Strand 3:

Technology in teacher education

ICTMT 5, Klagenfurt, 6-9 August 2001

(Schedule, tentative as of 08/06/01)

Chair: Jaime Carvalho e Silva

Monday 15:15 - 16:00 Chair: J. Carvalho e Silva

Internet as a tool in the preparation of future mathematics teachers

Jaime Carvalho e Silva*, José Carlos Balsa, Maria José Ramos (Portugal, jaimecs@mat.uc.pt)

Monday 16:15 - 17:00 Chair: J. Carvalho e Silva

Innovations in Mathematics, Science and Technology Teaching (IMST²) - First outcomes of a nation-wide initiative for upper secondary schools in Austria

Konrad Krainer (Austria, konrad.krainer@uni-klu.ac.at)

Monday 17:00 - 17:45 Chair: J. Carvalho e Silva

Innovations in Mathematics, Science and Technology Teaching (IMST²) - First outcomes of a nation-wide initiative for upper secondary schools in Austria - Workshop

Konrad Krainer (Austria, konrad.krainer@uni-klu.ac.at)

Practical applications of CAS using sinusoidal functions

George Adie*, Bogdan Zoltowski (Sweden, Poland, george.adie@te.hik.se)

Tuesday 8:30 - 9:15 Chair: J. Carvalho e Silva

Computers in school mathematics - a pilot training programme for Estonian mathematics teachers

Rein Prank (Estonia, prank@cs.ut.ee)

Tuesday 9:30 - 10:15 Chair: J. Carvalho e Silva

Supervision of students' projects

Li Ma (Sweden, mali@itn.liu.se)

Tuesday 10:30 - 11:15 Chair: J. Carvalho e Silva

What teachers can request from CAS designers

Walther A. Neuper (Austria, neuper@ist.tu-graz.ac.at)

Tuesday 14:15 - 15:00 Chair: J. Carvalho e Silva

Plenary:

Teacher training: the role of technology

Branca Silveira (Portugal, branca@esb.ucp.pt)

Tuesday 15:15 - 16:00 Chair: J. Carvalho e Silva

CASCADE-IMEI: Web site support for student teachers to learn realistic mathematics in Indonesia

Zulkardi (Netherlands, zulkardi@edte.utwente.nl)

Tuesday 16:15 - 17:00 Chair: J. Carvalho e Silva

Internet materials in mathematics teaching

Maria Zajac (Poland, mzajac@wsp.krakow.pl)

Tuesday 17:00 - 17:45 Chair: J. Carvalho e Silva

A modern approach to limit process

Primo Brandi, Anna Salvadori* (Italy, mateas@unipg.it)

Wednesday 8:30 - 9:15 Chair: J. Carvalho e Silva

Computers and calculators in the preparations of future mathematics teachers - an experience

Ana Isabel Rosendo*, Jaime Carvalho e Silva (Portugal, jaimecs@mat.uc.pt)

Wednesday 9:30 - 10:15 Chair: J. Carvalho e Silva

Current educational theories and new tech - development of a training programme for math teachers in the Philippines

Auxencia Limjap (Philippines, cosaal@mail.dlsu.edu.ph, ching_limjap@yahoo.com)

Wednesday 10:30 - 11:15 Chair: J. Carvalho e Silva

Using computers in mathematics teacher training programmes: a reflection upon an experiment

Elizabeth Belfort*, Rafael Barbastefano, Luiz Carlos Guimarães (Brazil, beth@dmm.im.ufrj.br, rafael@fgv.br, lcg@centroin.com.br)

Thursday 8:30 - 9:15 Chair: J. Carvalho e Silva

Investigating teachers' perceptions on their preparation to use IT in classroom instruction

Adnan Baki (Turkey, adnanbaki@usa.net)

Thursday 9:30 - 10:15 Chair: J. Carvalho e Silva

Integration ICT into teaching and learning the subject Discrete Mathematics

Eva Milkova*, Milan Turcani (Czech Rep., eva.milkova@uhk.cz, mturcani@ukf.sk)

Thursday 10:30 - 11:15 Chair: J. Carvalho e Silva

Using DERIVE for beginner courses of recursion theory

Nelson Urrego P. (Columbia, nurrego@javeriana.edu.co)

Thursday 15:15 - 16:00 Chair: J. Carvalho e Silva

Changing the classroom practices - the use of technology in mathematics teaching

Isabel Fevereiro*, Carmo Belchior (Portugal, isabel.fevereiro@des.min-edu.pt)

Thursday 16:15 - 17:00 Chair: J. Carvalho e Silva

Integrated Teaching Mathematics with Elements of Computer Science

Henryk Kakol (Poland, henkakol@wsp.krakow.pl

Abstracts:

Plenary: Branca Silveira (Portugal):

