Some heuristics about the ecosystem of mathematics research data

Like in other sciences, research data play a growing role in mathematics, but in contrast to classical objects like measurements in physics they are much more heterogeneous. They may take the shape of abstract objects like the collection of integer sequences in OEIS, algorithms and their implementations as mathematical software, libraries of test problems or statistical data. From an infrastructure viewpoint, which aims at sustainable and connected data repositories which facilitate researchers to use existing information efficiently, it is essential to define an appropriate framework that allows not just storage but also connection and retrieval of the various types of data. Recently, there have been promising attempts to define standards for mathematical software, but the general task remains a big challenge, which is also addressed within the recently initiated GDML working group of the IMU. This is especially important in the fields of applied mathematics where research is often connected to research data originating from applications. The goal of this talk is a first attempt to analyse the diverse ecosystem of research data based on reference data from zbMATH. This approach has worked quite well for mathematical software, resulting in the formation of the swMATH database. Though reference data involve always a bias, the collected information of about 16 million reference data in zbMATH may be useful to identify the recent needs of researchers in different fields pertaining mathematical research data, and we discuss several aspects of such an analysis. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

What environmental studies students think about mathematics and what could be done about it

Mathematics is playing an increasing role in environmental studies, which causes problems for many students because of their low mathematical ability. A survey among first year environmental studies students revealed a significant number both of negative experiences in learning mathematics and negative feelings towards the subject. A proposal to design an alternative curriculum which aims to link the maths more closely with environmental studies is outlined as an answer to the problem of negative attitudes to the required mathematics.     

Cultivating inquiry about space in a middle school mathematics classroom

During 46 lessons in Euclidean geometry, sixth-grade students (ages 11, 12) were initiated in the mathematical practice of inquiry. Teachers supported inquiry by soliciting student questions and orienting students to related mathematical habits-of-mind such as generalizing, developing relations, and seeking invariants in light of change, to sustain investigations of their questions. When earlier and later phases of instruction were compared, student questions reflected an increasing disposition to seek generalization and to explore mathematical relations, forms of thinking valued by the discipline. Less prevalent were questions directed toward search for invariants in light of change. But when they were posed, questions about change tended to be oriented toward generalizing and establishing relations among mathematical objects and properties. As instruction proceeded, students developed an aesthetic that emphasized the value of questions oriented toward the collective pursuit of knowledge. Post-instructional interviews revealed that students experienced the forms of inquiry and investigation cultivated in the classroom as self-expressive.     

Theories in practice: mathematics teaching and mathematics teacher education

Whilst research on the teaching of mathematics and the preparation of teachers of mathematics has been of major concern in our field for some decades, one can see a proliferation of such studies and of theories in relation to that work in recent years. This article is a reaction to the other papers in this special issue but I attempt, at the same time, to offer a different perspective. I examine first the theories of learning that are either explicitly or implicitly presented, noting the need for such theories in relation to teacher learning, separating them into: socio-cultural theories; Piagetian theory; and learning from practice. I go on to discuss the role of social and individual perspectives in authors’ approach. In the final section I consider the nature of the knowledge labelled as mathematical knowledge for teaching (MKT). I suggest that there is an implied telos about ‘good teaching’ in much of our research and that perhaps the challenge is to study what happens in practice and offer multiple stories of that practice in the spirit of “wild profusion” (Lather in Getting lost: Feminist efforts towards a double(d) science. SUNY Press, New York, 2007).     

Conceptions of Turkish mathematics teachers about the effectiveness of classroom teaching

This study investigated how Turkish mathematics teachers evaluate the effectiveness of classroom teaching in terms of improving students’ mathematical proficiency. To this purpose, teachers were asked to evaluate a mathematics lesson as presented them in a vignette. By means of cluster analysis, the participants’ evaluations of the lesson were described in five thematic dimensions, which could be further assembled into two overriding categories: students’ understanding of the subject, and teachers’ classroom practices. The overall aim of the current paper is to propose a preliminary model of the framework that Turkish mathematics teachers use to evaluate a mathematics lesson.     

Prior decisions and experiences about mathematics of students in bridging courses

We report on the survey responses of 51 students attending mathematics bridging courses at a major Australian university, investigating what mathematics, if any, these students had studied in the senior years of schooling and what factors affected their decisions about the level of mathematics chosen. Quantitative findings are augmented by qualitative responses to open-ended questions in the survey as well as excerpts from follow-up emails. The findings show that the major reasons for students taking lower levels of mathematics in senior year(s), or dropping mathematics, include finding enough time for non-mathematics subjects, confidence in mathematical capability, advice and maximizing potential ranking for university admission.     

Learning cycles for mathematics: An investigative approach to middle-school mathematics

Middle-school-aged students are a complex mixture of often conflictive social, intellectual, and physical ingredients while middle-school mathematics content becomes increasingly abstract and procedure driven. Preparation for algebra and higher mathematics often ignores the developmental and social needs of the middle-school student while overemphasizing computational facility with previously learned elementary mathematics content. The need to explore and question will be encouraged by a classroom atmosphere and instructional strategies that provide for active problem solving and cooperative group learning. This article articulates the philosophical and research bases forlearning cycle pedagogy which, when applied to mathematics teaching, is especially appropriate for the special needs of the middle-school student. The components of, and theoretical/research bases for, the learning cycle are described. Learning cycle pedagogy is the embodiment of the vision of mathematics classroom instruction depicted in the Standards (NCTM, 1989).     

