It matters which class you are in: student-centred teaching and the enjoyment of learning mathematics

The 2007 Trends in International Mathematics and Science Survey highlighted how attitudes to mathematics had declined sharply for students in many of the high attaining countries in the survey, England being no exception. There is a notable drop in positive attitudes to mathematics between 9 and 14, as well as a remarkable decline for 14 year olds over time. This paper explores survey data collected from over 3000 11-year-olds in 16 schools during 2008 with the goal of exploring possible factors that might be contributing to this attitudinal decline. The association between student-centred teaching and enjoyment of learning mathematics is reported as part of a multi-scale analysis that shows the extent to which student experiences differ between schools and between classes within schools.     

Changing teaching practices toward effective mathematics instruction in the Korean context: characteristics and implications

Student-centered pedagogy has been consistently emphasized in many reform documents. This paper traces the process of changing traditional teacher-centered instruction toward a student-centered approach in the Korean context. By looking closely at the teacher’s successes and struggles, the paper attempts to understand better what constitutes the process of implementing new ideals into actual classroom contexts. The paper also analyzes what has changed and not changed in this teaching practice in order to reveal culturally specific values and expectations of mathematics instruction. Given that teaching practices of Korea have rarely been studied in international contexts, this paper is expected to foster an increase in the recent interest in effective mathematics instruction across different education systems.     

Renewing textbooks to align with reformed curriculum in former colonies: Ugandan school mathematics textbooks

Several nations have reformed both their mathematics pedagogy and curriculum. The remaining challenge is to review teaching and learning resources to support the renewed pedagogy and curriculum. This paper responds to the following question: what pedagogy and curriculum are depicted in textbooks used in Uganda? Ugandan textbooks were analyzed in terms of mathematics content structure and genre, and presentation of written and non-written voice and looks (appearance). Whereas certain Ugandan mathematics textbooks used the narrative form and others chose to eliminate the use of extensive text, these textbooks include common characteristics such as spiral coverage of mathematics content. A few strides toward reform pedagogy, such as use of contexts familiar to learners in development of rules and concepts, were evinced among selected Uganda textbooks. More strides are needed in revising a majority of textbooks to align with the renewed curricula on certain aspects including integrating learning tools—digital and non-digital—within the textbook resources. A critical reflection on curriculum renewals adopted from other countries is needed when designing textbooks to match these renewals.     

Changing behaviours in defence acquisition: a game theory approach

Why do so many major defence contracts fail to deliver to the contractually agreed performance, time and cost requirements? This paper identifies the conspiracy of optimism as an important factor in the initiation of many projects. Using a combination of Game Theory and participatory workshops, we formulate a theory on the conspiracy of optimism and test it experimentally. This work forms part of a culture and behaviour change initiative within Defence Acquisition involving the Ministry of Defence and many defence contractors.     

Conservation science and technology identity instrument: Empirically measuring STEM identities in informal science learning programs

Our research centered on developing the Conservation Science and Technology Identity (CSTI) instruments as an empirical way to measure STEM identities and the intersection of identity constructs such as competence, performance, recognition, and ways of seeing and being. The surveys were used in a large funded multi-year project for teens and adults learning geospatial technologies and conservation science to use in intergenerational community conservation projects. We investigated whether an informal STEM learning program was developing new STEM identities or advancing well-developed identities. The instruments’ content validity was determined through a vetting process from national STEM identity research experts. Reliability was estimated with Cronbach coefficient alpha. Mann-Whitney and Wilcoxon Signed Rank tests were used to determine participants’ STEM identities and the workshop’s effect on specific identity constructs. We found teens and adults had historically similar STEM identities, with stronger conservation science than technology. Both science and technology competences, as well as technology ways of seeing and being, significantly increased, suggesting CSTI can be a valuable instrument in empirically assessing STEM identities.     

