Brady Corey - Uses of Technology in Upper Secondary Mathematics Education
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Main Topics You Can Find in this ICME-13 Topical Survey -- Introduction -- Survey on the State-of-the-art -- Summary and Looking Ahead.;This survey addresses the use of technology in upper secondary mathematics education from four points of view: theoretical analysis of epistemological and cognitive aspects of activity in new technology mediated learning environments, the changes brought by technology in the interactions between environment, students and teachers, the interrelations between mathematical activities and technology, skills and competencies that must be developed in teacher education. Research shows that the use of some technologies may deeply change the solving processes and contribute to impact the learning processes. The questions are which technologies to choose for which purposes, and how to integrate them, so as to maximize all students agency. In particular the role of the teacher in classrooms and the content of teacher education programs are critical for taking full advantage of technology in teaching practice.
Brady Corey: author's other books
Who wrote Uses of Technology in Upper Secondary Mathematics Education? Find out the surname, the name of the author of the book and a list of all author's works by series.
David Buckingham
Marc J. de Vries
N. V. Varghese
Marilyn E. Strutchens Rongjin Huang Leticia Losano
Farr Fiona (editor)
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The Author(s) 2017
Stephen Hegedus , Colette Laborde , Corey Brady , Sara Dalton , Hans-Stefan Siller , Michal Tabach , Jana Trgalova and Luis Moreno-Armella Uses of Technology in Upper Secondary Mathematics Education ICME-13 Topical Surveys 10.1007/978-3-319-42611-2_1Uses of Technology in Upper Secondary Mathematics Education
Stephen Hegedus 1 , Colette Laborde 2, Corey Brady 3, Sara Dalton 4, Hans-Stefan Siller 5, Michal Tabach 6, Jana Trgalova 7 and Luis Moreno-Armella 8
(1)
Dean of School of Education, Southern Connecticut State University, Connecticut, CT, USA
(2)
Cabrilog, Fontaine, France
(3)
Vanderbilt University, Nashville, TN, USA
(4)
Mathematics Department, University of Massachusetts Dartmouth, Massachusetts, MA, USA
(5)
Mathematisches Institut, University of Koblenz and Landau, Koblenz, Germany
(6)
School of Education, Tel Aviv University, Tel Aviv, Tel Aviv, Israel
(7)
Matre de Confrences, Claude Bernard University, Lyon, France
(8)
Cinvestav-IPN, Mexico D.F., Mexico
Stephen Hegedus
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Keywords
Technology Mediated activity Cognitive tools Multimodality Connectivity Teacher educationIntroduction
The use of technology in upper secondary mathematics education is a multifaceted topic. This topical survey addresses several dimensions of the topic and attempts at referring to international research studies as it is written by a team of several authors from five countries of three different continents. The survey is structured into four subchapters, each of them addressing a theme of the TSG 43 at ICME 13.
- Technology in secondary mathematics education: theoryTechnology is often arousing enthusiasm as well as reluctance among teachers and mathematics educators. Therefore it was necessary to start the survey with a theoretical analysis of features of digital technologies from an epistemological and a cognitive perspective. A unique epistemological feature of mathematics is their symbolic dimension. It is impossible to gain direct access to mathematical objects as to physical objects. The only way is to access them is through representations. Digital technologies mediate mathematics and some of them offer new kinds of representations, like dynamic and socially distributed representations. Based on a Vygostkian perspective and an instrumentation approach, the use of digital technologies is analyzed as a coaction or a creative interplay between tool and human and as social coaction with socially distributed technology. This theoretical analysis is presented in the first subchapter and the second subchapter also refers to it.
- The role of new technologies: changing interactionsPart of the role of new technologies is to change the process toward an outcome for learning. This process includes developing a mathematical discourse, providing opportunities to conjecture and test, and active not passive learning. New technologies can add to these processes by connecting learners in different ways with each other and the phenomena under study, mediating learning in different ways, and can offer the opportunity for students to build on the work of one another through the ability to share products or problem solving strategies. In particular technologies offering mobility, multimodality (using various sensory modalities: sight, touch, sound) and connectivity can support student learning. The knowledge and practices that result from the process of learning using digital technologies might be new. Through operationalizing the definition of new in terms of how we interact with the learning environment, three organizing principles structures this subchapter: 1. Advances in Activity Spaces, 2. Multimodality, and 3. Moving from Outside to Inside the classroom.
- Interrelations between technology and mathematicsDigital tools support visualization of mathematical concepts in various ways of expressions, and as such may foster versatile thinking, especially when these representations are dynamically linked. At the upper secondary education, these tools can be used for exploring and discovering mathematical correlations and for modeling real complex phenomena. New possibilities are offered by the combination of different environments like CAS and dynamic mathematics environments.The use of all these possibilities foster processes that cannot be developed so well in absence of technology, for example: exploration and experimentation, interpretation processes or checking processes. A major consequence is that teaching should be organized differently. Those issues are discussed in the third subchapter.
- Teacher education with technology: what, how and why?The preceding subchapters show that teachers need new knowledge and skills to efficiently use technology in upper secondary education. The institutional demands differ from the required teacher competencies elicited by research studies. Usually the institutional demands are not subject matter specific whereas often research studies link a specific type of technology with a mathematical domain. There are many attempts for organizing professional development developing new knowledge and skills, especially in interaction with research. The evaluation of these courses may vary deeply from dissatisfaction to successful outcomes. The theoretical frameworks and research methods on professional development of teachers in using technology as well as their rationale are also presented in this subchapter.
Survey
2.1 Technology in Secondary Mathematics Education: Theory
2.1.1 The Challenges of Mathematical Reference
As we approach mathematical cognition in classroom learning environments, the symbolic dimension of mathematics becomes sharply salient. Mathematical discourse is always social, always culturally situated and always shaped by its institutional context; thus the semiotic dimension is always important. However, in learning settings the nature of mathematical objects is very often in question and not (yet) taken-as-shared, so that efforts to evoke these objects and to communicate clearly about them receive particular attention and social pressure.
As a way of framing the problems involved in the relationships between mathematical representations and objects, consider Magrittes The Treachery of Images . This famous painting explores issues of representation, in ways that are relevant to mathematical representations. The artist has written Ceci nest pas une pipe (This is not a pipe), in painted script, under the painted image of a pipe. The focus is on the viewers idea of a pipe: within the painting, there are two explicit pipesthe pictorial image of a pipe and the painted words une pipe. The painting puts these two pipes in conversation with one another and with the viewers Pipe idea. The image falls short of the idea: it is not a pipeone cannot hold it, fill it with tobacco, or smoke it.
Now suppose, instead of a pipe, Magritte had painted a circle with the inscribed legend, Ceci nest pas un cercle. A different dynamic would have emerged. Magritte would not, even in theory, have been able to reach into his pocket and produce the geometric circle that had served as the model for the painting, and that the painted image is not . In fact, one might argue that the legend, Ceci nest pas un cercle would be false : at least in the sense that every representation of a circle does express circle-ness in some degree, and that, further, nothing except a collection of such representations does so.
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