we do not know how producing versus observing gesture impacts deeper learning outcomes such as generalization and retention across time. Moreover, not all children benefit (...) equally from gesture instruction, suggesting that there are individual differences that may play a role in who learns from gesture. Here, we consider two factors that might impact whether gesture leads to learning, generalization, and retention after mathematical instruction: (1) whether children see gesture or do gesture and (2) whether a child spontaneously gestures before instruction when explaining their problem‐solving reasoning. For children who spontaneously gestured before instruction, both doing and seeing gesture led to better generalization and retention of the knowledge gained than a comparison manipulative action. For children who did not spontaneously gesture before instruction, doing gesture was less effective than the comparison action for learning, generalization, and retention. Importantly, this learning deficit was specific to gesture, as these children did benefit from doing the comparison manipulative action. Our findings are the first evidence that a child's use of a particular representational format for communication (gesture) directly predicts that child's propensity to learn from using the same representational format. (shrink)

In this handbook, I put into practice my philosophical views on children's mathematics. The handbook contains brief instructions and examples of mathematical activities. In the INSTRUCTIONS section, instructions are given on how, and in part why that way, to help preschool children in their mathematical development. In the ACTIVITIES section, there are examples of activities through which the child develops her mathematical abilities.

Sequences play a great role in mathematical communication. In mathematical notation, we use sequence ellipsis (. . . ) to denote "obvious" sequences like 1, 2, . . . , 7, and in conceptualizations sequence constructors like (i 2+1) i∈N. Furthermore, sequences have a prominent role as argument sequences of flexary functions. While the former cases can adequately be represented and reasoned about as domain objects in Open- Math and MathML, argument sequences are at the language level, and (...) can only be represented, but not reasoned with, since the necessary (sequence-schematic) axioms cannot be represented in the language. (shrink)

This essay argues that defences of strategic fouling in sport are enriched and supported by better recognizing the role of play in sport. A common characteristic of play is its disengagement from the everyday, in particular its moral disengagement. If sport in its best manifestations is a species of play, then we should expect to find some moral disengagement there. And indeed we do in a variety of ways. Strategic fouling affords a useful example to illustrate and (...) support this claim and to examine the limits of that sort of disengagement. It is argued that while strategic fouling is morally problematic, it can be a sort of playful ‘competitive shenanigan’ that should be tolerated at times for the way it adds to the challenge and drama of sport. This allows us to better recognize the complexity and depth of sport and the way it reflects fundamental human values. Like everyday life, sport challenges us to weigh morality, perfection, and play against each other in ways that give each sphere of value its due and that contribute to rewarding and meaningful activities and lives. (shrink)

Dreaming can provide a marvelous opportunity for the “playful” exploration of dramatic events. But the chance to learn to deal with danger is only a small part of it. More important is the chance to discover what it is like to be the subject of strange but humanly significant mental states. [Revonsuo].

The role that trust plays in blockchain-based systems is understood and portrayed in various manners. The blockchain technology is said to enable and establish trust as well as to redirect it, to substitute for it, and to make it obsolete. Furthermore, there is disagreement on whom or what users have to trust when using the blockchain technology: code, math, algorithms, and machines, or still human actors. This paper hypothesizes that the divergences of the depictions largely rest on implicitly adhering (...) to different accounts of trust. Thus, the goal of this paper is to outline how the current lack of a shared understanding of the term “trust” leads to diverging interpretations of the blockchain technology’s core features. Furthermore, it shows how this lack of common understanding obstructs scholars from referring to one another meaningfully in the discourse on blockchain technology. To do so, this paper outlines the most prominent depictions of the setup of relevant trust relationships within blockchain-based systems and traces their roots to different underlying assumptions on the nature of trust. (shrink)

Within the literature that circulates in the discourses organizing nursing education, there are embedded assumptions that link student performance on maths examinations to safe medication practices. These assumptions are rooted historically. They fundamentally shape educational approaches assumed to support safe practice and protect patients from nursing error. Here, we apply an institutional ethnographic lens to the body of literature that both supports and critiques the emphasis on numeracy skills and medication safety. We use this form of inquiry to open an (...) alternate interrogation of these practices. Our main argument posits that numeracy skills serve as powerful distraction for both students and teachers. We suggest that they operate under specious claims of safety and objectivity. As nurse educators, we are captured by taken‐for‐granted understandings of practices intended to produce safety. We contend that some of these practices are not congruent with how competency actually unfolds in the everyday world of nursing practice. Ontologically grounded in the materiality of work processes, we suggest there is a serious disjuncture between educators' assessment and evaluation work where it links into broad nursing assumptions about medication work. These underlying assumptions and work processes produce contradictory tensions for students, teachers and nurses in direct practice. (shrink)

The purpose of this article is to complete, and build on, the theories of a certain number of scholars, chiefly philosophers of previous generations, and a few eminent performers of classical music who all bring to the fore the essential link between music and play. Because of their impulse value and appealing character, tones and other elements of the performance could generate a playful attitude in the musicians. Play is understood as a reciprocal interaction with something that plays (...) with the player: indeed, tones play with the musicians and, reciprocally, the musicians play with them. While engaging in a musical play, they draw on the remarkable creative abilities of their body, namely its spontaneity, sensibility, and “imaginative” anticipation. The satisfaction provided by the playful activity comes, in part, from the possibility of experiencing the body as a source of creative power and original performance. (shrink)

