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• W778591210 abstract "The aim of the study is to throw light on how experienced, Danish upper secondary teachers deal with technology enhanced mathematics in their teaching practice. In particular, we find the relations between these teachers’ personal view on mathematics and the use of ICT tools may be of interest.We have chosen the very first lessons with the new tool as object forthis study because explicit arguments and reflections on the use of ICT were most likely to be given by the teacher at these occasions. Besides, we expected the teachers to be especially aware of the students impression of the role of ICT when they prepared these first lessons and, thereby, revealing their viewpoints. The study aims to contribute to the rich variety of examples of good practice, to inspration for colleagues with more or less experience themselves. In contrast, the study does not aim at setting up a strict correspondance between teachers’ beliefs and their handling ICT in practice. Neither, we aim to rate different approaches or to assess them with regard to students’ learning outcome. 1. Background for this study: “the world class math and science project” During almost one decade, the introduction and use of CAS in mathematics (and, when relevant, in other school subjects) was subject to small scale research – and development projects, and teaching experients, in Danish upper secondary school. Main projects were ‘World Class Math and Science I + II’ 2000 – 2004 and 2004 – 2006, resp., and Danish Science Gymnasiums (DASG) 2006 2010 [1, 2, 3, 4, 6]. One of these projects’ overall objectives was to initiate sustainable professional development for matheatics teachers locally, in their schools, with regard to integration of CAS and ICT tools into their mathematics teaching. In addition, the idea was to launch research – practice collaborations. For example, one goal of the World Clas Math and Science I was formulated like this (quoted from [2] p 25): ‘ ICT in mathematics: A number of reports point out, that inclusion of ICT in math teaching strongly influences the students’ acquisition of mathematical concepts and methods. The intention is to inquire, whether math software makes the acquisition of the content possible in a way that ensures better understanding and makes applications within other subjects easier. (...)’ The evaluation of subprjoect A: use of CAS, part of the World Class Math and Science I project, was summarised in [2 p. 31]: ‘The experiences from the World Class A project demonstrated that it was possible to teach almost as usual, even with the use of computer and CAS. Though, golden opportunities for radical changes of teaching mathematics and science were also demonstrated. The benefits in mathematics were clear: Use of CAS gave a lift. A large variety in students’ attitudes towards mathematics was revealed: From students, who saw mathematics as a tool-subject of applications and widely included the use of computer in their mathematical activities, to students, who regarded understanding and overview based on proofs and based on hand-working as being the main issues. These differences did not solely reflect distinct teaching viewpoints as far as there were huge discrepancies between students from the same classes, taught by the same teachers.’ A common experience for the teachers during the projects was the hurdle, to overcome the students’ initial resistance. When the teacher introduced for example MathCad, TI89 or n’spire, major parts of the students often were reluctant to invest time and efforts in the instrumental genesis. In such cases, the teacher had to be persuasive and, if necessary, force the students to start the process. It was also a common experience that in general, the students graduately developed a positive attitude towards the tool. Some of them even became entusiastic time after time. The following excerpt from the evaluation of the ‘Danish Science Gymnasiums’ project [4 p.11] (my translation from Danish) shows one example of this common experience: – they believe it is cheating and they think, you know, we have things to do, we must start now! Here are some hurdles to overcome. Which really pays back. You have to invest, but it is hard for them to believe from the beginning. You know, I don’t know if I handle it wrong, I think I do my best but it really is a hurdle! But they become very happy with it! I totally agree! Yes! and ...And I totally agree with you, it is an investment and you alsmost experience an atmospherein the classroom of we-want-to-kill-the-teacher... Apparently, the issue of generating a new tool for learning and doing mathematics frequently engaged both teacher and students emotionally. This engagement is the outset of the present study. 2. Themes and relation to theory The themes that we deal with in this paper are (1) teacher practice when introducing ICT in their mathematics classes, and (2) teachers conception of mathematics and the role of ICT in their mathematics teaching. The outset of the study is the observations from the world class project, described above, namely that students tend to resist this integration and teachers tend to insist that this integration occurs. In order to sharpen our look at the teaching-learning situation we use some concepts from the theory of didactical situations [5]. This means that we use the concept of didactical contract to describe the mutual expectations between teacher and learners, the distinction between didactical situations (controlled by the teachers instructions) and adidactical situations (controlled by the students voluntary and selv directed interaction with the learning environment and problem situations) to describe the inteplay between teacher control and students self directedness. We will also adopt the notion of “obstacle” to describe the specific challenge that students meet in their work. Broussau distinguishes between didactical obstacles (due to the way a topic is taught, should in general be avoided) and epistemological obstacles (due to the nature of the the topic taught, these are more or less necessary for learning to occur). In order to describe the teachers role in the more loosely framed “reform paradigm” for educational planning we lean on an extension of the notion of forced autonomy as introduced by Skott [8]. We return to this notion in the section below concerning the teachers’ insistence on students’ generation of new, pesonal tools. Before that, we clarify the meaning of the term personal tool: In order to describe the influence of technology on mathematical activity we will use the instrumental approach developed by Luc Trouche [9], partly from the discipline cognitive ergonomics (Verillion & Rabardel, [10]), and partly from the theory of conceptual fields (Vergnaud [11]). The basic premise of the instrumental approach is that people use artefacts for various purposes and hereby create personal instruments. An artefact is a material or abstract object, aiming to sustain human activity. An instrument is what the subject builds from the artefact. [9 p.144]. The process of building an instrument from an artefact is referred to as instrumental genesis (fig. 1) and consists of two simultaneous processes, instrumentation and instrumentalisation. Instrumentalisation is the process where the subject gets to know and control the artefact and applying it to ones own very specific needs. Instrumentation the process where that artefact shapes the subject in the sense that the subject adapts to the new possibilities and constraints the artefact posses." @default.
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• W778591210 date "2009-01-01" @default.
• W778591210 modified "2023-09-27" @default.
• W778591210 title "Teachers' dealing with Technology-Enhanced Mathematics in Teaching Practice" @default.
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