Humans-with-media and continuing education for mathematics teachers in online environments

This paper begins by situating online mathematics education in Brazil within the context of research on digital technology over the past 25?years. I argue that Brazilian research on technology in mathematics education can be divided into four phases, and then present an example that ??blends?? aspects of the second and third phases. Phase two can be characterized by research with software designed to address traditional mathematics topics, such as functions, while the third phase is characterized by online courses. The data presented show creative solutions for a problem designed for collectives of humans-with-function-software. The paper is analyzed from a perspective that emphasizes the role of different technologies as teachers and professors collaborate to produce knowledge about the use of mathematical software in regular face-to-face classrooms. A model of online education is presented. Finally, the paper discusses how technology may change collaboration and teaching approaches in continuing education, as it allows for greater integration of online learning with teachers?? classroom activities in schools. In this case, the online platform plays an active role in the learning collective composed of humans-with-media.     

Design and research potential of interactive textbooks: the case of fractions

The transition from classical to electronic textbooks seems to be a logical step in the digitization advancing worldwide. However, developing an e-book ought to be more than digitizing text: key features of computer-based learning environments such as interactive exercises, adaptive demands, or automatic feedback should be integrated to take advantage of the digitization. The “ALICE:fractions” project aims at designing and evaluating an interactive mathematics textbook for introducing fractions in the classroom. It is based on research in mathematics education and includes the elements just mentioned. This paper describes the electronic textbook’s implementation and its theoretical background. Moreover, it introduces aspects that allow further information on learning processes to be gleaned. As an example, time on task is regarded in a study with 6th graders who used the electronic textbook in the classroom. Linear mixed models revealed a negative effect of time on task on task success. The effect was moderated by exercise difficulty and slightly by student competence: the effect was less pronounced in difficult exercises and for low-achieving students, whereas for high-achieving students or in easier exercises, the effect intensified.     

Digital technologies and the challenge of constructing an inclusive school mathematics

This article addresses research related to the use of digital technologies in the teaching and learning of mathematics in Brazil. Its scope is limited to the context of school mathematics and, more specifically, to an ongoing research programme which involves the development of collaborative research partnerships with teachers of mathematics. The paper begins with a brief presentation of the introduction of computers into the Brazilian educational scenario in the 1980s, highlighting how computer technology was heralded as a key to permitting new pedagogical approaches appropriate to the constructivist philosophy of that time. It goes on to consider recent developments in the theoretical frameworks used to interpret mathematics learning in the presence of digital technologies and the importance of focusing on the learning system as a whole, considering epistemological, cognitive and pedagogic dimensions concomitantly. In this vein, it is argued that for any real integration to take place, the mathematical practices afforded by digital tools must be considered legitimate by all the actors in this process and, perhaps most notably, by teachers. The rest of the paper focuses on our approaches to involve teachers in making decisions about technology use in their own classrooms. The strategy used was based on the realisation of research activities underpinned by the idea of the collaborative design of learning situations and the goal of including the wide diversity of learners that characterises Brazilian mathematics classrooms.     

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.     

Shifts of mathematical thinking in adolescence

This theoretical paper relates key features of the mathematics adolescents are expected to learn in school to other aspects of adolescent development. Difficulties in mathematical learning at that age include changes in perspective and in the actions that are mathematically productive. Commonly-recommended methods of trying to engage adolescents in mathematics do not necessarily enable students to shift to new perceptions and new ways of constructing mathematical understandings, yet the shifts students need to make are in accord with other aspects of adolescent development.     

Digital game‐based learning for K–12 mathematics education: A meta‐analysis

Digital games (e.g., video games or computer games) have been reported as an effective educational method that can improve students' motivation and performance in mathematics education. This meta‐analysis study (a) investigates the current trend of digital game‐based learning (DGBL) by reviewing the research studies on the use of DGBL for mathematics learning, (b) examines the overall effect size of DGBL on K‐12 students' achievement in mathematics learning, and (c) discusses future directions for DGBL research in the context of mathematics learning. In total, 296 studies were collected for the review, but of those studies, only 33 research studies were identified as empirical studies and systematically analyzed to investigate the current research trends. In addition, due to insufficient statistical data, only 17 out of the 33 studies were analyzed to calculate the overall effect size of digital games on mathematics education. This study will contribute to the research community by analyzing recent trends in significant DGBL research, especially for those who are interested in using DGBL for mathematics education.     

