Proceedings of the 12th International Conference on Technology in Mathematics Teaching ICTMT 12

Innovation, inclusion, sharing and diversity are some of the words that briefly and suitably characterize the ICTMT series of biennial international conferences – the International Conference on Technology in Mathematics Teaching. Being the twelfth of a series which began in Birmingham, UK, in 1993, under the influential enterprise of Professor Bert Waits from Ohio State University, this conference was held in Portugal for the first time. The 12th International Conference on Technology in Mathematics Teaching was hosted by the Faculty of Sciences and Technology of the University of Algarve, in the city of Faro, from 24 to 27 June 2015, and was guided by the original spirit of its foundation. The integration of digital technologies in mathematics education across school levels and countries, from primary to tertiary education, together with the understanding of the phenomena involved in the teaching and learning of mathematics in technological environments have always been driving forces in the transformation of pedagogical practices. The possibility of joining at an international conference a wide diversity of participants, including school mathematics teachers, lecturers, mathematicians, mathematics educators and researchers, software designers, and curriculum developers, is one facet that makes this conference rather unique. At the same time, it seeks to foster the sharing of ideas, experiences, projects and studies while providing opportunities to try-out and assess tools or didactical proposals during times of hands-on work. The ICTMT 12 had this same ambition, when embracing and welcoming just over 120 delegates who actively and enthusiastically contributed to a very packed program of scientific proposals and sessions on various topics

Bringing Nordic mathematics education into the future. Proceedings of Norma 20, The ninth Nordic Conference on Mathematics Education

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How online small groups co-construct mathematical artifacts to do collaborative problem solving

Developing pedagogies and instructional tools to support learning math with understanding is a major goal in math education. A common theme among various characterizations of mathematical understanding involves constructing relations among mathematical facts, procedures, and ideas encapsulated in graphical and symbolic artifacts. Discourse is key for enabling students to realize such connections among seemingly unrelated mathematical artifacts. Analysis of mathematical discourse on a moment-to-moment basis is needed to understand the potential of small-group collaboration and online communication tools to support learning math with understanding.This dissertation investigates interactional practices enacted by virtual teams of secondary students as they co-construct mathematical artifacts in an online environment with multiple interaction spaces including text-chat, whiteboard, and wiki components. The findings of the dissertation arrived at through ethnomethodologically-informed case studies of online sessions are organized along three dimensions: (a) Mathematical Affordances: Whiteboard and chat spaces allow teams to co-construct multiple realizations of relevant mathematical artifacts. Contributions remain persistentlyavailable for subsequent manipulation and reference in the shared visual field. The persistence of contributions facilitates the management of multiple threads of activities across dual media. The sequence of actions that lead to the construction and modification of shared inscriptions makes the visual reasoning process visible.(b) Coordination Methods: Team members achieve a sense of sequential organization across dual media through temporal coordination of their chat postings and drawings. Groups enact referential uses of available features to allocate their attention to specific objects in the shared visual field and to associate them with locally defined terminology. Drawings and text-messages are used together as semiotic resources in mutually elaborating ways.(c) Group Understanding: Teams develop shared mathematical understanding through joint recognition of connections among narrative, graphical and symbolic realizations of the mathematical artifacts that they have co-constructed to address their shared task. The interactional organization of the co-construction work establishes an indexical ground as support for the creation and maintenance of a shared problem space for the group. Each new contribution is made sense of in relation to this persistently available and shared indexical ground, which evolves sequentially as new contributions modify the sense of previous contributions.Ph.D., Information Science and Technology -- Drexel University, 200

High school mathematics teachers’ learning experiences, during a professional development intervention to improve their understanding of linear and quadratic functions using GeoGebra

