ICT and mathematics learning (ICTML)

Transcription

1 Application to NRF for KUL: ICT and learning Project description, AB Fuglestad ICT and mathematics learning (ICTML) Developing communities for learning with technology. 1 Introduction New technology seems to have a growing impact on school, and it will probably more and more be incorporated within school practice. This makes it urgent to identify the crucial points according to which one might organise the use of computers and related new technology in education programmes. It is important to understand how technology influences education, and why. Mathematics in education is related to technology and technology to mathematics, thus deep knowledge of the influences of ICT on mathematics learning attracts high interest. Like the change between an informal practical situated mathematics to a formal, generalised mathematics, the inclusion of technology may induce qualitative new aspects on its education. ICT may serve as a tool for learning powerful mathematical concepts, for getting insight and understanding and to do problem solving. A critical issue is how these functions may be started and sustained. What are organising matters, what are obstacles, what goals may be obtained, and what are indicators of reaching specific educational goals. According to L97 (KUF, 1999) students should develop independence and self-reliance in their learning. Self-regulated learning seems to be an interest in many subject areas (Boekaerts, Pintch, & Zeidner, 2000), in general, and in mathematics education. The students are active, take responsibility and organise their problem solving. Development of selfregulated learning and power to build their own knowledge and self-reliance is an important goal for the students. To use appropriate technological tools that students can judge as appropriate in different tasks, is part of this goal. 2 Learning mathematics In order to exploit fully the power of mathematics in their lives students need a relational or principled understanding of significant mathematical concepts (Skemp, 1986). This means that not only should they develop mathematical skills, know number facts, apply arithmetical procedures correctly, recognise and relate shapes and use statistical formulae. They should perceive the meaning and relatedness of concepts and develop connected understandings that they can apply to problems in their everyday world (Askew et al, 2000). They should be able to draw on mathematics knowledgeably in making informed decisions in life and work. Such principled knowledge ability requires understanding of the nature of mathematics itself in generalisation and abstraction However, despite innovative and forward looking curricula, research shows that many students find mathematics difficult and boring, beyond their comprehension and irrelevant to their needs (Alseth, Breiteig, & Brekke, 2003). Despite that ICT-tools are included in L97 as support for teaching and learning, there seems to be only limited use of it in teachers practice. We should, as a matter of urgency, explore further the concepts and attitudes of students both in school and beyond to perceive the roots of such disaffection and address the issues mathematical, social and didactic that sustain it. Here, we need to recognise students thinking, aspirations and participation in society as central to their mathematical learning improvement. 1

2 Different kinds of technologies and tools have been used for centuries in mathematics, e.g. tools for measurement, calculations and mathematical notation and symbol systems. These are cognitive technologies that help the students transcend the limitations of the mind (Pea, 1987). Computer software is a special powerful cognitive technology for learning mathematics. This can take the form of an amplifier, which means doing more efficient the same as before without changing its basic structure. Pea and Dörfler argues that we should regard ICT tools as reorganisers which have wide implications for the objects we work on, and leads to more activity on meta level with more emphasis on planning and judging methods (Pea, 1987). ICT tools will be a part of the cognitive system (Dörfler, 1993), and computer visualisations will extend and expand the students cognition and should be available at any time. This has implications for the kind of software that we choose as tools in mathematics classrooms. Software should give opportunity to develop conceptual fluency, provide an environment for exploration and investigation, integrate different representations and stimulate reflection. 