Preservice teachers learning to teach proof through classroom implementation: Successes and challenges

Proof and reasoning are central to learning mathematics with understanding. Yet proof is seen as challenging to teach and to learn. In a capstone course for preservice teachers, we developed instructional modules that guided prospective secondary mathematics teachers (PSTs) through a cycle of learning about the logical aspects of proof, then planning and implementing lessons in secondary classrooms that integrate these aspects with traditional mathematics curriculum in the United States. In this paper we highlight our framework on mathematical knowledge for teaching proof and focus on some of the logical aspects of proof that are seen as particularly challenging (four proof themes). We analyze 60 lesson plans, video recordings of a subset of 13 enacted lessons, and the PSTs’ self- reported data to shed light on how the PSTs planned and enacted lessons that integrate these proof themes. The results provide insights into successes and challenges the PSTs encountered in this process and illustrate potential pathways for preparing PSTs to enact reasoning and proof in secondary classrooms. We also highlight the design principles for supporting the development of PSTs’ mathematical knowledge for teaching proof.     

Transforming the mathematical practices of learners and teachers through digital technology*

ABSTRACT

This article argues that mathematical knowledge, and its related pedagogy, is inextricably linked to the tools in which the knowledge is expressed. The focus is on digital tools and the different roles they play in shaping mathematical meanings and in transforming the mathematical practices of learners and teachers. Six categories of digital tool-use that distinguish their differing potential are presented: (1) dynamic and graphical tools; (2) tools that outsource processing power; (3) tools that offer new representational infrastructures for mathematics; (4) tools that help to bridge the gap between school mathematics and the students’ world; (5) tools that exploit high-bandwidth connectivity to support mathematics learning; and (6) tools that offer intelligent support for the teacher when their students engage in exploratory learning with digital technologies. Following exemplification of each category, the article ends with some reflections on the progress of research in this area and identifies some remaining challenges.     

Mathematics Education & Digital Technologies: Facing the Challenge of Networking European Research Teams

This paper introduces the IJCML Special Issue dedicated to digital technologies and mathematics education and, in particular, to the work performed by the European Research Team TELMA (Technology Enhanced Learning in Mathematics). TELMA was one of the initiatives of the Kaleidoscope Network of Excellence established by the European Community (IST-507838—2003–2007) to promote the joint elaboration of concepts and methods for exploring the future of learning with digital technologies. TELMA addressed the problem of fragmentation of theoretical frameworks in the research field of mathematics education with digital technologies and developed a methodology based on the in field cross-experimentation of educational digital environments for maths. Six European research teams engaged in cross-experimentation in classrooms as a means to begin to develop a common language and to analyse the intertwined influence played, both explicitly and implicitly, by different contextual characteristics and theoretical frames assumed as reference by the diverse teams participating in the initiative.     

Cultural and linguistic problems in the use of authentic textbooks when teaching mathematics in a foreign language

This paper is a part of a longitudinal study focusing on qualitative aspects of learning in a foreign language in the development of cognitive processes in mathematics. The aim of the paper is to present a more complex analysis of textbook-based obstacles to communication. These obstacles originate in the process of vocabulary and grammar acquisition within a particular multicultural and sociocultural context. The study was carried out using mathematics textbooks from English-speaking countries which are used when teaching mathematics in English to Czech students.     

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.     

OR and the management of electronic services

This review paper is meant to provide some insight to the relation between operations research and the management of electronic services. We use the term electronic services, within the broader e-business context, to refer to any service that is delivered to the customer via electronic means, mainly the Internet as a new channel to communicate with customers, but also through mobile and other digital communications. During the last years we have experienced an explosion in the development of electronic services, which is creating abundant opportunities for operations research (OR) applications, required to empower several types of technology-mediated interactions, exploit the large-scale digital data sources, and automate the recurring operational decisions. In this paper we summarise the various aspects in which operations research may support the management of electronic services, taking into account the different characteristics of alternative electronic media, such as the Internet, mobile communications, interactive television etc.     

On music production in mathematics teacher education as an aesthetic experience

ZDM – Mathematics Education - This paper addresses the integrated use of the arts and digital technology in mathematics education—specifically involving aspects of preservice...     

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.     