Teacher training: the role of technology

We can't have a change in our schools without teachers and teachers don't change if they are not convinced that the change is going to improve something. The world is changing, society is changing, pupils are changing, and the schools? How are schools coping with this? Technology is everywhere. No discussion about that. Everyday appears new software, new computers, new calculators, etc. Are the schools ready for this? Does technology play a significant role in the change of the curriculum? How do teachers face this? Are they prepared to use technology effectively? Which kind of difficulties do teachers face? Some teachers have been using technology; did they really changed their methodologies or are they using them in a inadequate environment? What about teacher training? Which kind of training is more effective? Initial training? In service training? But, what should we do for making teachers include technology in their practice? More computers? More training? A different schedule for the classroom? Making the use of technology compulsory? In Portugal the use of graphic calculators is compulsory in secondary schools, so, everybody has to use them. Should we do the same with computers and other technology? What about Internet? How should we train teachers for the use of Internet in the classroom? How can teachers develop the ability to analyse and integrate in an intelligent way, in their teaching the technological developments to come (software, hardware, communication...)?

Those are some of the questions we are going to discuss in this talk, based on the Portuguese experience, focusing my point of view as a teacher, as a teacher trainer and as a member of the board of directors of APM (the Portuguese "Association of Teachers of Mathematics").

George Adie, Sweden:

Practical applications of CAS using sinusoidal functions

A lot of physics is involved with the study of sinusoidal variation. In this talk we will show how handheld technology with CAS changes our approach making the physics more accessible for students and allowing the physics course to become deeper and more meaningful. We will also discuss appropriate changes in the students´maths course.

Adnan Baki, Turkey:

Investigating teachers' perceptions on their preparation to use IT in classroom instruction

The researcher taught a two-term required course within mathematics teacher education program to train student teachers and to investigate perceptions on their preparation to use computers in their own teaching. This paper describes issues emerging from the analysis of the course. Data were gathered through questionnaires. Students who felt prepared made the link between computer-based activities and school mathematics, and had more experience on the instructional software during the course than others. The implications of these results for the designing and implementing of computer-based undergraduate courses and further research in this field are discussed.

Elizabeth Belfort*, Rafael Barbastefano, Luiz Carlos Guimaraes, Brazil:

Using Computers in Mathematics Teacher Training Programs: a Reflection upon an Experiment

As part of the requisites for an in service graduate course at our university, Secondary school teachers attend a discipline regarding the use of computers for teaching mathematics. Among other activities, they are asked to produce their own instructional materials, which should be supported by one of the educational computer packages made available to them during the course. The authors have designed this discipline and have also been ministering it for the past three years. Meanwhile, we have been investigating its consequences on teacher's opinions and practices. In this article, we analyse qualitatively the instructional materials produced during the course of the discipline by these teachers, as well as some medium term consequences of these activities for their subsequent classroom work.

Jaime Carvalho e Silva*, José Carlos Balsa, Maria José Ramos, Portugal:

Internet as a tool in the preparation of future mathematics teachers

We describe a project that was developed with two groups of seven future mathematics teachers (7th-12th grades) that worked in different schools (30km apart). They sent messages with weekly reports of their activities, comments, and files to a mailing list. The participation was considered to be very fruitful, and these future mathematics teachers became more aware of activities outside their daily routine, developing at the same time their communication skills; they exchanged more than 90 messages and 50 files (mainly with activities and exams). All considered this project to be a very important part of their preparation as teachers of mathematics, showing how they can get new ideas and fight their isolation using the Internet. This project showed that the Internet is a very powerful tool for the preparation of teachers and should be used more frequently.

Isabel Fevereiro*; Carmo Belchior, Portugal:

Changing the Classroom Practices. The use of Technology in Mathematics Teaching

Since 1997/98 the Department of Secondary Education, Ministry of Education of Portugal, has created a training teachers NET constituted by 80 mathematics teachers to improve meetings and promote training sessions and workshops with mathematics teachers in all secondary schools in Portugal. The aim of this project is to change the classroom practices according to the curriculum guidelines, which focus on experimental teaching/learning process, centred in the students themselves, in knowing how to do, and with a strong emphasis in the use of technology. Since then, after three years, the use of the graphic calculators in the classroom is generalised (the use of the graphic calculators is compulsory in the final national 12ª grade exams). We will take a look at the final exams. Since our truing teachers are working with many different activities in the classroom we will take a look in some of these activities

Henryk Kakol, Poland:

Integrated Teaching Mathematics with Elements of Computer Science

At present nearly all Polish schools have computer rooms well equipped while teaching mathematics generally is traditional. During school lessons chalk and blackboard are still teaching instruments frequently applied. What are the reasons for such a situation? There are many of them. It will be list some of them. Special Programme of Teaching Mathematics with Elements of Computer Science in Gymnasium eliminates many of the above mentioned problems. It offers teaching mathematics and elements of computer science in the form of one thematic block.

