Policy learning and innovation theory: an interactive and co-evolving process

This paper explores links between the development of innovation theory since the late 1970s, and the evolution of innovation policy ideas, primarily in the 1990s. The argument is that there is a close connection between theory and policy, so that theory and policy learning can be seen as an integrated, co-evolving and interactive process. We analyse the theory-policy learning link in terms of two phases. We suggest that the complex economic crisis of the 1970s created an opening for rival analyses of events. During the 1980s, the development of evolutionary theories (pioneered by Nelson and Winter) and of empirically-based theories of the innovation process (pioneered by Nathan Rosenberg) created a framework in which policy agencies could consider heterodox ideas concerning objectives and instruments of public policy. By the early 1990s policy-makers, particularly in Europe, came to see RTD and innovation policies not just as important arenas of action in themselves, but as instruments towards more wide ranging policy objectives. The policy agencies involved, though hierarchical, were characterised by relatively open structures that permitted a degree of intellectual diversity: so organisations like the OECD and the European Commission played a central role, whereas the World Bank, for example, did not. Increasing policy interest stimulated a second phase of research in the 1990s, sponsored both nationally and by various EU programmes, in which expanding the innovation-oriented knowledge base became a significant objective for policy-makers. The paper argues that the theory-policy link has been central to the intellectual development of this field, which would have been impossible within the constraints of existing disciplinary structures and university funding systems. At the same time the analytical achievements have permitted a wide expansion in the conceptualization of policy targets and in the design of instruments available to policy-makers. In a sense, this is itself an evolutionary story: of a crisis and a conjunctural niche that permitted the creation and (so far) survival of a set of diverse and certainly non-conventional ideas.     

Coefficient relationship between rook and chromatic polynomials

It is shown that a p+q node graph G_c representation can be drawn for a chessboard C(p,q) i.e. an array of p rows and q columns. It is shown further that the coefficients of the rook polynomial for C(p,q) correspond 1:1 inversely with the coefficients of the chromatic polynomial for G_c written in factorial form.     

Dealing with ‘fragile identities’: resistance and refiguring in women mathematics students

Many learners may be successful in mathematics but nevertheless see themselves as existing only on the margins of the practice, or as lacking stability in it – in this sense, they have what can be called a fragile identity. Although this kind of relationship with mathematics is not limited to girls and women, they do appear to express such fragile identities more often or more readily. Drawing on qualitative and quantitative data from undergraduates in three English universities, this paper presents an analysis of the way in which university mathematics is differentially experienced by men and women, and of the part this may play in women’s ongoing narratives of self as mathematicians. It is suggested that some women resist traditional positionings in the mathematics world, drawing on local resources which enable a sense of agency as successful students and a refiguring of their relationships with mathematics.     

Why and how mathematicians read proofs: an exploratory study

In this paper, we report a study in which nine research mathematicians were interviewed with regard to the goals guiding their reading of published proofs and the type of reasoning they use to reach these goals. Using the data from this study as well as data from a separate study (Weber, Journal for Research in Mathematics Education 39:431–459, 2008) and the philosophical literature on mathematical proof, we identify three general strategies that mathematicians employ when reading proofs: appealing to the authority of other mathematicians who read the proof, line-by-line reading, and modular reading. We argue that non-deductive reasoning plays an important role in each of these three strategies.     

Implementation integrity in peer tutoring of mathematics

A two-year randomised controlled trial of peer tutoring in mathematics using the Duolog Math technique was operated in 80 schools. The aim was to achieve adequate implementation quality with modest pre-intervention training for teachers, who received brief didactic training and no process feedback (but they were to train pupils using modelling, practice and feedback). Implementation integrity was observed in Year 1 in 29 randomly selected schools; in Year 2 in 30 randomly selected schools. In both years some observed variables of class-wide context and individual technique were high; however, some were lower. There were deficits in: teachers introducing the problem, suggesting ways to concretise the problem and holding plenary sessions. Crucially, there was very little summarising or generalising. Thus, implementation was partial in both years, but better in Year 2. The implications for future intensity of training are explored.     

Critically engaging the ethics of AI for a global audience

Ethics and Information Technology - This article introduces readers to the special issue on Selected Issues in the Ethics of Artificial Intelligence. In this paper, I make a case for a wider...     

Errors of programming and ownership of the robot concept made by trainee kindergarten teachers during an induction training

Education and Information Technologies - Computational thinking in the educational environment has awaken a rising interest, having been included as part of the curricula from the very beginnings...     

Fine Motor Control is Related to Cognitive Control in Adolescents with Down Syndrome

The connection between human cognitive development and motor functioning has been systematically examined in many typical and atypical populations; however, only a few studies focus on people with Down syndrome (DS). Twelve adolescents with DS participated and their cognitive control, measured by the Corsi-Block tapping test (e.g., visual working memory), the Auditory Memory span test (e.g., verbal working memory) and the Tower of London test (e.g., cognitive planning), and motor control, measured by the Purdue Pegboard (e.g., fine motor control), were measured in this study. Results indicate that if people with DS have better performance in fine manual dexterity, they will have better performance in cognitive planning and verbal working memory abilities. The co-activation hypothesis of the prefrontal area and the cerebellum may support this positive relationship. Hence, it is suggested people with DS will obtain benefits in cognitive control by participating in further motor intervention.     

Examination of a Group Counseling Model of Career Decision Making With College Students

The authors examined the effectiveness of a group career counseling model (Pyle, 2007 ) on college students’ career decision‐making abilities. They used a Solomon 4‐group design and found that students who participated in the career counseling groups had significantly greater increases in career decision‐making abilities than those who did not participate in the groups. Implications for counseling and future research are discussed.