Designing complex products involves working with uncertainties as the product, the requirements and the environment in which it is used co-evolve, and designers and external stakeholders make decisions that affect the evolving design. Rather than being held back by uncertainty, designers work, cooperate and communicate with each other notwithstanding these uncertainties by making assumptions to carry out their own tasks. To explain this, the paper proposes an adaptation of Kendall Walton’s make-believe theory to conceptualise designing as playing games of make-believe (...) by inferring what is required and imagining what is possible given the current set of assumptions and decisions, while knowing these are subject to change. What one is allowed and encouraged to imagine, conclude or propose is governed by socially agreed rules and constraints. The paper uses jet engine component design as an example to illustrate how different design teams make assumptions at the beginning of design activities and negotiate what can and cannot be done with the design. This often involves iteration – repeating activities under revised sets of assumptions. As assumptions are collectively revised, they become part of a new game of make-believe in the sense that there is social agreement that the decisions constitute part of the constraints that govern what can legitimately be inferred about the design or added to it. (shrink)

In "The Ends of Man," when talking about a deconstructive process of writing, Jacques Derrida says that "what we need, perhaps, as Nietzsche said, is a change of "style," and if there is style, Nietzsche reminds us, it must be plural". On his debt to Nietzsche, Derrida remains elusive, although it is obvious that there are many manifestations of Nietzsche's presence throughout Derrida's writings. As this quote suggests, if there is not a similarity in style between Nietzsche and Derrida, there (...) are some definite similarities of approach and intent. While their arguments are far more intricate than the similarities on which this article will focus can communicate, I will argue that Nietzsche's concept of 'perspectivism' could perhaps be seen as a paradigm for Derrida's concept of 'différance.' The aim of this article, then, will be to argue that in 'perspectivism' and 'différance,' a notion of "play" problematizes the traditional concept of the subject, but in doing so it allows for ethical possibilities. These issues will be explored in two parts. The first section, "The Subject as Play," argues that in Nietzsche's 'perspectivism' and Derrida's 'différance' there is a refusal to hypostasise the subject, and this refusal is evidenced in both Nietzsche's and Derrida's playing with the "proper name." In the second section, "Ethical Possibilities," in contradistinction to critical readings of Nietzsche and Derrida that label their writings—because of their switching of styles and their manipulation of the subject—irresponsible and nihilistic, I will argue that it is precisely because of their subversive techniques that ethical possibilities are generated. (shrink)

Arguments by Sorkin (Impossible measurements on quantum fields. In: Directions in general relativity: proceedings of the 1993 International Symposium, Maryland, vol 2, pp 293–305, 1993) and Borsten et al. (Phys Rev D 104(2), 2021. https://doi.org/10.1103/PhysRevD.104.025012 ) establish that a natural extension of quantum measurement theory from non-relativistic quantum mechanics to relativistic quantum theory leads to the unacceptable consequence that expectation values in one region depend on which unitary operation is performed in a spacelike separated region. Sorkin [ 1 ] labels (...) such scenarios ‘impossible measurements’. We explicitly present these arguments as a no-go result with the logical form of a reductio argument and investigate the consequences for measurement in quantum field theory (QFT). Sorkin-type impossible measurement scenarios clearly illustrate the moral that Microcausality is not by itself sufficient to rule out superluminal signalling in relativistic quantum theories that use Lüders’ rule. We review three different approaches to formulating an account of measurement for QFT and analyze their responses to the ‘impossible measurements’ problem. Two of the approaches are: a measurement theory based on detector models proposed in Polo-Gómez et al. (Phys Rev D, 2022. https://doi.org/10.1103/physrevd.105.065003 ) and a measurement framework for algebraic QFT proposed in Fewster and Verch (Commun Math Phys 378(2):851–889, 2020). Of particular interest for foundations of QFT is that they share common features that may hold general morals about how to represent measurement in QFT. These morals are about the role that dynamics plays in eliminating ‘impossible measurements’, the abandonment of the operational interpretation of local algebras \({\mathcal {A}}(O)\) as representing possible operations carried out in region _O_, and the interpretation of state update rules. Finally, we examine the form that the ‘impossible measurements’ problem takes in histories-based approaches and we discuss the remaining challenges. (shrink)

This paper gives a framework for understanding causal counterpossibles, counterfactuals imbued with causal content whose antecedents appeal to metaphysically impossible worlds. Such statements are generated by omissive causal claims that appeal to metaphysically impossible events, such as “If the mathematician had not failed to prove that 2+2=5, the math textbooks would not have remained intact.” After providing an account of impossible omissions, the paper argues for three claims: (i) impossible omissions play a causal role in the actual world, (...) (ii) causal counterpossibles have broad applications in philosophy, and (iii) the truth of causal counterpossibles provides evidence for the nonvacuity of counterpossibles more generally. (shrink)

On the surface, developing a social psychology of science seems compelling as a way to understand how individual social cognition – in aggregate – contributes towards individual and group behavior within scientific communities (Kitcher, 2002). However, in cases where the functional input-output profile of psychological processes cannot be mapped directly onto the observed behavior of working scientists, it becomes clear that the relationship between psychological claims and normative philosophy of science should be refined. For example, a robust body of social (...) psychological research demonstrates implicit gender bias in the evaluation of others (e.g., Steinpreis, Anders, & Ritzke, 1999). Many expected implicit bias to be a major cause of women’s underrepresentation in math intensive fields of science; however, quantitative sociological research of hiring and manuscript and grant evaluation has discovered no gender disparity in outcomes (Ceci & Williams, 2011). Why might this be so? This paper will discuss methodological challenges that go beyond classic problems of external validity in extrapolating psychological effects and explanations to scientific communities. These problems include more complex external validity issues raised by the introduction of multi-process models of cognition (e.g., implicit versus explicit social cognition) as well as the reflexive role that folk and experimental theories of social psychology play in guiding the behavior of scientists at the individual and community level. (shrink)