3 Research and Development Many researchers argue that use of ICT have a huge potential in mathematics classrooms, to help students learn significant mathematical concepts, understand better and help solving mathematical tasks. A lot of reports and papers have been written. However, there seems to be limited knowledge of the impact on the students learning. According to a meta analysis of 662 publications concerning ICT in mathematics teaching, from 1994 to 1999, only 37% of the publications dealt with research (Lagrange, Artigue, Laborde, & Trouche, 2001). In particular this article analyses publications on computer algebra and reveals that the majority dealt with technical descriptions of possibilities for using the tools (53%) or innovative classroom activities (13%). These publications are potentially interesting for the use of technology, but seem in general to be weakly supported by systematic experimentation and reflection and can not address the complexity of the educational situation. The same seems to be the case with other kinds of computer tools. We find good descriptions of the tools and ideas for teaching and development, but fewer publications that reported from research using the tools studying their consequences for the students learning and achievement in mathematics. The report from the IMPACT2 1 study in England show that high use of ICT give positive results concerning students performance on National Tests and GCSE examinations. The IMPACT2 is a large-scale study on the use of ICT in different subjects in school and on student s use of ICT at home, initiated by the Government. On basis of the report, the DfES and Becta contend that although ICT is only one of many factors in successful schools, it is a prominent one. Most students use of computers outside schools exceeds greatly the time spent on computers in school, and students are aware of the influence of ICT on the society. We have recently some reports from Norwegian schools, from developmental projects, that imply that the computers have a positive influence on the students test results. However, we still have little research in Norway in this area concerning student s deeper understanding of concepts and ability to problem solving processes in mathematics. The CompuMath project provides long time experience on computer tools (Hershkowitz et al., 2002) and curriculum development which includes the use of technology. After several years of experimenting with different software, they chose to concentrate on the use of spreadsheets, dynamic geometry and curve plotting program. The reasons for their choice were, in addition to the generality of the tools, the potential to support mathematization by students working on problem situations and the communicative power of the tool. All the 1 On Becta website 2

3 three criteria are closely related to the multi-representational nature of the tools, which make it possible to do manipulations of objects and transformations between different representations (verbal, numerical, algebraic, graphic/visual). The tools have sufficient openness and flexibility to give opportunities for doing experiments and explorations, which we see as important in developing mathematical concepts in a constructivist setting. In an article concerning students different attitudes and activity using computers, Blomhøj describes three different patterns of activity and how they may affect students learning process, (Blomhøj, 2001). He describes three groups of students. The insecure and defensive students are feeling very unsafe and reveal only instrumental understanding. The solutions oriented students see their goal as solving many tasks and not to develop their concepts and understanding. The third category, the reflective students are motivated by the subject contents, stop and reflect over the work and results, they show personal interested in the relation between mathematical connections and the solution of the present task. 4 ICT in Norwegian mathematics classrooms How and to what extent are computers used in mathematics classrooms in Norway? In the TIMSS project 2, dealing with knowledge, attitudes and teaching in mathematics and natural sciences, there were also a few questions about ICT in mathematics. A small report from this given in 1997, Je bruker itte IT (I don t use IT) (Holmboe, 1997) revealed that only few teachers used computers in their mathematics teaching. Internationally compared, according to this report Norway was behind other Scandinavian countries and USA concerning teachers use of computers. About 2/3 of the students involved, responded they did not use ICT in mathematics and natural sciences. According to this research there appears to be no connection between the students performance and their use of ICT. In 1995 and 1997 Statistics Norway 3 performed a survey of the situation for IT use in schools. As a part of the MISS project 4, in spring 1997 a small research in secondary schools in Vest Agder, Norway was done. The results revealed that IT had only a marginal effect on the teaching. The conclusions are confirmed by more informal experiences from visits to schools and contact with teachers. Some main reasons for this was suggested: Computers in separate rooms make the availability difficult. Not sufficient opportunity or time for problem solving using computers. There is a lack of good software developed to support the textbooks or curriculum material, and a lack of support material giving methods for use of for example spreadsheet. The reports referred to shows that in spite of some commitment to use computers in teaching through some years, it has not become more common to integrate ICT in mathematics teaching. However, since these reports are already some years old, we must expect that some development have taken place and the situation has improved. The tendency over the recent years has been to use more of software tools, and less special software developed for use in schools. On the other hand, children and young people in their leisure time, use a lot of computer games and the Internet. Some computer games have mathematics built into them, but an analysis of some of these games 5 revealed that they were just simple drill and practice tasks, with only little explanations and help with wrong answer and often with no connection to the rest of the game (Gran, 2000). 2 TIMSS Norge 3 Statistisk Sentralbyrå 4 MISS Mathematics in school and society 5 Done by a master student at AUC 3

