Connecting social perspectives on mathematics teacher education in online environments

This article explores theoretical issues underpinning the design and use of online learning environments in mathematics teacher education. It considers the contribution of social theories of learning to conceptualising technology-mediated interaction, focusing specifically on community of practice models and the notion of digital mathematics performance. The article begins by introducing social perspectives on collaboration. Because of the diversity of theories within this broad research paradigm, the next section outlines networking strategies that have been proposed for connecting theoretical approaches. There follows a discussion of studies that illustrate the community of practice and performance-based approaches to research into online mathematics teacher education. The main purpose of the article is to show how these approaches could be connected by examining the same teaching and learning scenarios through different theoretical lenses. The final section identifies implications of this exploration for the design of online learning environments in mathematics teacher education to capitalise on the affordances of Web-based technologies.     

Online education for in-service secondary teachers and the incorporation of mathematics technology in the classroom

This paper reviews existing research on how in-service high school teachers have learned about, worked on or thought about the incorporation of mathematics technology into their teaching practices. The paper reviews different scenarios of instruction issuing from important research related to teacher professional development. Specifically, we will deal with contributions to online in-service mathematics teacher education that refer to the use of digital technologies in classroom teaching practices. The different articles reviewed belong to a range of teams of researchers from several universities and countries, and who have implemented distinct online education approaches. That work has allowed the gaining of knowledge on the specificities of using Web 2.0 tools for mathematics professional development (MPD), the function that online teacher interaction has in teacher learning, and the actual classroom conditions in which mathematics technology is incorporated into instructional practice. This paper describes and discusses the design features of those approaches emphasizing the main concepts and their underpinning theoretical frames, noting important design elements, and specific results. Finally, the paper discusses how some of these research findings are connected with emergent issues in the field of MPD.     

Effective design of massive open online courses for mathematics teachers to support their professional learning

Three MOOCs for Educators (MOOC-Eds) were designed for mathematics and statistics teachers based on principles of effective online professional development     

Prospective mathematics teachers’ development of noticing in an online teacher education program

In this study we aimed to characterize the development of prospective mathematics teachers’ noticing in an online teacher education program. Prospect     

Teaching teachers mathematics through programming

There are two main arguments underlying the claims for the value of interactive computer programming used by students to model mathematical ideas. One is concerned with mathematical content, i.e. with mathematics as an object of study. The other is concerned with mathematical activity, i.e. doing mathematics, or ‘Mathematicking’ [1]. Both content and activity include processes and these provide the main links with programming. Examples of processes in the content of mathematics are addition, transformation and integration, and these can be described by instructions in a computer program. Examples of process in the activity are problem‐solving, proof generation and pattern finding which can be described by analogy to program building and debugging. We assess the arguments for programming, in relation to the training of teachers, and describe a pilot‐study in which student teachers with mathematical difficulties were taught the programming language LOGO. Observation of the students, learning the language and using it to manipulate computer models of mathematical ideas, which they had not understood previously, highlights both advantages and disadvantages in this approach. The problem of the representation of mathematical ideas within programming projects is discussed.     

Metacognition and mathematics education

The role of metacognition in mathematics education is analyzed based on theoretical and empirical work from the last four decades. Starting with an overview on different definitions, conceptualizations and models of metacognition in general, the role of metacognition in education, particularly in mathematics education, is discussed. The article emphasizes the importance of metacognition in mathematics education, summarizing empirical evidence on the relationships between various aspects of metacognition and mathematics performance. As a main result of correlational studies, it can be shown that the impact of declarative metacognition on mathematics performance is substantial (sharing about 15–20% of common variance). Moreover, numerous intervention studies have demonstrated that “normal” learners as well as those with especially low mathematics performance do benefit substantially from metacognitive instruction procedures.     

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).     

Chinese elementary mathematics teachers’ knowledge in mathematics and pedagogy for teaching: the case of fraction division

In this study, we investigated the extent of knowledge in mathematics and pedagogy that Chinese practicing elementary mathematics teachers have and what changes teaching experience may bring to their knowledge. With a sample of 18 mathematics teachers from two elementary schools, we focused on both practicing teachers’ beliefs and perceptions about their own knowledge in mathematics and pedagogy and the extent of their knowledge on the topic of fraction division. The results revealed a gap between these teachers’ limited knowledge about the curriculum they teach and their solid mathematics knowledge for teaching, as an example, fraction division. Moreover, senior teachers used more diverse strategies that are concrete in nature than junior teachers in providing procedural justifications. The results suggested that Chinese practicing teachers benefit from teaching and in-service professional development for the improvement of their mathematics knowledge for teaching but not their knowledge about mathematics curriculum.     