On a research programme concerning the teaching and learning of linear algebra in the first-year of a French science university

The paper discusses the current approach to the teaching of linear algebra in the first year at a French science university and the main difficulties that students have with this material. A brief account is given of the first steps towards the design of a teaching experiment. From a joint didactical and historical survey a first hypothesis is drawn: epistemological specificity, the use of ‘meta-lever’, the use of changes of settings and points of view, and the importance of the concept of rank. The main aspects and objectives of the teaching design with which we experimented over a whole teaching semester for five years with around 200 students are presented. Finally, the type of evaluations that were set up and the difficulties encountered are explained. The conclusion deals with issues on the teaching and learning of linear algebra as well as issues on methodological and theoretical points in relation to the original didactical framework.     

Functions: a modelling tool in mathematics and science

It is difficult for the students to transfer concepts, ideas and procedures learned in mathematics to a new and unanticipated situation in science. An alternative to this traditional transfer method stresses the importance of modelling activities in an interdisciplinary context between mathematics and science. In the paper we introduce a modelling approach to the concept of function in upper secondary school is introduced. We discuss pedagogical and didactical issues concerning the interplay between mathematics and science. The discussion is crystallized into a didactical model for interdisciplinary instruction in mathematics and science. The model is considered as an iterative movement with two phases: (1) the horizontal linking of the subjects: Situations from science are embedded in contexts which are mathematized by the students, (2) the vertical structuring in the subjects: The conceptual anchoring of the students' constructs from the horizontal linking in the systematic and framework of mathematics and science respectively.     

Dancy Cartwright: Particularism in the philosophy of science

This paper aims to explore the space of possible particularistic approaches to Philosophy of Science by examining the differences and similarities between Jonathan Dancy’s moral particularism—as expressed in both his earlier writings (e.g., Moral Reasons, 1993), and, more explicitly defended in his book Ethics without Principles (2004)—and Nancy Cartwright’s particularism in the philosophy of science, as defended in her early collection of essays, How the Laws of Physics Lie (1983), and her later book, The Dappled World: A Study of the Boundaries of Science (1999). I shall argue that Dancy’s particularism is more radical, but also more plausible, than Cartwright’s, concluding that we have good reason to embrace a scientific particularism that is far closer to Dancy’s ethical particularism than any view defended by Nancy Cartwright, or any other philosopher from the ‘Stanford school’ of scientific theory.     

Challenges in data science: a complex systems perspective

The ability to process and manage large data volumes has been proven to be not enough to tackle the current challenges presented by “Big Data”. Deep insight is required for understanding interactions among connected systems, space- and time- dependent heterogeneous data structures. Emergence of global properties from locally interacting data entities and clustering phenomena demand suitable approaches and methodologies recently developed in the foundational area of Data Science by taking a Complex Systems standpoint. Here, we deal with challenges that can be summarized by the question: “What can Complex Systems Science contribute to Big Data? ”. Such question can be reversed and brought to a superior level of abstraction by asking “What Knowledge can be drawn from Big Data?” These aspects constitute the main motivation behind this article to introduce a volume containing a collection of papers presenting interdisciplinary advances in the Big Data area by methodologies and approaches typical of the Complex Systems Science, Nonlinear Systems Science and Statistical Physics.     

The Cricket and the Ant: Organizational Trade-offs in Changing Environments

Organizations face trade-offs when they adopt strategies in changing resource environments. The type of trade-off depends on the type of resource change. This paper offers an organizational trade-off model for quantitative resource changes. We call it the “Cricket and Ant” (CA) model, because the pertaining strategies resemble the cricket and ant's behavior in La Fontaine's famous fable. We derive theorems in this CA model in First Order Logic, which we also use to demonstrate that two theory fragments of organizational ecology, i.e., niche width theory and propagation strategy theory, obtain as variant cases of CA; their predictions on environmental selection preferences derive as theorems once their respective boundary conditions are represented in the formal machinery.     