4 We have only little systematic knowledge of the situation concerning use of computers in Norwegian schools. The reports referred to here reveal that only few teachers have integrated ICT systematically in their teaching. The evaluation of tne Norwegian curriculum reform R97, published a few months ago, indicate only little use of ICT in mathematics classrooms (Alseth, Breiteig, & Brekke, 2003). On the background of discussions with practising teachers it seems that use of computers is limited, although there is some improvement. Teachers apparently need good models of teaching situations in order to understand how computer software may be integrated as a tool for teaching, learning and solving problems in mathematics classroom. This is an area open for developmental research in order to both develop teaching practice and research on the effects on learning. There is a need to give teachers better knowledge of how computer software can support different views on learning, to make the computer software support their own preferred view of learning, (Fuglestad, 2003; Fuglestad, 1999). 5 Research at AUC In the ICT Competence Project, conducted by Fuglestad, the aim is that the students during grades 8-10 in school should develop their competence and self-reliance to choose suitable computer tools for themselves not just rely a the teacher telling them what to use for a specific task. The emphasis in this project is on the computer tools, and the rationale given by the aim of the curriculum plan and an emphasis on general computer tools (Fuglestad, 2003b; Fuglestad, 2003a). More on this can be found in paragraph 7. Another local project deals with developing teacher students competence, in co-operation with students practice supervisors and the teacher educators. At AUC we have had several masters degree students working on problems connected to use of computers or calculators in mathematics classroom. At present we have a doctoral student working on ICT to support learning of probability, and we have two master students with their thesis in this area. 6 Software tools for mathematics General tools are applicable in a variety of situations and subject domains. The general tools we consider particularly appropriate are spreadsheets, dynamic geometry, graph plotters and computer algebra systems. However, new developments may focus on and give new interesting opportunities that we will consider. A spreadsheet, Excel, is an open software tool that can be utilised for many purposes: for example economical calculations, statistics, simulations and for exploring number patterns and other tasks. Some researchers argue that a spreadsheet is valuable for learning algebra (Sutherland & Rojano, 1993) whereas other discuss the limitations (Dettori, Garuti, Lemut, & Netchitailova, 1995). In spite of limitations, when teachers are aware of it, a spreadsheet can in many cases give a simple start for the students and act as an introductory tool before other software is used. Dynamic geometry (DGS), like Cabri, the Geometers Sketchpad and others, seems to give new dimensions to the school geometry, as well as on higher level with a clear invitation to experiment with and explore geometrical constructions and connections. Experiences show that students very much appreciate to work with DGS systems. DGS system has raised a lot of research interest, and results reveal that DGS have a potential to stimulate not just experiments but also the need for justification and proof (Mariotti, 2001; Hölzl, 2001). A 4

5 series of articles about DGS have been published recently in special issues of the journals Educational Studies in Mathematics and the International Journal of Computers for Mathematical learning. This documents that there is a lot of publications in other countries in this area. A graph plotter is characterised as an generic organiser by David Tall (Tall, 1989). By utilising the zoom tool in the software specific features of function graphs might be highlighted. Also this kind of software are natural tools for mathematics. Graph plotting can be performed also with a spreadsheet or even with a dynamic geometry package. A combination of tools may give the best support for learning, since the different tools can support different phases in the student s conceptual development. Computer Algebra System (CAS) represents a huge challenge for teaching in upper secondary schools and at university level. What are the appropriate uses, such that the students do not experience just