The emergence of mathematical probability has something to do with dice games: all the early discussions (Cardano, Galileo, Pascal) suggest as much. Although this has long been recognized, the problem is that gambling at dice has been a popular pastime since antiquity. Why, then, did gamblers wait until the sixteenth century ce to calculate the math of dicing? Many theories have been offerred, but there may be a simple solution: early-modern gamblers played different sorts of dice games than in (...) antiquity. While ancients diced at communal risk, early-moderns diced at individualized risk. These individual wager-games, for example, the game “hazard”, incentivized solving questions like “how likely is it to roll a triple-six?”. Before the early modern period there was no gambling game to which working out mathematical probability would have brought an advantage. (shrink)

Learning disabilities are highly prevalent on college campuses, yet students with learning disabilities graduate at lower rates than those without disabilities. Academic and psychosocial supports are essential for overcoming challenges and for improving postsecondary educational opportunities for students with learning disabilities. A holistic, multi-level model of campus-based supports was established to facilitate culture and practice changes at the institutional level, while concurrently bolstering mentors’ abilities to provide learning disability-knowledgeable support, and simultaneously creating opportunities for students’ personal and interpersonal development. Mixed (...) methods were used to investigate implementation of coordinated personal, interpersonal, and institutional level supports for undergraduate science, technology, engineering, and math (STEM) students with learning disabilities. A one-group pre-test post-test strategy was used to examine undergraduate outcomes. Participants included 52 STEM undergraduates with learning disabilities, 57 STEM graduate student mentors, 34 STEM faculty mentors, and 34 university administrators and personnel as members of a university-wide council. Enrolled for two years, undergraduates were engaged in group meetings involving psychoeducation and reflective discussions, development of self-advocacy projects, and individual mentorship. Undergraduates reported improved self efficacy (p =.001), campus connection (p <.001), professional development (p ≤.002), and self advocacy (p <.001) after two academic years. Graduate student mentors increased their understanding about learning disabilities and used their understanding to support both their mentees and other students they worked with. Council members identified and created opportunities for delivering learning disability-related trainings to faculty, mentors and advisors on campus, and for enhancing coordination of student services related to learning and related disorders. Disability-focused activities became integrated in broader campus activities regarding diversity. This research explicates a role that college campuses can play in fostering the wellbeing and the academic and career development of its students with developmental learning and related disorders. It offers an empirically tested campus-based model that is multilevel, holistic, and strengths-based for supporting positive outcomes of young people with learning disabilities in STEM. Moreover, findings advance the knowledge of supports and skills that are important for self-regulating and navigating complex and multi-faceted disability-related challenges within both the post-secondary educational environment and the young adults’ sociocultural context. (shrink)