Charting the microworld territory over time: design and construction in mathematics education

The study discusses the development of theoretical ideas and constructs related to digital microworlds within the mathematics education community and their implications for interpretations of mathematics learning. Starting from Papert’s introduction of the concept during ICME 2 in 1972, we trace the evolution of theoretical approaches concerning the essence of the idea in an attempt to situate the notion of constructionism in the light of contemporary frameworks. We argue that microworlds, and the search for a learnable mathematics, have a continued relevance to mathematics education, but that the lens research attention has shifted over time, with the current foci on communal design, situated and embodied approaches and artefacts whose use crosses boundaries between different practices. To illustrate these shifts and the challenges that still remain, we present examples from our current work involving the use of microworlds for learning and teaching through communication, design and construction.     

Cognitive Demands and Second-Language Learners: A Framework for Analyzing Mathematics Instructional Contexts

The issues involved in teaching English language learners mathematics while they are learning English pose many challenges for mathematics teachers and highlight the need to focus on language-processing issues related to teaching mathematical content. Two realistic-type problems from high-stakes tests are used to illustrate the complex interactions between culture, language, and mathematical learning. The analyses focus on aspects of the problems that potentially increase cognitive demands for second-language learners. An analytical framework is presented that is designed to enable mathematics teachers to identify critical elements in problems and the learning environment that contribute to increased cognitive demands for students of English as a second language. The framework is proposed as a cycle of teacher reflection that would extend a constructivist model of teaching to include broader linguistic, cultural, and cognitive processing issues of mathematics teaching, as well as enable teachers to develop more accurate mental models of student learning.     

Students' attitude towards computer algebra systems (CAS) and their choice of using CAS in problem-solving

We explore students choice of using computer algebra systems (CAS) in problem-solving relative to their self-reported attitude towards learning mathematics with CAS. Our research design is a case study of nine Norwegian upper-secondary mathematics students with a wide range of attitude towards CAS. Our findings on routine problems indicate that (1) students use CAS whenever students perceive the problem as time-consuming regardless of their attitude towards CAS, and (2) students attitude affects their use of CAS whenever students perceive the problem as non-time-consuming. Norway, among other countries, has implemented CAS as an essential digital resource towards learning mathematics in upper-secondary school. Our discussion focuses on the implications of our findings have on local mathematics educators and national policy-makers.     

Comparison of performance due to guided hyperlearning,unguided hyperlearning,and conventional learning in mathematics: an empirical study

In this paper, the use of guided hyperlearning, unguided hyperlearning, and conventional learning methods in mathematics are compared. The design of the research involved a quasi-experiment with a modified single-factor multiple treatment design comparing the three learning methods, guided hyperlearning, unguided hyperlearning, and conventional learning. The participants were from three first-year university classes, numbering 115 students in total. Each group received guided, unguided, or conventional learning methods in one of the three different topics, namely number systems, functions, and graphing. The students’ academic performance differed according to the type of learning. Evaluation of the three methods revealed that only guided hyperlearning and conventional learning were appropriate methods for the psychomotor aspects of drawing in the graphing topic. There was no significant difference between the methods when learning the cognitive aspects involved in the number systems topic and the functions topic.     

Cognitive Demands and Second-Language Learners: A Framework for Analyzing Mathematics Instructional Contexts

The issues involved in teaching English language learners mathematics while they are learning English pose many challenges for mathematics teachers and highlight the need to focus on language-processing issues related to teaching mathematical content. Two realistic-type problems from high-stakes tests are used to illustrate the complex interactions between culture, language, and mathematical learning. The analyses focus on aspects of the problems that potentially increase cognitive demands for second-language learners. An analytical framework is presented that is designed to enable mathematics teachers to identify critical elements in problems and the learning environment that contribute to increased cognitive demands for students of English as a second language. The framework is proposed as a cycle of teacher reflection that would extend a constructivist model of teaching to include broader linguistic, cultural, and cognitive processing issues of mathematics teaching, as well as enable teachers to develop more accurate mental models of student learning.     

Making mathematics and science integration happen: key aspects of practice

The integration of mathematics and science teaching and learning facilitates student learning, engagement, motivation, problem-solving, criticality and real-life application. However, the actual implementation of an integrative approach to the teaching and learning of both subjects at classroom level, with in-service teachers working collaboratively, at second-level education, is under-researched due to the complexities of school-based research. This study reports on a year-long case study on the implementation of an integrated unit of learning on distance, speed and time, within three second-level schools in Ireland. This study employed a qualitative approach and examined the key aspects of practice that impact on the integration of mathematics and science teaching and learning. We argue that teacher perspective, teacher knowledge of the ‘other subject’ and of technological pedagogical content knowledge (TPACK), and teacher collaboration and support all impact on the implementation of an integrative approach to mathematics and science education.