pressing buttons obtaining a surface understanding, but achieve deep understanding? A lot of research is going on in different parts of the world, and there is even a journal dedicated to this area, the International Journal of Computer Algebra in Mathematics Education. In this context, symbolic calculators can now perform almost the same as computer based symbolic systems. Another area of interest could be software dedicated to teach specific topics in mathematics. This could be in the form of simulations or interactive software that let the user experiment with certain areas. Research reveal both positive and negative gains from this. Outcome can be represented in the negative experiences from Integrated learning systems by Hativa (Hativa, 1988) or positive influences from using the computer to pose problems and changing partly the role of the teachers (Fraser et al., 1988). It is important that we are open and flexible to try out methods and software of different kinds, for example for simulations, interactive applications 6 on the Internet, and dynamic systems (Choate, 1993). 7 Co-operation teachers and researchers We have applied to KUL for a project, named Learning Communities in Mathematics 7 where use of technology is a part of the domains of study. The collaborative learning experience and building of a learning community that involve students in schools, teachers, teacher students and researchers will be seen as a fundament for the work in the project we describe in the present application. We work from a basic premise that people learn through responsible participation in a collaborative enterprise whose aims are central to their well-being and aspirations, and in which their aspirations, qualities and potential to contribute are respected and valued. We work from Vygotskian principles of the social rootedness of human learning (e.g., Vygotsky, 1979) and recognise the dialectic of individual in community as a productive force for development (Wertsch, 1991; Cobb, 1994). We draw on Wenger s (1998) notion of identity within community of practice and relate this to metacognitive inquiry as a collaborative discourse (Wells, 1999). We draw on a rich tradition of inquiry in the learning and teaching of mathematics developing from problem solving in mathematics itself, through inquiry approaches to learning mathematics in classrooms to teacher inquiry in which teachers take on the mantle of researcher to explore questions about effective means of stimulating and sustaining their students mathematical growth (Schoenfeld, 1992; Lambdin, 1993; Jaworski, 1994, 1998; Mason, 2000; Bjuland, 2002). 6 Some colleagues work on animations and interactive webpages: 7 LCM project: 5

6 Research shows that when professionals reflect critically on and inquire into aspects of their professional lives, issues are revealed, questions refined and socially significant action can be taken in clearly directed and knowledgeable ways (Carr and Kemmis, 1986; Schon, 1987; Mason, 2002). The ICTML project will be a large-scale inquiry involving professionals - teachers, didacticians and researchers - in inquiry at some level. At any level, those involved will engage in inquiry according to their own particular roles, aims and expertise (Jaworski, 2002). Thus, both teachers and didacticians will engage in research relating to their own domains of knowledge. The project involves researching aspects of students learning with ICT and use of ICT as support for teaching. In close co-operation with researchers in other areas in our Faculty, (eg. in the LCM project), we will also study the very nature of inquiry as a means for sustained effective educational development in mathematics. At AUC, we have experience in co-operation with teachers and researcher in a three-year project, ICT competences in mathematics (Fuglestad, 2003b). In the project, the aim is to develop the students competence using ICT tools in such a way that they are able to choose tools for themselves, not rely just on the teacher telling them what to use. To achieve this, a group of teachers and a researcher work together and discuss teaching ideas, which are then implemented in the classes. Experience so far, reveals a need for the teachers to develop their own competence both using the software and utilise this with their students in an experimental and challenging way. In order to develop students competence and self-reliance the students need good introductions to the features of the software and open tasks that can challenge their understanding and use of the tools. The project is running from 2001 to 2004 and is now in the last year when we will evaluate students competence and our experience. In the AUC community, one research fellow is now undertaking a doctor degree study program on ICT and learning probability concepts, studying uncertainty as a significant concept in his project Children s probabilistic understanding with and without the use of ICT. 8 Research focus in the project The aim is to develop a long term and sustaining research capacity. This should materialise in production of research reports, papers in an international community. A main goal is to produce two doctor degrees on