Our likes and dislikes--our senses and sensibilities--did not fall ready-made from the sky, argues internationally acclaimed author John D. Barrow. We know we enjoy a beautiful painting or a passionate symphony, but what we don't necessarily understand is that these experiences conjure up latent instincts laid down and perpetuated over millions of years. Now, in The Artful Universe, Barrow explores the close ties between our aesthetic appreciation and the basic nature of the Universe, challenging the commonly held view that our (...) sense of beauty is entirely free and unfettered. Barrow argues that the laws of the Universe, its environments and its astronomical appearance, have imprinted themselves upon our thoughts and actions in subtle and unexpected ways. Why do we like certain types of art or music? What games and puzzles do we find challenging? Why do so many myths and legends have common elements? Who created the cornucopia of constellations in the night sky? And why? In this eclectic and entertaining survey, Barrow answers these questions and more as he explains how the landscape of the Universe has influenced the development of philosophy and mythology, and how millions of years of evolutionary history have fashioned our attraction to certain patterns of sound and color. Barrow casts the story of human creativity and thought in a fascinating light, considering such diverse topics as our instinct for language, the origins and uses of color in Nature, why we divide time into intervals as we do, the sources of our appreciation of landscape painting, and whether computer-generated fractal art is really art. Barrow reconsiders the question of whether intelligent extraterrestrial life exists, showing that the benefits (and even the likelihood) that might follow from the discovery of life on other worlds could be very different from what we might have been led to expect. Remarkably, we find that some of the properties of the Universe that are essential for the existence of any form of life play a key role in determining psychological and religious responses to the Cosmos. Drawing on a wide variety of examples, from the theological questions raised by St. Augustine and C.S. Lewis to the relationship between the pure math of Pythagoras and the music of the Beatles, The Artful Universe covers new ground and enters a wide-ranging debate about the meaning and significance of the links between art and science. It will change our view of the creation of art and the way we see the world in which we live. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy, Psychiatry, & Psychology 11.2 (2004) 125-128 [Access article in PDF] Comparing Psychoanalytic and Cognitive-Behavioral Perspectives on Control Bruce N. Waller Keywords freedom, locus of control, psychoanalysis, self-efficacy, volition Cognitive behavioral research on locus of control and self-efficacy has produced an extensive body of empirical results that might prove useful to psychoanalytic researchers endeavoring to strengthen the empirical foundation of psychoanalytic therapy. Cognitive-behaviorists and psychoanalysts share a common interest (...) in the importance of perspectives and belief systems and their impact on individual freedom, and comparative research on therapeutic effectiveness could yield benefits for both therapeutic approaches.Locus of control and self-efficacy are central elements in cognitive-behavioral psychology, and they play an important role in cognitive-behavioral therapy. Although the psychoanalytic approach does not explicitly employ those concepts, psychoanalytic therapists are obviously concerned with problems of effective action and internal obstacles to action. Attention to these two perspectives and their overlapping interests offers potential benefits for both the cognitive-behavioral and the psychodynamic approaches to psychological research and therapy.One potential benefit is the development of useful tools for advancing empirically based research on psychoanalysis. As Lehrer (1999) states, it is advantageous to ground psychoanalysis in "firm empirical evidence whenever possible." Although there have obviously been significant positive steps in that direction (Singer 2003; Weiss 1995, 1988; Weiss and Sampson 1986), psychoanalytic researchers have recognized that one source of difficulty is in finding clearly measurable research objectives and hypotheses (Burgin 2002). Cognitive-behavioral research on locus of control and self-efficacy has produced an extensive body of research using clear measurement standards that could prove useful in the empiricist approach to psychodynamic theories. In particular, those cognitive-behavioral research findings might offer a means of extending empirical investigation of psychodynamic theory in a direction usually regarded as difficult to test empirically: the study of psychoanalytic effectiveness to "change your way of seeing" (Lieberman 1999). Shifting locus of control or efficacy expectations in specific domains (Bandura 1997) [End Page 125] would empirically confirm the effectiveness of psychoanalytic techniques. It might well be that some efficacy expectations are enhanced more effectively by psychodynamic processes than by cognitive-behavioral therapy, or that psychoanalysis is effective in enhancing some specific efficacy expectations but not others. This could potentially extend the empirical examination of psychoanalytic theory as well as provide a base of comparison with cognitive-behavioral therapy techniques.Although self-efficacy enhancement might be a fruitful empirical test for psychodynamic therapy, therapeutic intervention to modify locus of control potentially could be even more productive. Current research indicates that one's orientation toward locus of control is a relatively stable characteristic, although it can be modified (Holyrod et al. 1984; Rotter 1979; Sadow and Hopkins 1993). One reason for locus of control stability may be that the locus of control imposes a perspective on the conceptualization of all one's experiences: from a strong internal locus of control perspective I view failures and successes as largely my own doing, whereas from an external locus perspective even my most effective efforts are seen as events that were outside my control: "I guess it was just my time to do well on a math exam," rather than "My hard work for that exam really paid off." (Lieberman makes this phenomenon quite clear in his excellent discussion of transparency.) Although locus of control is not easily modified, it is important to find effective means of helping subjects to achieve such changes, because research shows that a strong internal locus of control is positively correlated with success in work, sports, studies, marriage, and psychological adjustment (Lefcourt 1981, 1992), as well as with better health care behavior and better health (Bandura 1977; Schorr and Rodin 1982; Schulz 1976; Schulz and Hanusa 1978; Wallston 1993). Those deeply enmeshed in an external locus of control enjoy less real freedom and suffer severe disadvantages.How does one effect a shift in such a basic orientation? Not easily. From a psychoanalytic approach, the key will lie in recognizing and reconceptualizing the beliefs that impede effective action. Cognitive-behaviorists are more likely to... (shrink)

