In a long-term study concerning mathematical tasks in primary schools, it was noted that teachers had difficulty in discussing mathematical processes and many lacked the vocabulary to do this. However, certain words and phrases such as 'pattern' or 'looking for pattern' were used with more confidence. With this in mind, discussions with teachers about commercial mathematics tasks were analysed based on mentions of pattern. It was found that the word was used frequently, but that some teachers had a wider and (...) more sophisticated view of 'pattern' than others. There were also variations in their views about teaching pattern, with some making it clear that they had strategies for helping children to see patterns. There was a feeling amongst some teachers that not all children could see patterns, and there was a tendency for this group to regard 'pattern spotting' as a top set activity. (shrink)
I develop a theory of counterfactuals about relative computability, i.e. counterfactuals such as 'If the validity problem were algorithmically decidable, then the halting problem would also be algorithmically decidable,' which is true, and 'If the validity problem were algorithmically decidable, then arithmetical truth would also be algorithmically decidable,' which is false. These counterfactuals are counterpossibles, i.e. they have metaphysically impossible antecedents. They thus pose a challenge to the orthodoxy about counterfactuals, which would treat them as uniformly true. What’s more, I (...) argue that these counterpossibles don’t just appear in the periphery of relative computability theory but instead they play an ineliminable role in the development of the theory. Finally, I present and discuss a model theory for these counterfactuals that is a straightforward extension of the familiar comparative similarity models. (shrink)
It is commonly held that the ascription of truth to a sentence is intersubstitutable with that very sentence. However, the simplest subclassical logics available to proponents of this view, namely K3 and LP, are hopelessly weak for many purposes. In this paper, I argue that this is much more of a problem for proponents of LP than for proponents of K3. The strategies for recapturing classicality offered by proponents of LP are far less promising than those available to proponents of (...) K3. This undermines the ability of proponents LP to engage in public reasoning in classical domains. (shrink)
It is commonly held that the ascription of truth to a sentence is intersubstitutable with that very sentence. However, the simplest subclassical logics available to proponents of this view, namely K3 and LP, are hopelessly weak for many purposes. In this article, I argue that this is much more of a problem for proponents of LP than for proponents of K3. The strategies for recapturing classicality offered by proponents of LP are far less promising than those available to proponents of (...) K3. This undermines the ability of proponents LP to engage in public reasoning in classical domains. (shrink)
This book has been written in the hopes of equipping teachers-in-training—that is, teacher candidates—with the skills needed for action research: a process that leads to focused, effective, and responsive strategies that help students succeed.
This paper addresses two related topics: 1. The disanalogies between elective cosmetic practices and sex reassignment surgery. Why does it seem necessary for me – an aging professional woman – to ignore the blandishments of hairdressers wielding dyes and dermatologists wielding acids and scalpels? Why does it not seem equally necessary for a transgendered person to repudiate sex reassignment procedures? 2. The role of the body in identity and agency. How do phenomenological insights regarding the constitution of selfhood in relation (...) to the interplay between the body image and corporeal know-how contribute to an account of the agency of transgendered individuals? Studying several paintings by contemporary feminist artist Jenny Saville has advanced my thinking on these topics. Saville’s imagery is an invaluable aid to reflection on these issues because she uses her painterly technique, which critics often dub “virtuoso,” to represent lived human bodies. In her work, viewers encounter representations of subjectivized, agentic corporeity, as distinct from inert, objectified flesh. Moreover, her sympathetic engagement with nonconformist, devalued bodies helps to reconfigure the standard gestalts of the human body that viewers typically carry with them and thus to convert fear and/or disgust into appreciation and understanding. In this paper, I consider three of Saville’s paintings. Plan, Saville’s self-portrait as a nude female whose body has been prepped for liposuction, conveys the pathos of this procedure. Matrix is a nude portrait of self-described “gender variant visual artist” Del LaGrace Volcano. In the words of one critic Saville’s depiction of Volcano’s nude intersexed body “restores beauty to the primitive [female] genital organ.” Passage, another nude portrait of an intersexed individual, is an image of vibrant sexuality despite the presumptively jarring juxtaposition of breasts and a penis. I argue that conceiving the agentic subject as a rational deliberative capability that uses a conjoined body as the instrument of its will makes it impossible to theorize the agency of transgendered people. In contrast, when agentic subjects are understood as embodied subjects and embodiment is understood as a dimension of practical intelligence, the agency of transgendered individuals is intelligible. (shrink)
The Middle Class—An Untidy Prominence: Verity Burgmann and Jenny Lee , A People's History of Australia Since 1788 Four Volumes: A Most Valuable Acquisition ; Making a Life ; Constructing a Culture ; Staining the Wattle.