the area of ICT, learning and mathematics. A spinoff will be an adjustment of educational software and teaching material, learning environments and plans, to our educational system and culture. Learning and ICT used in mathematics in an international perspective is crucial. Hence the research foci will be general. Although most data will be collected from Norwegian schools, also different cultures will be represented. A longitudinal perspective of students development will be emphasised, and thus different age groups and school levels will be used in the study, and developmental strands identified and studied. This opens for also placing cross-subject perspectives on the research, from areas as language, art, social subjects and science. In our planning, this will be elaborated further. How much, what kind of, and with what aims are ICT used in Norwegian Schools today, especially related to mathematics? What are the teachers and the students attitudes in this connection? In order to understand the future potential, we need to have a precise documentation of the status. We plan for a survey to find out about state of the art in this field, both with statistical data and with interviews with teachers and students in school. The focus will be on the quality of learning, and the survey has to take this into account. 6

7 As a project based on the co-learning perspective described in a previous KUL application and briefly in this document, implies that research and development are part of the same. The recent development of portable technology implies that ICT can be a personal technology and a tool for frequent use. As Dörfler (1993) argues, computers should be readily available at any time. We can achieve this with the use of palmtop or laptop computers, and symbolic calculators. We want to explore the implications this might have on students learning and their way of using ICT technology. 9 Methods and expected outcome The research focus outlined in the previous paragraph implies the use of a variety or methods. There will be a combination of large-scale statistical surveys and qualitative interviews and observations in classes. In a learning community where the research is combined with development, we will use classroom observations, interviews and discussions. This is a further development of action research, towards developmental research. In the first part of the project we will develop methods further on basis of further studies of research and ideas described in this document. The outcome is planned to be two doctoral thesis, some research papers and better knowledge of use and influence of computers in schools. The developmental research involving personal technology may for a basis for further planning of teaching environment and material. We plan a series of publications and presentations at international conferences for mathematics education, e.g. PME, ICME and others. 10 Research Community at AUC Agder University College (AUC) has developed as a strong centre for mathematics education and development in recent years. In 1993 the college was given the right to offer the hovedfag (masters degree) and the candidates the title Cand Scient in mathematics education. So far about 50 students have graduated with supervisors both internal and external and examiners from universities and colleges in Scandinavia. Qualitative research in classrooms has been a key feature with important areas of cognitive development of mathematical concepts, history of mathematics in relation to teaching and use of ICT in mathematics teaching. In 2002, AUC was granted permission to establish a Doctoral Programme in Mathematics Education and to appoint 3 new professors to contribute to this programme, in addition to the existing staff. The first year four doctoral students started their work, and later six more were registered in our program. We also have students from other countries attending courses in our doctoral program. The research community in mathematics education at AUC has considerable contacts with similar communities in Norway and other countries, co-operating on research projects and evaluations for example, the KIM-project, the evaluation of L97, the Kassel-Exeter project, the SOFF project concerning development of distance education ( Research with colleagues at Telemarksforsking-Notodden ( on the L97 project has paved the way for further co-operation between academics at these colleges. Locally we are engaged currently in the Lillesand Project (EMIL) for school development, the Kristiansand Project, a programme for developing mathematical competence, where researchers at AUC have designed and are carrying out research among the teachers, students 7