The obscured Thomas precessionof the special theory of relativity (STR) has been soared into prominence by exposing the mathematical structure, called a gyrogroup,to which it gives rise [A. A. Ungar, Amer. J. Phys.59,824 (1991)], and the role that it plays in the study of Lorentz groups [A. A. Ungar, Amer. J. Phys.60,815 (1992); A. A. Ungar, J. Math. Phys.35,1408 (1994); A. A. Ungar, J. Math. Phys.35,1881 (1994)]. Thomas gyrationresults from the abstraction of Thomas precession.As such, its study sheds (...) light on relativistic velocity spaces and their symmetries which are concealed in Thomas precession. In order to uncover new properties of relativistic gyrogroups, we employ in this article the group theoretic concepts of divisible groupsand two-torsion free groupsto construct midpointsin gyrogroups. Systems of successive midpoints then describe straight gyrolinesand suggest a new, natural distance function that involves a Thomas gyration. These, in turn, reveal a new, interesting geometry that underlies relativistic velocity spaces. In this resulting gyrogeometrythe straight gyrolines form geodesics under a distance function which turns out to be the Poincaré hyperbolic distance function relaxed by a Thomas gyration. These geodesics do obey the parallel axiom of Euclidean geometry. Ironically, (i) attempts to understand the parallel postulate of Euclidean geometry gave rise to hyperbolic geometry in which the parallel postulate disappears;(ii) hyperbolic geometry gave rise to Einstein's STR; (iii) Einstein's STR established the bizarre and counterintuitive relativistic effect called Thomas precession, the abstraction of which is called Thomas gyration; and (iv) Thomas gyration now repairs in this article the Poincaré distance function of hyperbolic geometry to the point where the parallel postulate reappears. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 39.1 (2005) 31-47 [Access article in PDF] Holistic Integrated Design Education: Art Education in a Complex and Uncertain World Christopher Nokes Egosystem All art is the solution to an initiating design problem that must be articulated, even if the problem is this: to create something without meaning. As such, all art is a literary process, whereby the idea is articulated before that idea is (...) re-presented as an art form. And this is precisely what I attempt to do in the classroom when I assign highly challenging, universal, socio-cultural based and interpretive design problems. Both intent and solutions are implicit in the design assignments given to students. In each case the design process is emphasised, and students define the problem, research (often collaboratively), brainstorm (diving deeply into the problem for potential solutions), develop alternative solutions, use free-hand sketches and storyboarding to track the design and decision-making process, and (finally) select the best design for development and evaluation. Definition of key terms, research and storyboarding are the initial steps in the process to solving each of the design problems. Some examples of problem solving performance tasks are provided below (Table 1).Regarding the last example, in my first year of teaching I accepted a position on agreement that I teach Grade 10 (sophomore) mathematics. Even though my teaching background favored art and history, this was not a hardship because my original degree was in architecture (University of Toronto, 1978). I realized quickly that my personal romance with D.N. Perkins's Knowledge as Design demanded that I attempt to teach mathematics as a design process (much to the dismay of the department head).1 Nevertheless, imaginative mathematical works of mind were explored, based on original "design problems." As well, collaborative math tests were developed (and structured as design problems), where students divided into groups or design teams, each team having a "competent mathematician" on [End Page 31] Click for larger viewTable 1 Works of Mind; Visual Arts as a Problem-Solving Design Process [End Page 32]board. Each team worked together to solve one challenging mathematical problem, or a series of challenging mathematical design problems, under a time limit. This ensured that each student had a role to play. A key group dynamic here is that students speak to each other as peers, in a way teachers cannot: "No! You don't do it that way, silly. It's like this!" says A. "Ok! Ok! Don't yell at me," says B tenderly. "It's like this?" "Yes!" says A. "See! You really are good at math!" It was a beautiful thing to watch. The so-called "stupid-at-math" students saw how the "brainy" math students interpreted and approached mathematics, while the "brainy" students pulled those students who always believed they were "stupid at math" up to their level. In the end (to say the least), it greatly increased the weaker students' comfort level entering the classroom, and (at best) it gave weaker math students confidence by dispelling some of the mystical mystery which mathematics seems to possess — mathematics is not a mystery, it is a problem waiting to be solved as any other design problem once you know the process. Click for larger viewTable 2 Components of the Egosystem This is holistic integrated design education (or HIDE). Transforming students from the traditional, isolated receiver of information to the holistic child requires a fundamental transformation of the associative-cognitive paradigm of learning behavior and psychology, based on the child's ego development in a kind of object-filled, symbolical, self-contained world.2 In actuality, the world is complex, multi-faceted, hyper-sensitive, with many people of different socio-cultural and intellectual frames of mind interacting; and it is (thus) hardly self-contained. The world has indeed evolved that far. Somehow, like all paradigms, the ego must undergo a similar evolution, a similar transformation.3 A new version of ego must be invented, one that takes into account all the stuff of objective reality — the... (shrink)

This article explores the idea of ‘play’ as a metaphor to understand the world as an always presupposed frame of all experiences and appearances. A large part of it is devoted to the work of Eugen Fink, who developed a notion of the world as play, as a speculative idea beyond phenomenology. This article argues firstly in favor of such an effort to understand the world as play, as an alternative to onto-theological metaphysics. However, it argues secondly, (...) that a stronger and more convincing concept of play can be found by elaborating on the views of Hans-Georg Gadamer and Jan Patočka. Gadamer discussed ‘play’ as a metaphor for art, while Patočka worked on the notion of ‘world’ as a phenomenological idea that serves as a frame for all experiences. A combination of these two ideas may result in a better alternative to both Fink’s approach and to traditional onto-theological metaphysics. (shrink)

David Wallace's `Dennett's Criterion' plays a key part in establishing realist claims about the existence of a multiverse emerging from the mathematical formalism of quantum physics, even after decoherence is fully appreciated. Although the philosophical preconditions of this criterion are not neutral, they are rarely explicitly addressed conceptually. I tease apart three: (I) a rejection of conceptual bridge laws even in cases of inhomogeneous reduction; (II) a reliance on the pragmatic notion of usefulness to highlight quasi-classical patterns, as seen in (...) a decoherence basis, over others; and (III) a structural realist or `functional realist' point of view that leads to individuating those patterns as real macroscopic objects at the coarse-grained level, as they are seen from the Classical Stance (analogous to Dennett's Intentional Stance). I conclude that the justification of Dennett's Criterion will be intimately tied up with the fate of strong forms of naturalism, and in particular that Wallacian quantum mechanics is a key case study for concretely evaluating his `math-first' structural realism (Wallace 2022). (shrink)

Individuals who experience stereotype threat – the pressure resulting from social comparisons that are perceived as unfavourable – show performance decrements across a wide range of tasks. One account of this effect is that the cognitive pressure triggered by such threat drains the same cognitive resources that are implicated in the respective task. The present study investigates whether mindfulness can be used to moderate stereotype threat, as mindfulness has previously been shown to alleviate working-memory load. Our results show that performance (...) decrements that typically occur under stereotype threat can indeed be reversed when the individual engages in a brief mindfulness task. The theoretical implications of our findings are discussed. (shrink)