Jenny Saville is a leading contemporary painter of female nudes. This paper explores her work in light of theories of gender and embodied agency. Recent work on the phenomenology of embodiment draws a distinction between the body image and the body schema. The body image is your representation of your own body, including your visual image of it and your emotional attitudes towards it. The body schema is comprised of your proprioceptive knowledge, your corporeally encoded memories, and your corporeal (...) proficiency with respect to various environments and activities. Saville is concerned with body image issues, and I discuss how she reconfigures representational practices with respect to feminine body images. However, the most exciting potential for feminist analysis of the state of the female nude derives from the concept of the body schema, for this concept endows the human body with subjectivity and agency. My key question, then, is by what pictorial means and to what extent Saville succeeds in representing agentic womanhood. I argue that interpreting Saville’s paintings from the standpoint of the body schema demonstrates the radicality of her remaking of the female nude and the rapport between her imagery and feminist values. (shrink)
: This essay examines an aesthetics of disgust through an analysis of the work of Scottish painter Jenny Saville. Saville's paintings suggest that there is something valuable in retaining and interrogating our immediate and seemingly unambivalent reactions of disgust. I contrast Saville's representations of disgust to the repudiation of disgust that characterizes contemporary corporeal politics. Drawing on the theoretical work of Elspeth Probyn and Julia Kristeva, I suggest that an aesthetics of disgust reveals the fundamental ambiguity of embodiment, allowing (...) us to critically attend to the aesthetic and cultural objectification of the female body. (shrink)
This essay examines an aesthetics of disgust through an analysis of the work of Scottish painter Jenny Saville. Saville's paintings suggest that there is something valuable in retaining and interrogating our immediate and seemingly unambivalent reactions of disgust. I contrast Saville's representations of disgust to the repudiation of disgust that characterizes contemporary corporeal politics. Drawing on the theoretical work of Elspeth Probyn and Julia Kristeva, I suggest that an aesthetics of disgust reveals the fundamental ambiguity of embodiment, allowing us (...) to critically attend to the aesthetic and cultural objectification of the female body. (shrink)
The last part of Wittgenstein's Blue Book consists of a discussion of Solipsism. In the course of that discussion there occur several remarks which are explicitly concerned with the concept of a person and with the criteria of personal identity. This section is replaced in the Philosophical Investigations by half a sentence which reads: ‘… there is a great variety of criteria for personal “ identity ”’. Wittgenstein has italicised the word ‘identity’, and has placed it in inverted commas: I (...) don't quite know why he does this, but it might be a hint to the effect that there is something slightly suspect about the notion of personal identity. (shrink)
“Ockham never wrote a commentary on Aristotle’s Metaphysics,” Jenny Pelletier tells us at the beginning of this monograph, “but the absence of such a commentary does not allow us to infer that he was uninterested in or skeptical of metaphysics” (1–2). Her central contention is that Ockham had a robust conception of metaphysics as a distinct branch of scientific knowledge concerning being and God. It is an argument worth making insofar as many scholars in recent years have held that (...) Ockham lacks a metaphysics or rejects the possibility of one. In opposing these claims, Pelletier also has much to say about what Ockham’s metaphysics includes and how it relates to other sciences. As the study of being, it considers .. (shrink)
In contrast to [Susan] Sontag, who used the tools of literary criticism to evaluate sexually explicit fiction, I will use the conventions of pornography to interpret a dramatic monologue in which an expected sexual encounter fails to take place. In analyzing Rossetti’s “Jenny,” I will employ an interpretive model based on the work of [Steven] Marcus, [Susan] Griffin, and [Andrea] Dworkin. Despite different assumptions about sexuality—Marcus is a Freudian, Griffin believes in a mystical eros residing in the psyche and (...) waiting to be rediscovered, Dworkin regards heterosexuality as a construct for subjugating women and masking men’s homoerotic drive—they share several ideas applicable to “Jenny.” Although pornography features, and indeed perpetuates, various kinds of masculine power, especially the powers of money, class, and culture, it purports to be ahistorical in order to obscure its status as ideology. It depicts male sexuality as fear-laden aggression resulting in very little pleasure; thus it is not liberating on either a political or a personal basis. Pornography does not include “others.” Women are present only to be silenced, objectified, treated as screens on which a man projects his fantasies. Marcus, Griffin, and Dworkin are all concerned with what Suleiman calls “the representational or fantasmatic content” of pornography and “the political implications of that content.” The risks of emphasizing the representational—most especially, the denigration of language and style that result from Dworkin’s approach—can, as Suleiman says, be mitigated by careful attention to a particular text .In Rossetti’s poem, a young man attempts to purchase a night’s pleasure with a London prostitute named Jenny. After she thwarts his plans by falling asleep, he spends the night meditating about her beauty, speculating about her past, present, and future, and thinking about the causes of prostitution. Although Rossetti’s subject matter is consistent with the etymological definition of pornography as “writing about prostitutes,” he avoids the explicit depiction of sexual activity which has been the common element in most modern accounts of the genre. Indeed, the only physical contact between the narrator and Jenny occurs at daybreak when he places coins in her hair and gives her a parting kiss. Robin Sheets is associate professor of English at the University of Cincinnati. She has written on Thackeray, George Eliot, and other Victorian writers and is coauthor of The Woman Question: Society and Literature in Britain and American, 1837-1883. (shrink)
Wars have been entered into as a means of gaining property, taking slaves and dominating and controlling peoples. The pacifist claims that no form of war can ever be justified. By contrast, just war theory holds that it is possible for a war to be morally justified, an idea that underlies much international law, as can be seen in the Geneva Conventions. Teichman introduces us to such thinkers as Aristotle, Cicero, Augustine, Aquinas, Hugo Grotius, John Rawls and Elizabeth Anscombe on (...) the very idea of a just war. (shrink)