8 and parents along the lifetime of the project, and the West Agder Project for mathematics teaching development in higher secondary schools. In the area of ICT, a three-year project exploring ICT competence of teachers and students is taking place in three schools aiming to develop students competence to choose computer tools for their solution of mathematical problems. These projects all involve partnerships between AUC and schools and local education personnel with agreed access to classrooms, teachers and students. Funding has been received by the AUC to establish a Centre for Mathematical learning which will be closely associated with research and development in schools. Members of the Mathematics Education Research group at AUC (MERGA) have attended the international conferences ICME, PME, CERME and NORMA in recent years and hold positions in International Programme Committees relating to these conferences as well as other specially convened international groups. A list of people in the research group, MERGA will be attached. Their expertise is sought in meetings and conferences throughout the Scandinavian countries. A recent proposal to NorFA, prepared at AUC for a Nordic Graduate School in Mathematics Education, has been awarded money to prepare a further proposal. The proposal links AUC with universities in Denmark, Sweden, and Finland as well as eminent scholars in these universities and others in Scandinavia. In 2004, PME28 will be held in Bergen and ICME 10 in Copenhagen. Complex preparations for these conferences, including preparatory seminars and conferences all involve AUC members. The journal NORMAT was for 5 years edited at AUC and the journal JMTE is currently edited here. A list of acronyms, with web references, is appended. In addition to the above links, we have relationships with the Norwegian Centre for Mathematics Education in Trondheim, Luleå Tekniska Universitet, Sweden, the Graduate School in Mathematics Education in Sweden, and with Iceland. 11 International co-operation With professors from six different countries, AUC in itself represents an international community with considerable international contacts. In paragraphs above our contacts in Scandinavian counties have been described, and participation in research conferences gives a rich opportunity to develop further contacts. For the ICT project in particular, we will develop further contacts with some key people working in this area. We have some contacts, for example with the Weizmann Institute in Israel (Dr. Rina Hershkowitz and colleagues), University of Melbourne (professor Kaye Stacey), Weingarten pädgogishe Hochschule (professor Heinz Schumann). We have contacted some people and will make further contacts and plan visits for research cooperation. Involvement in international organisations and conferences for mathematics education, e.g. PME, ICME and CERME implies contact with an international research environment. 12 Crossing subject borders We see connections to other subject where mathematics is used as a tool, and mathematical understanding is important. We had some co-operation with physics, on the use of 8

9 datalogging and understanding of function graphs and of derivatives 8. We think of language teaching, as in building of concepts and understanding of a specific language connected with mathematics and use of computers we have common interests. We have not developed this further at this stage, but are open to possibilities for co-operation on cross-subject areas. 13 Project management Project leader: Anne Berit Fuglestad, høgskoledosent (professor). She has a PhD from University of Nottingham, on the use of computers in mathematics classroom, and has been a tutor for more than 10 master students working on ICT in mathematics teaching. She is now a co-supervisor for a PdD student and project leader for the ICT Competence Project. A project management group will be established, with other colleagues and school teachers. Some of our colleagues have a special interest in ICT and mathematics teaching. A list of the MERGA group at AUC is attached. 14 Project personnel We ask for 2 fellow researchers (doctoral stipends) and one research position (on post doctor level), for technical assistance and secretarial help. 15 References Alseth, B., Breiteig, T. & Brekke, G. (2003). Endringer og utvikling ved R97 som bakgrunn for videre planlegging og justering - matematikkfaget som kasus. Notodden: Telemarksforsking. Askew, M., Brown, M., Denvir, H. & Rhodes, V. (2000). Describing primary mathematics lessons observed in the Leverhulme numeracy research programme: A qualitative framework. In T. Nakahawa & M.Koyama (Eds.), Proceedings of PME24. Hiroshima: Hiroshima University. Bjuland, R. (2002). Problem solving in geometry. Reasoning processes of student teachers working in small groups: A dialogical approach. Published doctoral dissertation. Bergen: University of Bergen. Blomhøj, M. (2001) Vilkår för lärandet i en computerbasert matematikundervisning - tre typer av elevvirksamhet. In B. Grevholm (Ed.), Matematikdidaktik - ett nordiskt perspektiv (pp ). Stockholm: Studentlitteratur Boekaerts, M., Pintch, P.P. & Zeidner, M. (2000). Handbook of self-regulaion. Academic Press. Burton, L., & Jaworski, B. (1995). Technology in Mathematics Teaching. London: Chartwell-Bratt. Carr, W. & Kemmis, S. (1986). Becoming Critical. London: The Falmer Press. Choate, J. (1993). Iterative models in the secondary mathematics curriculum: some examples. In T. Breiteig, I. Huntley & G. Kaiser-Messmer (Eds.), Teaching and learning mathematics in context (pp ). New York: Ellis Horwood Dettori, G., Garuti, R., Lemut, E. & Netchitailova, L. (1995). An analysis of the