Does science also prefer a ternary pattern?

Nothing is as difficult to see as the obvious (B. Malinowski)

Through the importance of the number three in our culture and the strange preference for a ternary pattern of our nature one can perceive how and why number theory degraded to numerology. The strong preference of our minds for simple patterns can be read as the key to understanding not only the development of numerology, but also why scientists were and are prone to give their discoveries or creations a structure that is based on simple patterns and, among them, especially the ternary pattern. If some numbers seem to appear quite often throughout the fabric of reality, like zero, one, two, and three, reality has, nevertheless, been preferentially analysed in a way to enhance its ternary character. The present excursion through some scientific domains where the ternary pattern has been used tries to offer an answer to the fascination that some numbers, and patterns based on them, exerted and exerts, even today, on human minds. Throughout the overall models created by the human mind, be they natural or spiritual, the models based on a ‘unary’ and on a ‘dualistic’ pattern are surely important, but the model based on a ternary pattern ended up assuming an archetypical character, which is quite intriguing, and deserves to be deepened. The paper is a useful resource for projects for students and background material for teachers of mathematics touching, as it does, on biology, chemistry and physics.     

Paul Painlevé and his contribution to science

The life and career of the great French mathematician and politician Paul Painlevé is described. His contribution to the analytical theory of nonlinear differential equations was significant. The paper outlines the achievements of Paul Painlevé and his students in the investigation of an interesting class of nonlinear second-order equations and new equations defining a completely new class of special functions, now called the Painlevé transcendents. The contribution of Paul Painlevé to the study of algebraic nonintegrability of the N-body problem, his remarkable observations in mechanics, in particular, paradoxes arising in the dynamics of systems with friction, his attempt to create the axiomatics of mechanics and his contribution to gravitation theory are discussed.     

The ‘invisible science’: operational research for the British Armed Forces after 1945

This paper presents an original account of the contribution of operational research (OR) to the formulation of tactics and strategy on behalf of the British Armed Forces in the four decades after 1945. The main focus is on the Cold War in the European theatre, where OR analysts devoted considerable time and effort to the modelling of warfare on behalf of the British Army of the Rhine. In the absence of combat data for nuclear weapons, OR analysts devised a sequence of war games which evolved in conformity with the development of NATO strategy in relation to the Warsaw Pact. Again in the context of the Cold War, the paper analyses the role of OR in relation to the early V bomber force and the introduction of ‘global war studies’ on behalf of the Royal Navy. The paper also comments on the organisational structure of British military OR following on the creation of a centralised OR facility within the Ministry of Defence in 1965. In conclusion, the paper notes the sea-change in military OR following the end of the Cold War in 1990 and the onset of a period of sustained ‘asymmetric’ military operations in the former Yugoslavia, the Middle East and Afghanistan.     

Robert Leslie Ellisʼs work on philosophy of science and the foundations of probability theory

The goal of this paper is to provide an extensive account of Robert Leslie Ellis?s largely forgotten work on philosophy of science and probability theory. On the one hand, it is suggested that both his ‘idealist’ renovation of the Baconian theory of induction and a ‘realism’ vis-à-vis natural kinds were the result of a complex dialogue with the work of William Whewell. On the other hand, it is shown to what extent the combining of these two positions contributed to Ellis?s reformulation of the metaphysical foundations of traditional probability theory. This parallel is assessed with reference to the disagreement between Ellis and Whewell on the nature of (pure) mathematics and its relation to scientific knowledge.     

Spreading the gospel of management science: operational research in Iron and Steel, 1950–1970

This paper builds on the author's earlier work on the history of operational research by presenting an analysis of the development of the discipline in Iron and Steel, an industry long regarded as one of the outstanding pioneers in the application of management science to decision-making processes. The contribution of Sir Charles Goodeve and BISRA to the diffusion and practice of operational research is well-documented. Less well known is the reaction to operational research within the managerial hierarchies of the private sector iron and steel companies. In the light of the development of dedicated operational research groups by the leading companies after 1950, it might be assumed that the industry was highly receptive to the discipline in terms of its perceived benefits. The present paper questions this assumption by highlighting the problems encountered by operational researchers in two of the largest Iron and Steel Companies which gave every appearance of being at the forefront of the practice of management science in British industry. Where appropriate, the paper draws contrasts and comparisons with the development of operational research within the nationalised Coal Industry.     

Assessing science students’ attitudes to mathematics: a case study on a modelling project with mathematical software

This article reports the attitudes of students towards mathematics after they had participated in an applied mathematical modelling project that was part of an Applied Mathematics course. The students were majoring in Earth Science at the National Taiwan Normal University. Twenty-six students took part in the project. It was the first time a mathematical modelling project had been incorporated into the Applied Mathematics course for such students at this University. This was also the first time the students experienced applied mathematical modelling and used the mathematical software. The main aim of this modelling project was to assess whether the students’ attitudes toward mathematics changed after participating in the project. We used two questionnaires and interviews to assess the students. The results were encouraging especially the attitude of enjoyment. Hence the approach of the modelling project seems to be an effective method for Earth Science students.     