One is a science, the other an art; one useful, the other seemingly decorative, but mathematics and music share common origins in cult and mystery and have been linked throughout history. Emblems of Mind is Edward Rothstein’s classic exploration of their profound similarities, a journey into their “inner life.” Along the way, Rothstein explains how mathematics makes sense of space, how music tells a story, how theories are constructed, how melody is shaped. He invokes the poetry of Wordsworth, the anthropology (...) of Le;vi-Strauss, the imagery of Plato, and the philosophy of Kant. Math and music, Rothstein shows, apply comparable methods as they create their abstractions, display similar concerns with ratio and proportion, and depend on metaphors and analogies to create their meanings. Ultimately, Rothstein argues, they reveal the ways in which we come to understand the world. They are images of the mind at work and play; indeed, they are emblems of Mind itself. Jacques Barzun called this book “splendid.” Martin Gardner said it was “beautifully written, marvelous and entertaining.” It will provoke all serious readers to think in new ways about the grand patterns in art and life. “Lovely, wistful. . . . Rothstein is a wonderful guide to the architecture of musical space, its tensions and relations, its resonances and proportions. . . . His account of what is going on in the music is unfailingly felicitous.”— New Yorker “Provocative and exciting. . . . Rothstein writes this book as a foreign correspondent, sending dispatches from a remote and mysterious locale as a guide for the intellectually adventurous. The remarkable fact about his work is not that it is profound, as much of the writing is, but that it is so accessible.”— Christian Science Monitor. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 38.4 (2004) 71-80 [Access article in PDF] The Arts and the Creation of Mind: Eisner's Contributions to the Arts in Education Arthur Efland Professor Emeritus, Department of Art Education The Ohio State University In the last four years at least three books in arts education have dealt with the subject of cognition in relation to the arts. I refer to Charles Dorn's Mind in (...) Art, my book Art and Cognition, and Elliot Eisner's The Arts and the Creation of Mind, with the publication of the latter providing the occasion for this article.1 Each of these texts makes its case for the arts in education on somewhat similar grounds. All three share the view that the creation and understanding of works of art, though endowed with feeling and emotion, are nevertheless cognitive endeavors. But why have so many books appeared on the topic of cognition at this time? To answer this question it becomes necessary to describe the changes in our understanding of cognition and the problems these have created for the arts in education.Once cognition was the term used to designate propositional thinking with verbal and numerical symbols, whereas the current sense of the term embraces all forms of thought including mental images obtained through perception. In short it includes all forms of sentience by which the human organism comes to know itself and its environment. This change was to have a major impact upon curriculum reform initiatives in all studies but it was to have a revolutionary impact upon education in the arts for reasons explained later in this essay. However, an adequate story of cognition in the arts cannot be told without a discussion of Eisner's contributions to this discourse. The Waning of Behaviorism For the first half of the twentieth century the psychology that dominated educational practice was behaviorism. Its proponents included psychologists like Edward L. Thorndike, James B. Watson, and B.F. Skinner.2 Each strove to create a science of psychology that would match the rigor of physics or chemistry, where causes in relation to effects would be carefully observed and measured, making the explanation, prediction, and control of phenomena possible, especially those behaviors that fall under the control of the classroom teacher. The formation of connections called stimulus-response (S-R) bonds had become the molar unit to explain learning, much [End Page 71] like the way that differences in the structure of the atom was used to explain the behavior of the chemical elements of the Periodic Table. This bond between environmental stimuli and the organism's response was seen as the elementary unit of behavior while the IQ had become its measure. Invisible notions like mind and imagination were banished to metaphysical philosophy, outside the legitimate bounds of science.Though behaviorists never denied the existence of higher order thinking that is, abstract, sense-free thinking as found in pure mathematics, they were unable to explain how these human capacities emerge through the accumulation of such rudimentary stimulus-response events. Nevertheless, they recognized that humans do have a capacity for thinking that relies heavily upon symbols like words, numbers and the like. Moreover, certain subjects that require reason and logic, like math and theoretical physics, would be inconceivable without such symbols and the rules by which these are manipulated. By contrast it was assumed that the arts, which relied on sensory images, either did not employ this type of propositional thought, or did so to a far lesser degree. Thus the arts could be dispatched to the noncognitive or affective domains with little or no reduction in the learner's cognitive capacities. Indeed, these noncognitive realms, which gave play to feelings and emotions, were often seen as inimical to the acquisition of rational powers of thought. Intellectual power as it was then understood, required that feelings and emotions be brought under the control of reason.As long as behaviorism served as the dominant paradigm, the school curriculum could be divided into two or three broad divisions... (shrink)

