Semantic alignment across whole-number arithmetic and rational numbers: evidence from a Russian perspective

ABSTRACT

Solutions to word problems are moderated by the semantic alignment of real-world relations with mathematical operations. Categorical relations between entities (tulips, roses) are aligned with addition, whereas certain functional relations between entities (tulips, vases) are aligned with division. Similarly, discreteness vs. continuity of quantities (marbles, water) is aligned with different formats for rational numbers (fractions and decimals, respectively). These alignments have been found both in textbooks and in the performance of college students in the USA and in South Korea. The current study examined evidence for alignments in Russia. Textbook analyses revealed semantic alignments for arithmetic word problems, but not for rational numbers. Nonetheless, Russian college students showed semantic alignments both for arithmetic operations and for rational numbers. Since Russian students exhibit semantic alignments for rational numbers in the absence of exposure to examples in school, such alignments likely reflect intuitive understanding of mathematical representations of real-world situations.     

Well-Being and Pluralism

It is a commonly expressed sentiment that the science and philosophy of well-being would do well to learn from each other. Typically such calls identify mistakes and bad practices on both sides that would be remedied if scientists picked the right bit of philosophy and philosophers picked the right bit of science. We argue that the differences between philosophers and scientists thinking about well-being are more difficult to reconcile than such calls suggest, and that pluralism is central to this task. Pluralism is a stance that explicitly drives towards accommodating and nurturing the richness and diversity of well-being, both as a concept and as an object of inquiry. We show that well-being science manifests a contingent pluralism at the level of methodology, whereas philosophy of well-being has largely rejected pluralism at the conceptual level. Recently, things have begun to change. Within philosophy, conceptual monism is under attack. But so is methodological pluralism within science. We welcome the first development, and bemoan the second. We argue that a joined-up philosophy and science of well-being should recognise the virtues of both conceptual and methodological pluralism. Philosophers should embrace the methodological justification of pluralism that can be found in the well-being sciences, and scientists should embrace the conceptual reasons to be pluralist that can be found in philosophical debate.

     

Fifteen minute stories about training

This panel presentation at the Journal's conference in St Petersburg responded to the conference theme of 'Ancestors in Personal, Professional and Social History' by relating it to the experience of training and being trained on the IAAP 'router' programme in Russia. The two organizers of the programme (JW and CC) have worked in Russia for over 12 years, bringing analysts from Britain to Moscow and St Petersburg on a 'shuttle' basis as supervisors and personal analysts. A few months after handing over the router programme in December 2010 to the Russian colleagues they had trained, they invited four analysts, three Russian and one Belarusian, to tell a short personal story about their training, linking it to the theme of 'the Ancestors'. The resulting four stories are very different but complement each other, using imagery to illustrate issues concerning both value and ambivalence. JW and CC jointly wrote their story about the programme in response to the four stories, reflecting on some of their themes and from them, giving consideration to the flexibility and limits of such a model of cross-cultural training. Themes in the stories included the possibility of mutual adaptation to another culture without losing tradition and identity; moving on from doctrinaire Soviet attitudes in education to embrace 'not knowing'; both organizers and routers learning from mistakes and from joint experience without guilt or shame; the need to protect reflective space amidst the constraints of time and geography. All Russian and UK contributors could finally acknowledge their shared luck to find themselves in the right place at the right time to respond to the collective revival of psychoanalytic practice in Russia.