Inquiry-based learning in mathematics and science: a comparative baseline study of teachers’ beliefs and practices across 12 European countries

In the European educational context, reports by expert groups have identified the necessity of a renewed pedagogy in schools to overcome deficits in science and mathematics teaching and to raise the standards of scientific and mathematical literacy. Inquiry-based learning (IBL) is considered the method of choice. However, it remains open to what extent IBL is actually used in day-to-day teaching. In the study presented here we elaborate—from the perspective of teachers—the current status of IBL in day-to-day teaching. Further, we explore what problems teachers anticipate when implementing IBL. In order to gain insight into the wide spectrum of practices in mathematics and science teaching in relation to IBL, a baseline study using teacher questionnaires was carried out in the 12 participating countries. We present selected results from this study that for the first time provides an overview of teachers’ beliefs and their reports on the current use of IBL practices in a European context. The results facilitate a cross-cultural comparison on the potentials and challenges of implementing IBL from the perspective of practicing teachers. Furthermore, the study reveals considerable differences between the teaching of mathematics and science subjects. The findings of the baseline study can serve as a reference line against which the impact of interventions to improve the quality of teaching and learning can be evaluated.     

Facilitating parental engagement in school mathematics and science through inquiry-based learning: an examination of teachers’ and parents’ beliefs

This study examined teachers’ and parents’ beliefs on the implementation of inquiry-based modeling activities as a means to facilitate parental engagement in school mathematics and science. The study had three objectives: (a) to describe teachers’ beliefs about inquiry-based mathematics and science and parental engagement; (b) to describe parents’ beliefs about inquiry-based mathematics and science and their engagement in inquiry-based problem solving; and (c) to explore the impact of an inquiry-based learning environment comprising a model-eliciting activity and Twitter. The research involved three sixth-grade teachers and 32 parents from one elementary school. Teachers and parents participated in workshops, followed by the implementation of a model-eliciting activity in two classrooms. Three teachers and six parents participated in semi-structured interviews. Teachers reported positive beliefs on parental engagement in the mathematics and science classrooms and the potential positive role of parents in implementing innovative problem-solving activities. Parents expressed strong beliefs on their engagement and welcomed the inquiry-based modeling approach. Based on the results of this aspect of a four-year longitudinal design, implications for parental engagement in inquiry-based mathematics and science teaching and learning and further research are discussed.     

Is reliability a new science? A paper from the panel session held at the 10th International Conference on Mathematical Methods in Reliability

The 10th International Conference on Mathematical Methods in Reliability, MMR 2017, held in Grenoble, France during July 3‐7, entailed a panel discussion entitled “Is reliability a new science?” with Mark Brown, Regina Liu, William Meeker, Sheldon Ross, and Nozer Singpurwalla as panelists. Bill Meeker also doubled as a chair and as a moderator of the panel. The panel discussion was spawned by the recent appearance of a book by Professor Paolo Rocchi, Docent Emeritus of IBM, titled “Reliability is a new science: Gnedenko was right” published by Springer in 2017. The panel discussion was well attended and enthusiastically received and could serve as a forerunner to other such panel discussions at future MMR conferences. This paper presents some elements from the lively debate generated by this discussion.     

“Do we teach subjects or students?” Analyzing science and mathematics teacher conversations about issues of equity in the classroom

Teachers involved in a Master's level course in diversity participated in virtual, synchronous, anonymized discussions around issues of ethnic and racial diversity, gender, and stereotypes that could impact their students’ participation in fields related to science, technology, engineering, and mathematics (STEM). Guided by theoretical frameworks from Social Cognitive Career Theory (SCCT) and Critical Race Theory (CRT), a convenience sample of 14 science and mathematics teachers participated in a series of virtual chats using open‐ended questioning and facilitated by two university instructors. Using conversation and critical discourse analyses, three primary themes emerged: understanding of issues related to stereotypes, encouragement of females and minorities to pursue careers in STEM, and the place for diversity discussions in science and mathematics classrooms. The teachers felt burdened by curricular and administrative constraints that inhibit their ability to participate in thought‐provoking critical conversations. The paper concludes with a discussion of ways teachers can assist in the STEM career identity development of their underrepresented females and students of color and calls for research that combines the key findings in SCCT and CRT to build confidence and capacity for teachers to effectively confront issues of racism, sexism, and stereotyping in science and mathematics classrooms.