In physics education, equations are commonly seen as calculation tools to solve problems or as concise descriptions of experimental regularities. In physical science, however, equations often play a much more important role associated with the formulation of theories to provide explanations for physical phenomena. In order to overcome this inconsistency, one crucial step is to improve physics teacher education. In this work, we describe the structure of a course that was given to physics teacher students at the end of (...) their master’s degree in two European universities. The course had two main goals: To investigate the complex interplay between physics and mathematics from a historical and philosophical perspective and To expand students’ repertoire of explanations regarding possible ways to derive certain school-relevant equations. A qualitative analysis on a case study basis was conducted to investigate the learning outcomes of the course. Here, we focus on the comparative analysis of two students who had considerably different views of the math-physics interplay in the beginning of the course. Our general results point to important changes on some of the students’ views on the role of mathematics in physics, an increase in the participants’ awareness of the difficulties faced by learners to understand physics equations and a broadening in the students’ repertoire to answer “Why?” questions formulated to equations. Based on this analysis, further implications for physics teacher education are derived. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Buddhist-Christian Studies 23 (2003) 39-41 [Access article in PDF] Wishing I Were Here:Postcards from My Religious Journey Grace G. Burford Prescott College Summer 1966, Bowling Green, Kentucky An energetic ten-year-old, sitting on a red-cushioned wooden pew in a Presbyterian church leans over to her mother to whisper, "Which is it? Are we supposed to be like little children, or leave behind our childish ways?" After church, her mother does (...) a reasonably good job at answering the question.Later, perhaps even later that day, this little girl has gleefully exchanged her dress and going-to-church shoes for a cotton shirt and shorts and blue Keds, and has escaped to her favorite spot in the woods behind her house. There she swings on vines in imitation of Tarzan and plays contentedly on her own for hours, feeling utterly at home.In this scene, we see that the little girl has discovered that she can best deal with a certain type of recurring physical pain by focusing her entire attention on her breath, as she silently repeats "breathing in, breathing out." Fall 1971, Bryn Mawr, Pennsylvania A group of eight or so teenagers attend their English literature class at an elite college-preparatory school for girls. Our hero, recently arrived, southern accent still quite in evidence, revels in real education; this a delightfully stark contrast to what she got from Kentucky public schools, then forty-ninth in the nation according to some poll or other—only Mississippi's were worse. In this particular class she finds herself defending Presbyterians against what she considers simply inaccurate descriptions of them by James Joyce. At the same time, she is waking up to the realization that she does not believe—and the suspicion that she never really has believed—the Christian doctrines she has been raised on. Indeed, she feels quite foolish for never having properly examined what exactly she had bought into when she participated in all those church activities. She can't recall ever actually believing in "God the Father, Almighty, Maker of Heaven and Earth," much less in "Jesus Christ, His only Son, Our Lord," and all the rest of it. [End Page 39] Spring 1975, Swarthmore, Pennsylvania Having thoroughly rejected religion—for she knows none other than the one she grew up with—our hero pursues study of astronomy, math, language, and music, quite intent on becoming a college professor of some subject or another. Somewhat annoyed that she must take two courses in the curricular area that includes religion, philosophy, anthropology, and sociology, but encouraged by her friends' assertions that religion courses are "not too bad," she signs up for religion and science, figuring that at least half of it will be rational. At the same time, she takes a course on Asian religions. Sometime in the middle of a clear spring night we find her engaged in her part-time job, seated at the eyepiece end of a twenty-meter-long, twenty-four-inch refracting telescope, patiently keeping a star placed just so on the cross-hairs in the siting scope, making fine adjustments to the telescope's precise tracking while the light of stars collects on glass plates coated with very fast photographic emulsion. Between clicks of the shutter she ponders the curiously attractive ideas she is encountering in her religion courses this term. Spring 1983, Evanston, Illinois Our hero earns a Ph.D. in the history and literature of religions, with a focus on Buddhism and Hinduism, and heads for Washington, D.C., to become what she had always aspired to be—a college professor. Summer 1997, Interstate 40 Having experienced a denial of tenure, the challenges of part-time college teaching, training and freelance work in the field of copyediting, life as a wildlife-wielding teacher of auditoria full of elementary school children, an administrative job as second-in-command to a self-described megalomaniac, and the vagaries of teaching two hundred students a term—this lifelong seeker eagerly moves across the country to start a job teaching at an alternative, experiential learning-based... (shrink)

The present research investigates gender gaps in the results of secondary school exit exams in mathematics in Poland in 2015. The analysis shows that, in the basic level exam, males are highly overrepresented at the upper end of the score distribution. The same pattern did not exist in the extended-level Matura. Two explanations are offered here. The differences are driven by gender self-selection in high school programs. Students who decide on maths-related tracks have more maths lessons than other students. Secondly, (...) a student who takes the extended Matura also has to take the basic Matura exam. As a result, the population of students taking the basic Matura is highly differentiated in terms of maths competence and motivation. Additionally, the analysis of differential item functioning shows that only a few items were flagged as having DIF. (shrink)

Global policy transfer has become increasingly popular in recent years, and one recent example of such policy transfer is the England–China Teacher Exchange, which was initiated in 2014 with the explicit aim of raising attainment in maths in English primary schools by trialling concepts used in Shanghai schools, Shanghai rising to the top of the PISA rankings in 2009. However, as this paper will argue this is an overly simplistic attempt to transfer a policy between two wholly different contexts, the (...) lack of success of the policy seen in the very limited impact on student attainment in the participating schools. Whilst such policy transfer has increasingly taken place in the context of isomorphism and global pressures to adopt policy from high performing education systems, it is argued that policy needs to be explicitly reconsidered in terms of the local context it is being imported into if it is to be embedded in an effective manner, as well as rooted firmly in research. It is also argued that the England–China Teacher Exchange reflects a broader ideological focus in coalition government policy on the marketisation of education alongside the PISA rankings, rather any wider consideration of how this particular policy would drive up standards. (shrink)

By comparing the insights of Jean-Francois Lyotard on various manifestations of the science question with feminists such as Luce Irigaray and Donna Haraway certain compromising contradictions in Lyotard's overall discourse are revealed.

