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.

Students in undergraduate chemistry courses find, as a rule, topics with a strong mathematical basis difficult to master. In this study we investigate whether such mathematically related problems are due to deficiencies in their mathematics foundation or due to the complexity introduced by transfer of mathematics to a new scientific domain. In the investigation we exposed a group of students to a chemistry instrument based on the Nernst equation in electrochemistry, and an equivalent group of students to a similar mathematics instrument in which the questions were stripped of all chemistry context. Both tests contained items requiring algebraic as well as graphical skills. Students experienced few problems with the algebraic questions in both the chemistry and mathematics tests. Their graphical construction and interpretation skills, on the other hand, are inadequate, as can be seen from the poor performance in both the mathematics and the chemistry results of the graphical question. Our conclusion is that the problem seems to lie at the mathematics side and is not due to the transfer of mathematics to an application. © Wiley Periodicals, Inc. J Res Sci Teach 45: 197–218, 2008.

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