relationship between spreadsheet and algebra. In L. Burton & B. Jaworski (Eds.), Technology in Mathematics Teaching (pp ). Chartwell-Bratt Dörfler, W. (1993). Computer use and the Views of the Mind. In C. Keitel & K. Ruthven (Eds.), Learning from Computers: Mathematics Education and Technology (pp ). Springer Fraser, R., Buckhardt, H., Coupland, J., Phillips, R., Pimm, D., & Ridgway, J. (1988). Learning Activities and Classroom Roles With and Without Computers. Journal of Mathematical Behaviour, 6, Fuglestad, A.B. (1999). Læring med datamaskiner i konstruktivistisk perspektiv. Tangenten, 10, Fuglestad, A.B. (2003a). IKT kompetanse i matematikk. In F. Vik (Ed.). IKT prosjekt i skolen Fagbokforlaget, In press Fuglestad, A.B. (2003). Konstruktivistisk perspektiv på datamaskiner i matematikkundervisning. In B. Grevholm (Ed.). Matematikk i skolen - en didaktisk utfordring Fuglestad, A.B. (2003b). Students' competence using ICT tools in mathematics. Proceeding PICME, Växjö, (available via Internet) 8 Two master students worked on this 9

10 Gran, M. (2000). Pedagogisk programvare - dataspill for matematikk. Vurdering av et utvalg dataspill og deres tilknytning til læring og undervisning av matematikk. Hovedoppgave. Kristiansand: Høgskolen i Agder. Hativa, N. (1988). Sigal's ineffective computer-based practice of arithmetic. A case study. Journal for Research in Mathematics Education, 19 (3), Hershkowitz, R., Dreyfus, T., Ben-Zvi, D., Friedlander, A., Hadas, N., Resnick, T., Tabach, M. & Schwarz, B. (2002). Mathematics curriculum development for computerized environments. A designer-researcherteacher-learner activity. In L.D. English, M. Bartolini Bussi, G.A. Jones, R.A. Lesh & D. Tirosh (Eds.). Handbook of international research in mathematics education. Directions for the 21st Century. (pp ). Mahwah NJ: Lawrence Erlbaum Associates Holmboe, C. (1997). "Je bruker itte IT" En rapport om informasjonsteknologi i norsk skole basert på resultater fra TIMSS undersøkelsen. Oslo: Universitetet i Oslo. Hölzl, R. (2001). Using dynamic geometry software to add contrast to geometric situations - a case study. International Journal of Computers for Mathematical Learning, Jaworski, B. (1994). Investigating Mathematics Teaching: A Constructivist Enquiry, London: The Falmer Press. Jaworski, B. (1998). Mathematics teacher research: Process, Practice and the development of teaching. Journal of Mathematics Teacher Education 1, Jaworski, B. (2002). The Student-Teacher-Educator-Researcher in the mathematics classroom - Co-learning partnerships in mathematics teaching and teaching development. (s 37-54) I C. Bergsten, G. Dahland och B. Grevholm (red), Research and action in the mathematics classroom. Proceedings of MADIF 2. Linköping: Linköpings universitet. Jaworski, B. and Phillips, D. (1999). (Eds.) Comparing Standards Internationally: Research and practice in mathematics and beyond. Oxford: Symposium Books. KUF (1999). The Curriculum for the 10-year Compulsory School in Norway. Oslo: The Royal Ministry of Education, research and Church Affairs. Lagrange, J.-B., Artigue, M., Laborde, C. & Trouche, L. (2001). A meta study on IC technologies in education. Towards a multidimensjonal framework to tackle their integration. In M. van den Heuvel-Panhuizen (Ed.). Proceedings of PME 25 (pp ). Utrecht: Freudenthal Institute, Faculty of Mathematics and Computer Science, Utrecht University, The Netherlands Lambdin, D. V. (1993). Monitoring moves and roles in cooperative mathematical problem solving. Focus on Learning Problems in Mathematics, 15, Mason, J. (2000). Asking mathematical questions mathematically. International Journal of Mathematical Education in Science and Technology, 31, Mason, J. (2002.) Researching Your Own Practice: The Discipline of Noticing. London: Routledge. Mariotti, M.A. (2001). Justifying and proving in the Cabri environment. International Journal of Computers for Mathematical Learning, 6, Pea, R.D. (1987). Cognitive technologies for mathematics education. In A. Schoenfeld (Ed.). Cognitive Science and Mathematics Education (pp ). Hillsdale, New Jersey: Lawrence Erlbaum Associates, Publishers Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition and sense making in mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning, New York, Macmillan. Schön, D. (1987). Educating the Reflective Practitioner. London: Jossey Bass. Skemp, R.R. (1986). The Psychology of Learning Mathematics. Penguin Books. Sutherland, R. & Rojano, T. (1993). A Spreadsheet Approach to solving Algebra problems. Journal of Mathematical Behaviour, 12, Tall, D. (1989). Concept Images, Generic Organizers, Computers and Curriculum Change. For the learning of Mathematics, 9 (3), Vygotsky, L. (1978). Mind in Society. The Development of the Higher Psychological Processes. Cambridge, Ma: Harvard University Press. Wells, G. (1999). Dialogic inquiry: Towards a sociocultural practice and theory of education. Cambridge: Cambridge University Press. Wenger, E. (1998). Communities of Practice. Learning Meaning and Identity. Cambridge: Cambridge University Press. Wertsch, J. V. (1991). Voices of the Mind. A Sociocultural Approach to Mediated Action. Cambridge, Na: Harvard University Press. 10