Exercising QS: quantitative skills in an exercise science course

This study seeks to bring the discipline of exercise science into the discussion of Quantitative Skills (QS) in science. The author's experiences of providing learning support to students and working with educators in the field are described, demonstrating the difficulty of encouraging students to address their skills deficit. A survey of students’ perceptions of their own QS and of that required for their course, demonstrates the difficulties faced by students who do not have the prescribed assumed knowledge for the course. Limited results from academics suggest that their perceptions of students’ QS deficits are even direr than those of the under-prepared students.     

Learning to teach science in urban schools: Context as content

The purpose of this phenomenological study was to explore how science teachers who persisted in urban schools interpreted and responded to the unique features of urban educational contexts. With 17 alumni who taught in metropolitan areas across seven states, the Science Educators for Urban Schools (SEUS) program provided a research setting that offered a unique view of science teachers’ development of knowledge of urban education contexts. Data sources included narratives of teaching experiences from interviews and open‐ended survey items. Findings were interpreted in light of context knowledge for urban educational settings. Findings indicated that science teaching in urban contexts was impacted by the education policy context, notably through accountability policies that narrowed and marginalized science instruction; community context, evident in teacher efforts to make science more relevant to students; and school contexts, notability their ability to creatively adjust for resource deficiencies and continue their own professional growth. Participants utilized this context knowledge to transform student opportunities to learn science. The study suggests that future science education research and teacher preparation efforts would benefit from further attention to the unique elements of urban contexts, specifically the out of classroom contexts that shape science teaching and learning.     

Probing interactions in exploratory teaching: a case study

This study investigates an exploratory teaching style used in an undergraduate geometry course to help students identify an ellipse. We attempt to probe beneath the surface of exploration to understand how the actions of teachers can contribute to developing students’ competence in justifying an ellipse. We analyse the complex interactions between student, content, and teacher, and discuss explicit pedagogical strategies that help students develop a higher level of geometric reasoning. The findings indicate that students engaged in guided explorations by the teacher and in group discussions with peers were able to identify an ellipse and justify their reasoning.     

Cost minimization models: Applications in a teaching hospital

The primary objective of this article is to explore the feasibility of the application of cost minimization analysis in a teaching hospital environment. The investigation is concerned with the development of cost per admission and cost per patient day models. These models are further used for determining the value of the length of stay that would minimize cost per patient day (projected length of stay) and for estimating the costs. This study is based on total of 109,060 observations (2002), obtained from a teaching hospital in South Florida. The top 10 diagnosis-related groups (DRGs) with the highest volume are selected for the study. The cost models are fitted to the data for an average R² value of 87.3%, and a mean absolute percentage error (MAPE) value of 16.1%. The result demonstrates that if a hospital can control the length of stay at the projected level, on average, the cost per admission and the cost per patient day will decrease. Based on 8703 admissions for the selected DRGs in 2002, the total cost per year and the cost per patient day are decreased by approximately 8.56% ($15,453,841) and 4.02% ($66.30), respectively. Overall, these results confirm that the concept of cost minimization analysis in economic theory can be applied to healthcare industries for the purpose of reducing of costs. Cost minimization and cost variation analyses offer useful information to hospital management for better decision-making. It would be an important aid in making management decisions, particularly for cost reduction.     

Ways of talking and ways of positioning: Students’ beliefs in an inquiry-oriented differential equations class

As part of developmental research for an inquiry-oriented differential equations course, this study investigates the change in students’ beliefs about mathematics. The discourse analysis has identified two different types of perspective modes - i.e., discourse of the third-person perspective and discourse of the first-person perspective - in the students’ mathematical narratives, depending on their ways of positioning themselves with respect to mathematics. In the third-person perspective discourse, the students positioned themselves as passive recipients of mathematics that has been established by some external authority. In the first-person perspective discourse, the students positioned themselves as active mathematical inquirers and produced mathematics by interweaving their own mathematical ideas and experiences. Over the semester, students’ mathematical discourse changed from third-person perspective narratives to first-person perspective narratives. This change in their discourse pattern is interpreted as an indication of change in their beliefs about mathematics. Finally, this article discusses the instructional features that promote the change.