Experienced engineers becoming mathematics teachers: preliminary perceptions of mathematics teaching

Engineers who choose to change careers and become mathematics teachers are a specific group as far as their mathematics learning in the context of engineering and their previous work experience are concerned. Regarding mathematics, they mainly engaged in applied mathematics associated with engineering, which is a highly practical field. This research explores experienced engineers’ perceptions of mathematics teaching-related topics, before starting their studies in a pre-service mathematics teacher preparation programme. This research explores their perceptions of mathematics as a discipline, mathematics teaching and mathematical understanding. The qualitative research involves three mechanical engineers, two industrial management engineers, and an electrical engineer. Semi-structured interviews were conducted before the beginning of the programme, and analysed qualitatively. The participants view engineering as an applied and changing discipline while perceiving mathematics as closed, rigorous, accurate, systematic, theoretical and as a tool for engineering. They mostly address general features of mathematics teaching while expressing a more multifaceted view of mathematical understanding. Due to the specific characteristics of the participants, this study may contribute to planning mathematics teacher preparation programmes for engineers.     

Pre-service teachers' point of views about learning history of mathematics: a case study in Turkey

This study examines pre-service teachers’ points of view about learning history of mathematics during their undergraduate education. An open-ended questionnaire was administered to one hundred and twenty pre-service teachers, during the fall semester of the 2013–14 academic year. The participants indicated that learning history of mathematics could increase their content knowledge as they understand how formulas, theories and relations were developed over time. In addition, it could develop them intellectually as they learn life stories of mathematicians. Also, it could help them to hold the attention of students, and answer some of the why questions. Particularly, they reported using history of mathematics knowledge while teaching Geometry and Numbers.     

The mathematics of ageing:

Central European Journal of Operations Research - Age is a crucial variable in social sciences and particularly in population dynamics. In this paper, we link methods from formal demography and...     

Locally logical mathematics: An emerging teacher honoring both students and mathematics

This case study explores the mathematics engagement and teaching practice of a beginning secondary school teacher. The focus is on the mathematical opportunities available to her students (the classroom mathematics) and how they relate to the teacher's personal capacity and tendencies for mathematical engagement (her personal mathematics). We use a mathematical process-and-action approach to analyze mathematical engagement and then employ the teaching triad—mathematical challenge, sensitivity to students, and management of learning—to situate mathematical engagement within the larger context of teaching practice. The article develops the construct of locally logical mathematics to underscore the cogency of mathematical engagement in the classroom as part of a coherent mathematical system that is embedded within a teaching practice. Contributions of the study include the process-and-action approach, especially in tandem with the teaching triad, as a tool to understand nuances of mathematical engagement and differences in demand between written and implemented tasks.     

From lessons to lectures: NCEA mathematics results and first-year mathematics performance

Given the recent radical overhaul of secondary school qualifications in New Zealand, similar in style to those in the UK, there has been a distinct change in the tertiary entrant profile. In order to gain insight into this new situation that university institutions are faced with, we investigate some of the ways in which these recent changes have impacted upon tertiary level mathematics in New Zealand. To this end, we analyse the relationship between the final secondary school qualifications in Mathematics with calculus of incoming students and their results in the core first-year mathematics papers at Canterbury since 2005, when students entered the University of Canterbury with these new reformed school qualifications for the first time. These findings are used to investigate the suitability of this new qualification as a preparation for tertiary mathematics and to revise and update entrance recommendations for students wishing to succeed in their first-year mathematics study.     

Contingent conceptions of accomplished practice: the cultural specificity of discourse in and about the mathematics classroom

Classroom discourse and professional discourse about classrooms constitute forms of social performance undertaken within affordances and constraints that can be both cultural and linguistic. The nature of those discourses performed in mathematics classrooms provides a key indicator of pedagogical principles underlying classroom practice and the theories of learning on which these principles are implicitly founded. The discourses about mathematics classrooms give expression to these pedagogical principles sometimes explicitly and sometimes through embedding privileged forms of practice in the naming conventions by which the mathematics classroom is described. The research reported in this paper suggests that each of these discourses is culturally and linguistically specific. As a consequence, conceptions of accomplished practice are contingent on the history of custom and insight embedded in the conventions of practice and the language with which that practice is described.     

A brief history of mathematics education in Turkey: K-12 mathematics curricula

In this study, we survey the history of mathematics education in Turkey starting with its historical roots in the foundation of the republic. The changes in mathematics education in Turkey over the last century are investigated through an analysis of changes in curricular documents for K-12 schools. We consider the factors and reasons affecting curriculum developments, changes in philosophy and structure in terms of standards, objective and instructions. This article utilizes archival research techniques by examining original sources and illustrates the nature of the changes benefiting from a historical perspective. As a result of such analysis of the aforesaid sources, we have seen that the main reasons for changing mathematics curricula are: to build up a modern civilization in Turkey; the reports of John Dewey and the recommendations of Kate Wofford, William C. Varaceus and Watson Dickerman; the desire to become a member of the European Union; international factors and political situations.