This book offers a unique analysis of how ideas about science and technology in the public and scientific imaginations (in particular about maths, logic, the gene, the brain, god, and robots) perpetuate the false reality that values and politics are separate from scientific knowledge and its applications. These ideas are reinforced by cultural myths about free will and individualism. Restivo makes a compelling case for a synchronistic approach in the study of these notoriously 'hard' cases, arguing that their significance reaches (...) far beyond the realms of science and technology, and that their sociological and political ramifications are of paramount importance in our global society. This innovative work deals with perennial problems in the social sciences, philosophy, and the history of science and religion, and will be of special interest to professionals in these fields, as well as scholars of science and technology studies. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Evidence, Authority, and Interpretation: A Response to Jason HelmsCarol PosterAs someone with a long-standing interest in Heraclitus, I am delighted that Philosophy and Rhetoric is providing a forum for an ongoing discussion of his work.1 Although Jason Helms and I do disagree on specific matters concerning Heraclitean interpretation, we are, I think, in full agreement concerning the importance of Heraclitus for both rhetorical and philosophical studies and intend these (...) essays as contributions to what, it is hoped, will be a fruitful ongoing discussion of Heraclitus within the interdisciplinary tradition of this journal. Rather than address many minor points of disagreement superficially, I will concentrate below on close analysis of a few specific issues that I consider paradigmatic of differences in method rather than merely in conclusions.Panta Rhei (All Things Flow)That Heraclitus was interested in establishing any sense of orthoepia plays down his insistence on the panta rhei (everything flows). To suggest any final rightness of words would suggest that everything flows but the Logos.(Helms, this issue)Actually, I do not use the phrase “final rightness of words” but, rather, describe Heraclitus as “focus[ing] on the problem of correctness of names” and as [End Page 288] “consider[ing] the possibility that one can learn something about the nature of things by examining the non-literal sense of their names” (2006, 15).2 Name is an English equivalent of the Greek onoma (Latin nomen, substantive as opposed to verb or particle), not rhêma (word, verb, phrase) or logos (word, account, speech, saying, story, ratio, reason, etc.). The phrase “correctness of names” alludes to an ongoing discussion among scholars in classics and philosophy about a specific problem in early Greek thought (normally discussed in relation to Heraclitus, Protagoras, Prodicus, Plato’s Cratylus, and Aristotle’s Categories and On Interpretation).More importantly, Helms seems to think it impossible a priori that Heraclitus might have considered some sort of doctrine of flux compatible with a belief in correctness of names. Ancient evidence, however, suggests that Heraclitus did, in fact, consider stability of logos, correctness of names, and sensible flux compatible in some manner.For logos as unchanging, dk22b1 begins, “Of the logos that exists always [eontos aiei] uncomprehending are men.”3 Although the syntax is ambiguous, eontos aiei suggests some stability of logos. Sextus Empiricus states that Heraclitus considered the “divine logos” stable and eternal and human reason grounded in its participation therein (Adv. Math. 7.126–33).4 The “commonality” of logos in dk22b2 also suggests some interpretive stability, in the sense of logos not varying with respect to the perception of the individual.The phrase panta rhei, although solidly entrenched in the reception history of Heraclitus, often as part of a “doctrine of flux,” is not actually a well-attested Heraclitean saying (included in the dk “b” fragments) but, rather, derived from early testimonia. Whether the phrase is a paraphrase, indirect quotation, or Platonic/Aristotelian recasting of Heraclitus is uncertain. The earliest sources are Platonic:Therefore you [Theaetetus] were quite right in saying that knowledge is nothing else than perception, and there is complete identity between the doctrine of Homer and Heraclitus and all their followers— that all things are in motion like streams [hoion rheumata kineisthai ta panta]—the doctrine of the great sophist Protagoras that man is the measure of all things—and the doctrine of Theaetetus that, since these things are true, perception is knowledge.(Theaet. 160d) [End Page 289]Those... would agree well enough with Heraclitus that all things move and nothing remains still [panta menein ouden].(Crat. 401d)Heraclitus says that all things move and nothing remains still [hoti panta chorei kai ouden menei], and he likens the universe to the current of a river, saying that you cannot step twice in the same stream.(Crat. 402a)Nor will he condemn himself and all things and say that there is no health in them, but that all things are flowing like leaky pots [panta hôsper keramia rhei], or believe that all things are just like people afflicted with catarrh, flowing and running all the time [rheumatos te kai katarrou panta ta chrêmata].(Crat. 440c–d... (shrink)

Theories of grounded and embodied cognition offer a range of accounts of how reasoning and body‐based processes are related to each other. To advance theories of grounded and embodied cognition, we explore the cognitive relevance of particular body states to associated math concepts. We test competing models of action‐cognition transduction to investigate the cognitive relevance of directed actions to students’ mathematical reasoning in the area of geometry. The hypotheses we test include (1) that cognitively relevant directed actions have a (...) direct effect on performance (direct cognitive relevance hypothesis), (2) that cognitively relevant directed actions lead to more frequent production of gestures during explanations, which leads to improved performance (mediated cognitive relevance hypothesis), and (3) that performance effects of directed actions are influenced by the presence or absence of gesture production during mathematical explanations (moderated cognitive relevance hypothesis). We explore these hypotheses in an experiment where high school students (N = 85) evaluated the truth of geometry conjectures after performing cognitively relevant or cognitively irrelevant directed actions while playing a movement‐based video game. Contrary to the direct and mediated cognitive relevance hypotheses, we found no overall differences in performance or gesture production between relevant and irrelevant conditions. Consistent with the moderated cognitive relevance hypothesis, cognitive relevance influenced mathematical performance, as measured by the accuracy of students’ intuitions, insights, and the validity of their proofs, provided that students produced certain kinds of gestures during mathematical explanations (i.e., with explanatory gestures as the moderator). Implications for theories of grounded and embodied cognition and the design of embodied forms of educational interventions are discussed. (shrink)