Symbolic Manipulators Affect Mathematical Mindsets

Symbolic calculators like Mathematica are becoming more commonplace among upper level physics students. The presence of such a powerful calculator can couple strongly to the type of mathematical reasoning students employ. It does not merely offer a convenient way to perform the computations students would have otherwise wanted to do by hand. This paper presents examples from the work of upper level physics majors where Mathematica plays an active role in focusing and sustaining their thought around calculation. These students still engage in powerful mathematical reasoning while they calculate but struggle because of the narrowed breadth of their thinking. Their reasoning is drawn into local attractors where they look to calculation schemes to resolve questions instead of, for example, mapping the mathematics to the physical system at hand. We model the influence of Mathematica as an integral part of the constant feedback that occurs in how students frame, and hence focus, their work

The Middle Way: East Asian masters students’ perceptions of critical argumentation in U.K. universities.

The paper explores the learning experiences of East Asian masters students in dealing with Western academic norms of critical thinking in classroom debate and assignment writing. The research takes a cultural approach, and employs grounded theory and case study methodology, the aims being for students to explain their perceptions of their personal learning journeys. The data suggest that the majority of students interviewed rejected full academic acculturation into Western norms of argumentation. They instead opted for a ‘Middle Way’ that synergizes the traditional cultural academic values held by many East Asian students with those elements of Western academic norms that are perceived to be aligned with these. This is a relatively new area of research which represents a challenge for British lecturers and students

Semantics of a Typed Algebraic Lambda-Calculus

Algebraic lambda-calculi have been studied in various ways, but their semantics remain mostly untouched. In this paper we propose a semantic analysis of a general simply-typed lambda-calculus endowed with a structure of vector space. We sketch the relation with two established vectorial lambda-calculi. Then we study the problems arising from the addition of a fixed point combinator and how to modify the equational theory to solve them. We sketch an algebraic vectorial PCF and its possible denotational interpretations

Multilingual gendered identities: female undergraduate students in London talk about heritage languages

In this paper I explore how a group of female university students, mostly British Asian and in their late teens and early twenties, perform femininities in talk about heritage languages. I argue that analysis of this talk reveals ways in which the participants enact ‘culturally intelligible’ gendered subject positions. This frequently involves negotiating the norms of ‘heteronormativity’, constituting femininity in terms of marriage, motherhood and maintenance of heritage culture and language, and ‘girl power’, constituting femininity in terms of youth, sassiness, glamour and individualism. For these young women, I ask whether higher education can become a site in which they have the opportunities to explore these identifications and examine other ways of imagining the self and what their stories suggest about ‘doing being’ a young British Asian woman in London

Beyond deficit-based models of learners' cognition: Interpreting engineering students' difficulties with sense-making in terms of fine-grained epistemological and conceptual dynamics

Researchers have argued against deficit-based explanations of students' troubles with mathematical sense-making, pointing instead to factors such as epistemology: students' beliefs about knowledge and learning can hinder them from activating and integrating productive knowledge they have. In this case study of an engineering major solving problems (about content from his introductory physics course) during a clinical interview, we show that "Jim" has all the mathematical and conceptual knowledge he would need to solve a hydrostatic pressure problem that we posed to him. But he reaches and sticks with an incorrect answer that violates common sense. We argue that his lack of mathematical sense-making-specifically, translating and reconciling between mathematical and everyday/common-sense reasoning-stems in part from his epistemological views, i.e., his views about the nature of knowledge and learning. He regards mathematical equations as much more trustworthy than everyday reasoning, and he does not view mathematical equations as expressing meaning that tractably connects to common sense. For these reasons, he does not view reconciling between common sense and mathematical formalism as either necessary or plausible to accomplish. We, however, avoid a potential "deficit trap"-substituting an epistemological deficit for a concepts/skills deficit-by incorporating multiple, context-dependent epistemological stances into Jim's cognitive dynamics. We argue that Jim's epistemological stance contains productive seeds that instructors could build upon to support Jim's mathematical sense-making: He does see common-sense as connected to formalism (though not always tractably so) and in some circumstances this connection is both salient and valued.Comment: Submitted to the Journal of Engineering Educatio

Using resource graphs to represent conceptual change

We introduce resource graphs, a representation of linked ideas used when reasoning about specific contexts in physics. Our model is consistent with previous descriptions of resources and coordination classes. It can represent mesoscopic scales that are neither knowledge-in-pieces or large-scale concepts. We use resource graphs to describe several forms of conceptual change: incremental, cascade, wholesale, and dual construction. For each, we give evidence from the physics education research literature to show examples of each form of conceptual change. Where possible, we compare our representation to models used by other researchers. Building on our representation, we introduce a new form of conceptual change, differentiation, and suggest several experimental studies that would help understand the differences between reform-based curricula.Comment: 27 pages, 14 figures, no tables. Submitted for publication to the Physical Review Special Topics Physics Education Research on March 8, 200

Framing interculturality: a corpus-based analysis of on-line promotional discourse of higher education intercultural communication courses

This paper examines how intercultural communication (ICC) and the notion of culture are framed in on-line promotional discourse of higher education intercultural communication courses. It analyses a specialised corpus comprised of 14,842 words from 43 course websites of master’s programmes in intercultural communication in the UK and the US—internationally, the two largest providers of such programmes. Through combining corpus tools with a ‘situated meaning’ approach, the analysis reveals that while a small number of courses acknowledge cultural ‘complexity’, culture is still very often reduced to an essentialised and static notion, despite growing criticism against such an approach in ICC literature. Intercultural communication is valorised as a combination of desirable skills and knowledge conducive to effective communication of different cultural groups and for those working in international arenas. Significant differences between the UK and US courses are identified with regard to the extent of associations with diversity-related social categories. The lack of interpretive, critical and constructivist positions on culture in promotional discourse is discussed in the context of neoliberal discourse and the current thinking towards professional competences dominant in Britain, North America, and other parts of the world

Meaning between, in, and around words, gestures and postures: multimodal meaning making in children's classroom communication

The view of language from a social semiotic perspective is clear. Language is one of many semiotic resources we employ in our communicative practices. That is to say that while language is at times dominant, it always operates within a multimodal frame and furthermore, at times modes other than language are dominant. The proposed 2014 National Curriculum for the UK, on the other hand, values pupils' face-to-face classroom interaction in terms of standard spoken English (i.e. in terms of the mode of language alone). This paper offers examples demonstrating how embodied modes such as gesture, posture, facial expression, gaze and haptics work in conjunction with speech in children's collaborative construction of knowledge. In other words, what may have been previously conceived as gaps and silences - often interpreted as an absence of language - are in fact instantiations of the work of semiotic modes other than language. In order to consider this closely, this paper offers evidence from a multimodal micro-analysis of pupil-to-pupil, face-to-face interaction in one science lesson in a Year Five UK Primary classroom. It demonstrates how children's meaning-making is achieved through apt use of all available semiotic resources