Konrad Krainer, Austria:

Innovations in Mathematics, Science and Technology Teaching (IMST²) - First outcomes of a nation-wide initiative for upper secondary schools in Austria

The bad results of Austrian high school students with regard to the TIMSS achievement test led to a research project where the results were analysed and additional investigations into the situation of mathematics and science teaching were started. As a consequence, a pilot project called IMST² - Innovations in Mathematics, Science and Technology Teaching - was launched in the school year 2000-01. The project aims at supporting mathematics and science teachers' efforts for raising quality in learning and teaching. 126 Austrian schools participated in this project, about one quarter collaborated more intensively with the IMST²-team and documented one or more innovations at their school. The concept, experiences and findings of IMST² will be presented and discussed.

Auxencia Limjap, Philippines:

Current Educational Theories & New Tech: Development of a Training Programme for Math Teachers in the Philippines

Reform movements on mathematics education in different parts of the world point out to the need to adopt a cognitivist view of instruction that focuses on the nature and process of mathematics learning. Proponents advocate constructive learning and gear teaching towards the development of meaningful quantitative thinking. They adhere to the social origins of cognition and situate learning in realistic settings. They harness technology as a learning resource that provides both context and support for meaningful problem solving activities. Consequently, learner centred educational theories proliferated with the advances in educational technologies. These developments in pedagogy and didactics pose a big challenge to school mathematics teachers especially those who have neither experienced the constructive process of learning mathematics in the classroom, nor employed the current educational technologies.

Li Ma, Sweden:

Supervision of students projects

This paper concerns supervising students projects in information technology.

Eva Milkova*, Milan Turcani ,Czech Rep.:

Integration ICT into teaching and learning the subject Discrete Mathematics

ICT enables new approach to the education of various subjects, also of mathematics. The education with help of visualisation is interesting and more understandable. Because our faculty disposes with good and modern equipment and there are several students who are able to prepare nice programs, we decided to improve lectures of the subject Discrete mathematics with help of students teaching packages. In our article three programs developed by students as part of their thesis will be briefly introduced.

Walther A. Neuper, Austria:

What teachers can request from CAS-designers

The basic functionality of computer algebra systems (CAS), increasingly introduced to math classes, is considered not yet optimal for education: CAS show up with the final result in one go, and do not show their built in knowledge. concept for re-engineering the interactive features of CAS is presented from the users point of view: An example session illustrates what a teacher (and a student!) can request w.r.t. the assistance in modelling and specifying a problem, and w.r.t. the user-guidance in stepwise solving a problem. Brief explanations point out, how the concept presented makes the example session work; and tasks for teachers are mentioned.

Rein Prank*, Eno Tonisson, Estonia:

Computers in School Mathematics - a pilot training program for Estonian Mathematics teachers

Most of the software for the national schools' computerisation program called 'Tiigrihüpe' (Tiger Leap) has been acquired in such a way that the programs are available to all/most of the schools in Estonia. This will also simplify the training of teachers. Each county has a well-equipped pilot school, which shall organise local training and consultation for teachers of different subjects. This report describes the training cycle (9 sessions with 144 hours plus homework in the scope of more than 300 hours) conducted for 40 teachers in 2000. The cycle consisted of thematic modules based on special packages (StudyWorks, dynamic geometry, computer algebra systems, graphing functions, proofs in geometry, probability theory and statistics, spreadsheets, testing software, Internet and distance education tools) and the final integrative module on the use of computers.

Ana Rosendo*, Jaime Carvalho e Silva, Portugal:

Computers and calculators in the preparation of future mathematics teachers - an experience

We will describe how future mathematics teachers are being prepared to use technology in mathematics teaching (at the Mathematics Department of the University of Coimbra)

Anna Salvadori*, Primo Brandi, Italy:

A modern approach of limit process

A new approach to limit process is proposed. The aim is to drive students from perception to usual epsilon-delta definition gradually. This path involves the three fundamental aspects: geometric, numeric, algebraic. To supply the graphic support a software ad hoc is implemented.

Nelson Urrego, Columbia:

Using DERIVE for beginner courses of recursion theory

In this Paper, the author gives a short introduction to the main concepts about Recursive Functions and some examples are programmed using DERIVE. These exercises can motivate students in the design of algorithms for solving rigorous arithmetic problems such as the implementation of a procedure for generate of a 1-1 Primitive Recursive correspondence between N2 and N.

Maria Zajac, Poland:

Internet materials in mathematics teaching

In the paper the idea of an Internet educational website will be presented. The learning materials are divided into three groups: Power Point presentations, web pages and lesson scenarios. All of them are intended to be a tool for computer assisted learning. The resources for Math lessons will be of special interest in the paper.

Zulkardi, Netherlands:

CASCADE-IMEI: Web site support for student teachers to learn realistic mathematics in Indonesia

CASCADE-IMEI is a learning environment in the form of a face-to-face course and a Web site (www.cascadeimei.com) which aims to support student teachers in Indonesia to learn Realistic Mathematics Education (RME). RME is an instructional theory in mathematics education that was originally developed in the Netherlands. So far, two prototypes have been developed and evaluated both by student teachers and several experts in the Netherlands. This paper presents the origins of the learning environment, with a more detailed on its Web site as well as the results of first two cycles of its prototyping process.