Boundary crossing through in-service online mathematics teacher education: the case of scenarios and half-baked microworlds

We address online mathematics teacher education as a means of immersing teachers into new kinds of collectives where professional development may be enhanced by crossing the boundaries of their habitual communities and the norms within these. We analyse the ways in which newly trained teacher educators interacted around their designs and productions for in-service courses they were giving to colleagues. We focus on their uses of scenarios and half-baked microworlds as two kinds of artefacts we had designed to play the role of improvable boundary objects. We consider these interactions as a forum for challenge and for professional development through frequent and relevant boundary crossing.     

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.     

CAS in general mathematics education

A rational discussion of the use of Computer algebra systems (CAS) in mathematics teaching in general education needs an explicit image of (general) mathematics education, an explication of global perspectives and goals on mathematics teaching focusing on general education (chapter 1). The conception of general education according to the «ability of communication with experts» described in chapter 2 can be such an orientation for analysing, considering, classifying and assessing the didactical possibilities of using CAS. CAS are materialised mathematics allowing for more or less exhaustive outsourcing of operative (also symbolically) knowledge and skills to the machine. This frees up space of time as well as mental space for the development of those competences being in our view relevant for general mathematics education. In chapter 3 the idea of outsourcing and the role of CAS for it is discussed more detailed as well as consequences being possible for the CAS-supported teaching of mathematics. Beyond, CAS can be didactically used and reflected as a model of communication between (mathematical) experts and lay-persons (chapter 4). Chapter 5 outlines some research perspectives.     

Conceptualizing inquiry-based education in mathematics

The terms inquiry-based learning and inquiry-based education have appeared with increasing frequency in educational policy and curriculum documents related to mathematics and science education over the past decade, indicating a major educational trend. We go back to the origin of inquiry as a pedagogical concept in the work of Dewey (e.g. 1916, 1938) to analyse and discuss its migration to science and mathematics education. For conceptualizing inquiry-based mathematics education (IBME) it is important to analyse how this concept resonates with already well-established theoretical frameworks in mathematics education. Six such frameworks are analysed from the perspective of inquiry: the problem-solving tradition, the theory of didactical situations, the realistic mathematics education programme, the mathematical modelling perspective, the anthropological theory of didactics, and the dialogical and critical approach to mathematics education. In an appendix these frameworks are illustrated with paradigmatic examples of teaching activities with inquiry elements. The paper is rounded off with a list of ten concerns for the development and implementation of IBME.     

Arnold Kirsch and mathematics education

This article pays tribute to the German mathematics educator Arnold Kirsch (1922–2013), especially for his contributions to calculus education. The main aim of his work was to make mathematics accessible to learners so that they are able to genuinely understand the subject.     

Three modes of STEM integration for middle school mathematics teachers

Of the four subjects in an integrated science, technology, engineering, and mathematics (STEM) approach, mathematics has not received enough focus. This could be in part because mathematics teachers may be apprehensive or unsure about how to implement integrated STEM education in their classrooms. There are benefits to integrated STEM in a mathematics classroom though, including increased motivation, interest, and achievement for students. This article discusses three methods that middle school mathematics teachers can utilize to integrate STEM subjects. By focusing on open‐ended problems through engineering design challenges, mathematical modeling, and mathematics integrated with technology middle school students are more likely to see mathematics as relevant and valuable. Important considerations are discussed as well as recent research with these approaches.     

Implementation and outcomes of inquiry-based learning in mathematics content courses for pre-service teachers

This mixed-methods study describes classroom characteristics and student outcomes from university mathematics courses that are based in mathematics departments, targeted to future pre-tertiary teachers, and taught with inquiry-based learning (IBL) approaches. The study focused on three two-term sequences taught at two research universities, separately targeting elementary and secondary pre-service teachers. Classroom observation established that the courses were taught with student-centred methods that were comparable to those used in IBL courses for students in mathematics-intensive fields at the same institutions. To measure pre-service teachers' gains in mathematical knowledge for teaching, we administered the Learning Mathematics for Teaching (LMT) instrument developed by Hill, Ball and Schilling for in-service teacher professional development. Results from the LMT show that pre-service teachers made significant score gains from beginning to end of their course, while data from interviews and from surveys of learning gains show that pre-service teachers viewed their gains as relevant to their future teaching work. Measured changes on pre-/post-surveys of attitudes and beliefs were generally supportive of learning mathematics but modest in magnitude. The study is distinctive in applying the LMT to document pre-service teachers' growth in mathematical knowledge for teaching. The study also suggests IBL is an approach well suited to mathematics departments seeking to strengthen their pre-service teacher preparation offerings in ways consistent with research-based recommendations.