Making sense of double number lines in professional development: exploring teachers’ understandings of proportional relationships

This study presents a qualitative analysis of the knowledge teachers in one professional development course used to reason about proportional relationships with double number lines. We work from the knowledge-in-pieces perspective to consider the existing knowledge the participants did or did not invoke when learning to reason with this new-to-them representation. We analyzed videotaped sessions of a group of urban middle-grade teachers across five class meetings. Our findings include discussion of the two pieces of knowledge that emerged as important for reasoning about proportions with the representation and three knowledge pieces that deterred meaning making. Implications for professional development are discussed as are the implications for conceptualizing teachers’ understanding through a knowledge-in-pieces lens.     

Automatic recommendation system based on hybrid filtering algorithm

Education and Information Technologies - Web recommendation systems are ubiquitous in the world used to overcome the product overload on e-commerce websites. Among various filtering algorithms,...     

Circadian rhythms

Over the series of articles on circadian rhythms, we saw that living organisms exhibit daily rhythms in multiple behaviours and physiological processes. Although some rhythms may be passive responses to 24 h environmental cycles, many are regulated by endogenous-rhythmgenerating machinery called circadian clocks. We have introduced the concept of circadian clocks, their organization and the underlying molecular mechanisms. In this article, we will dwell upon one of the most fundamental questions pertaining to circadian clocks, ‘Why do we have them?’. The aim of this article is not to provide answers, but to discuss the efforts and strategies used to address this question and critically evaluate explanations proposed till date.     

Doctoral program selection using pairwise comparisons

This article illustrates the application of a pairwise comparison methodology to the doctoral program selection process. The first section includes a brief discussion of the pairwise comparison methodology better known in the literature as Saaty's Analytic Hierarchy Process. In the next section, a hierarchy for structuring and facilitating the doctoral program selection decision is described. This section is followed by an illustration of the methodology using the hierarchy for which four MBA students contemplating a doctoral program provided pairwise comparisons. Next, the results obtained above are discussed, and followed by our summary and conclusions.     

Students’ and teachers’ perceptions of classroom learning environment in Bhutanese eighth-grade mathematics classes

This paper reports a study of students’ and teachers’ perceptions of their classroom learning environment in Bhutanese eighth-grade mathematics classes. Research suggests that positive perceptions of the learning environment can have a positive influence on students’ learning outcomes, interest and engagement in classroom activities. The study was conducted in 2013, using the survey samples of 608 students and 98 teachers from 22 lower- and middle-secondary schools in western Bhutan. Students’ and teachers’ perceptions of the classroom environment were measured using the Mathematics Classroom Learning Environment Survey (MCLES). Students and teachers mostly perceived their classroom environments favourably on the MCLES scales irrespective of gender, school level and school location. The study is significant for understanding and evaluating the implementation of new mathematics curriculum in Bhutanese schools because it could guide the development of strategies for more-productive mathematics classroom learning. It is also significant from the perspective of Bhutan’s national goal of Gross National Happiness because perceptions and happiness always go hand-in-hand.     

UNIX: Genesis and design features

UNIX was primarily designed by Ken Thompson and Dennis Ritchie at Bell Labs. It was, and continues to be, regarded as a seminal contribution to operating systems design methodology, architecture and research. The primary strengths of UNIX lie in the soundness of underlying design principles. This article aims at providing insights into the making of UNIX and in particular, how the notion of open software helped in taking a utility- and tool-driven approach. This approach provides both usability1 and extensibility besides maintainability. In fact, we see that the designers used best software architecture practices. We discuss UNIX shell and its operating environment, kernel, file systems, process creation and management, version management and documentation standard. Every effort has been made to quote from authentic sources to trace history.     

An extension of the general Struble's method for solving an nth order nonlinear differential equation when the corresponding unperturbed equation has some repeated eigenvalues

This paper attempts to show the more suitability of the extended general Struble's technique than the unified Krylov-Bogoliubov-Mitropolskii (KBM) method in solving the problems that occur during the critical conditions. Recently a critically damped condition of an nth, n=2,3, … order weakly nonlinear autonomous ordinary differential equation has been investigated by the unified KBM method, in which the corresponding unperturbed equation has some real (negative) repeated eigenvalues. But there are more important critical conditions, which are still untouched. One of them occurs when a pair of complex eigenvalues is equal to another. It is complicated to formulate as well as to utilize the KBM method to investigate this condition. However, the extended general Struble's technique is applicable to both autonomous and non-autonomous systems. Solutions obtained for different critical conditions as well as for different initial conditions show a good agreement with the numerical solutions. The method is illustrated by an example of a fourth-order nonlinear differential equation whose unperturbed equation has repeated complex eigenvalues. A steady-state solution is determined for the non-autonomous equation. Moreover, a critical condition of a fourth-order nonlinear equation is investigated when two real eigenvalues of the unperturbed equation are non-positive and equal.     

Paradigm wars, dialogue or dance: is rapprochement possible and/or desirable?

In focusing on the Kincheloe and Tobin paper, ‘The Much Exaggerated Death of Positivism,’ this forum explores the hegemony of positivism in the professional practices of a group of educators whose research expertise lies in the fields of science education, mathematics education and leadership education. Responding to the first question, ‘What is your personal/professional experience of the hegemony of positivism?’, four key issues arise: is positivism part of the external world or is it within us (and thus what is our agency)?, the role of positivism as a driver of Western cultural imperialism, dualism as the chief logic of positivism, and the difficulty of responding to positivism from a pluralist perspective. The second question, ‘Is rapprochement between positivism and other paradigms possible and/or desirable without being re-colonised?’, raises a number of key issues that, although relatively new to science education, are of increasing interest to cultural studies researchers keen to embrace alternative research paradigms with which to create culturally inclusive science curricula. The discussants reveal their personal experiences of being marginalised by the hegemony of positivism and give voice to a range of opinions about how best to respond. The integral perspective of spiral dynamics is proposed as a model of paradigm evolution, our fundamental assumptions about modern progress are questioned, and the non-dualist logic of dialectics is explored as a more inclusive rationality for researchers. In the spirit of counter-hegemonic cultural studies, the discussants draw on their personal Buddhist and Hindu perspectives to open new doorways into complex ontological systems lying beyond the simplistic materialism of crypto-positivism. We are given a glimpse of powerful means of generating new insights into the emergent universe (within and without) that an evolving science endeavours to explain.