Abstract:In this literature survey we focus on identifying recent advances in research on digital technology in the field of mathematics education. To conduct the survey we have used Internet search engines with keywords related to mathematics education and digital technology and have reviewed some of the main international journals, including the ones in Portuguese and Spanish. We identify five sub-areas of research, important trends of development, and illustrate them using case studies: mobile technologies, massive open online courses (MOOCs), digital libraries and designing learning objects, collaborative learning using digital technology, and teacher training using blended learning. These exemplary case studies may help the reader to understand how recent developments in this area of research have evolved in the last few years. We conclude the report discussing some of the implications that these digital technologies may have for mathematics education research and practice as well as making some recommendations for future research in this area.

Growing use of the internet in educational contexts has been prominent in recent years. In this survey paper, we describe how the internet is transforming the mathematics classroom and mathematics teacher education. We use as references several reviews of use of the internet in mathematics education settings made in recent years to determine how the field has evolved. We identify three domains in which new approaches are being generated by mathematic educators: principles of design of new settings; social interaction and construction knowledge; and tools and resources. The papers in this issue reflect different perspectives developed in the last decade in these three domains, providing evidence of the advances in theoretical frameworks and support in the generation of new meanings for old constructs such as 'tool', 'resources' or 'learning setting'. We firstly highlight the different ways in which the use of digital technologies generates new ways of thinking about mathematics and the settings in which it is learnt, and how mathematics teacher educators frame the new initiatives of initial training and professional development. In this survey paper, we identify trends for future research regarding theoretical and methodological aspects, and recognise new opportunities requiring further engagement.

The parable of the man and the dog (adapted from other old stories) Once upon a time there was a man who studied at a university how to teach dogs to bark. After completing his degree he could not get employment, so he continued with his studies and completed a PhD in his field, and was appointed at his university to train students to teach dogs how to bark. Not many students studied with him. Then a terrible virus, affecting dogs and causing them to lose their ability to bark, hit the world and caused a worldwide pandemic. Not everybody was equally unhappy-after all, barking dogs can be rather noisy. Rumours, that this virus could be man-made, were heard. The virus spread exponentially and soon few dogs remained that could bark. And the world was quite quiet. Suddenly his discipline was very popular and all over the world new experts started writing important articles and books and blogs on how dogs should be taught how to bark. International companies launched big money-making projects and many teachers and scholars boarded the bandwagon. Unfortunately not all attempts were successful-teaching a dog how to bark does not always imply that the dog will learn how to bark. But some were. And the man had a little smile. And more students. And, although somewhat differently, they could live happily ever after.

This paper reports on different underlying structures of the derivative schema of three undergraduate students that were considered to be at the trans level of development of the derivative schema (action-process-object-schema). The derivative schema is characterized in terms of the students' ability to explicitly transfer the relationship between a function and its first derivative to the derivative function and the second derivative. This conscious shift of properties of derivatives is differently manifested by the students in the trans level of development of the derivative schema and can be considered evidence of the different characteristics of the thematization of derivative schema. From here we suggest that there are different underlying structures in the constructed schema due to the consciousness in which students use the relations between a function and its derivative.

This study investigates the development of proportional and additive methods along primary and secondary school. In particular, it simultaneously investigates the use of additive methods in proportional word problems and the use of proportional methods in additive word problems. We have also studied the role played by integer and non-integer relationships between the given numbers and the nature of quantities (discrete or continuous) in the development of these phenomena. A test consisting of additive and proportional missing-value word problems was solved by 755 primary and secondary school students (from fourth to tenth grade). The findings indicate that the use of additive methods in proportional situations increased during primary school and decreased during secondary school whereas the use of proportional methods in additive situations increased along primary and secondary school. Moreover, the presence or absence of integer ratios strongly affects this behaviour but the nature of quantities only has a small influence on the use of proportional methods.

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This study explores how preservice primary teachers became engaged in meaning-making mathematics teaching when participating in online discussions within learning environments integrating video-clips of mathematics teaching. We identified different modes of participation in the online discussions and different levels of knowledge-building. The data can be explained by the type of task set in the learning environments and by a gradually improved shared understanding of the teaching. The structure of the learning environments supported inquiry into meaningful topics and knowledge-building through activities like identifying, interpreting and designing. These findings suggest that the different types of task and conditions of online discussion in the learning environments influence the nature of the interaction showing the correspondence between synergistic interaction and higher-order thinking.