Thesis (PhD)--Stellenbosch University, 2021.ENGLISH SUMMARY : Mathematics is a compulsory subject at all levels of pre-tertiary Namibian education and mathematical functions are key concepts of the mathematics curriculum. Personal experience has shown that teaching and understanding functions is a challenge in the Namibian high school curriculum. There are several difficulties in learning algebra due to misconceptions and errors such as misunderstanding the meaning of numerical and literal symbols, the shift from numerical data or language representation to variables or parameters with functional rules or patterns, and their cognition. Hence, there is a need to integrate the use of information and communication technologies (ICTs) in order to improve the understanding and teaching of mathematical functions. However, successful integration depends on providing teachers with learning opportunities in using ICTs. The focus of this research was to investigate a selected number of high school mathematics teachers‟ learning experiences during a professional development intervention aimed at improving the understanding of functions using GeoGebra. This study provides answers to the following questions: (1) What are high school mathematics teachers‟ learning experiences, during a professional development intervention to improve their understanding of linear and quadratic functions using GeoGebra? (2) What does research have to say about the potential of GeoGebra in aiding the understanding functions? The study was conducted in the Ohangwena region in Namibia and grounded on the interpretive paradigm. The sample population consisted of ten high school mathematics teachers. Sampling of the participants was guided by convenience sampling procedures. Five workshops of 2-3 hours were organised with the selected teachers. During these workshops, guidance and time were given to the teachers to explore different activities related to multiple representations of mathematical functions. The teachers were interviewed while they interacted with a set of GeoGebra activities. A group discussion was held to explore and develop an understanding of the concept of functions, the nature of GeoGebra and its possible pedagogical affordances. Multiple methods were used to collect data, namely semi-structured interviews; focus group interviews; audiotaped discussions; observations; and field notes. Based on a qualitative analysis of the data generated, the findings indicated that teachers benefited significantly from the use of GeoGebra as mathematical digital software in various ways, ranging from personal mathematics exploration, attitudes toward mathematics and mathematics teaching of functions to pedagogical reflections, including the nature of mathematics and teachers interactions. These changes are well aligned with the emphases of the ongoing mathematics education reforms in Namibia, including the integration of technology into education. The research findings also revealed that in its design GeoGebra affords fast and consistent feedback and that teachers need more opportunities where they learn to experience relations between the pragmatic and epistemic dimensions of GeoGebra use, when it comes to linear and quadratic functions, for example.AFRIKAANSE OPSOMMING : Wiskunde is „n verpligte vak in al die fases van voortersiêre onderwys in Namibië en wiskundige funksies is van die kernkonsepte in die wiskundekurrikulum. Persoonlike ervaring wys daarop dat die onderrig en verstaan van funksies „n uitdaging in die Namibiese hoërskoolkurrikulum blyk te wees. Daar is verskeie struikelblokke in die leer van algebra. Dit kan te wyte wees aan wanopvattings en foute soos die misverstaan van numeriese en lettersimbole, die skuif van numeriese data of taalverteenwoordiging na veranderlikes of grense met funksionele reëls of patrone en die herkenning daarvan. Vandaar die behoefte om die gebruik van inligting- en kommunikasietegnologieë (IKTs) te integreer ten einde die verstaan en die onderrig van wiskundige funksies te verbeter. Die sukses van hierdie insluiting hang egter af van die mate waartoe ondewysers toegang tot leergeleenthede in die gebruik van IKTs gegun word. Met hierdie navorsing is daar gefokus op die ondersoek na „n gekose aantal hoërskool-wiskundeonderwysers se leerervarings tydens „n professionele ontwikkelingsintervensie, wat daarop gemik was om die verstaan van wiskundige funksies te bevorder deur die gebruik van GeoGebra. Met hierdie studie is daar gepoog om antwoorde op die volgende vrae te vind: (1) Wat is hoërskool-wiskundeonderwysers se leerervarings gedurende die bywoning van „n professionele ontwikkelingsintervensie wat daarop gemik is om die verstaan van wiskundige funksies te bevorder deur die gebruik van GeoGebra? (2) Wat is die bevindings van navorsing oor die moontlikhede van GeoGebra in die ontwikkeling van „n beter begrip van funksies? Die ondersoek is onderneem in die Ohangwena-distrik in Namibië en dit is gegrond op die interpretatiewe paradigma. Die deelnemers vir die steekproef bestaan uit tien hoërskool-wiskundeonderwysers. Die keuse van deelnemers is gelei deur doelbewuste steekproefprosedures. Vyf werkswinkels van 2 tot 3 ure elk is vir die gekose onderwysers gereël. Gedurende hierdie werkswinkels is die onderwysers begelei en daar is tyd gegee om verskillende aktiwiteite met betrekking tot die veelvuldige voorstellings van wiskundige funksies te ondersoek. Onderhoude is met die onderwysers gevoer, terwyl hulle besig was met „n stel GeoGebra-aktiwiteite. „n Groepsbespreking het plaasgevind oor die begrip wiskundige funksies om die verstaan daarvan te ontwikkel. Die aard van GeoGebra is ook bespreek en die moontlikhede daarvan as „n pedagogiese hulpmiddel is ondersoek. „n Verskeidenheid metodes is aangewend om data in te win, soos die voer van deelsgestruktureerde onderhoude, fokusgroeponderhoude, die maak van oudio-opnames van gesprekke, deur waarneming en met die byhou van veldnotas. Gebaseer op die kwalitatiewe ontleding van die gegenereerde data is daar bevind dat onderwysers beduidend kan baat vind by die gebruik van GeoGebra as „n wiskundige, digitale grensobjek (WDGO). Dit kan op verskeie wyses aangewend word, soos byvoorbeeld tydens persoonlike ondersoeke na wiskunde, in die aanspreek van die houding jeens wiskunde, by die onderrig van wiskundige funksies of tydens pedagogiese refleksies oor die aard van wiskunde, asook tydens onderwyserinteraksies. Hierdie veranderinge klop met die volgehoue hervorming van wiskundeonderwys in Namibië wat ook die integrasie van tegnologie in opvoeding insluit. Die navorsingsbevindige bring voorts aan die lig dat GeoGebra, as „n WDGO, vinnige en deurlopende terugvoer toelaat en dat onderwysers meer geleenthede behoort te kry waartydens hulle die verhouding tussen die pragmatiese en die epistemiese dimensies van GeoGebra-gebruik kan ervaar, veral wanneer dit kom by liniêre en drievoudige funksies.Doctora

Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education

International audienceThis volume contains the Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education (ERME), which took place 9-13 February 2011, at Rzeszñw in Poland

Task Design in Mathematics Education. Proceedings of ICMI Study 22

Proceedings of ICMI Study 22International audienceThere has been a recent increase in interest in task design as a focus for research and development in mathematics education. This is well illustrated by the success of theoretically based long term design research projects in which design and research over time have combined to develop materials and approaches that have appealed to teachers. One area of investigation is how published tasks are appropriated by teachers for complex purposes and influences mathematics teaching. Tasks generate activity which affords opportunity to encounter mathematical concepts and also to use and develop mathematical thinking and modes of enquiry. Tasks also arise spontaneously in educational contexts, with teachers or learners raising questions or providing prompts for action by drawing on a repertoire of past experience. We are interested in how these are underpinned with implicit design principles. It is important to address also the question of sequences of tasks and the ways in which they link aspects of conceptual knowledge. The communities involved in task design are naturally diverse: designers, professional mathematicians, teacher educators, teachers, researchers, learners, authors, publishers and manufacturers, and individuals acting in several of these roles. We wish to illuminate the diverse communities and methods that lead to the development and use of tasks

Proof and Proving in Mathematics Education

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