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Sumary of Project Year 2PART 2: DESCRIPTION OF PROJECT ACTIVITIES 2.1 Summary of activities undertaken Start and end dates
Type of activity
Aims The aim of the project is to make available to teachers in Primary and Secondary schools a quality in-service education course which will influence, sensitise, motivate and enhance their work within school mathematics. The topics comprising the project will be developed by an established network of staff from three European institutions, which will base the project on current results of international, especially European research into mathematics education, particularly the outcomes of their own contribution to this research. All materials will be developed in co-operation with and trialled by teachers in the school systems of the countries involved, and will be disseminated in two European languages Czech and English. Locations
Expected benefits
Products and results Four prototype modules have been developed and all of them have been piloted and discussed at conferences and seminars (see table 1 in part 3) and actually used in the first in-service course held from 7th to 14th August 2001 in Prague. Several publications have been written (see table 2 in part 3). Partners responsible
Other organisations/contacts involved
2.2 Description of activitiesAims and objectives One of the main goals for the second year of the project was to consolidate all four modules so that they could be used in the course. These measures were taken to achieve it:
Partner meetings were assessed by all those attending who evaluated the meetings individually. The taught course was assessed by an individual anonymous questionnaire given to participants, a general meeting of participants at which comments were requested, partners giving deep evaluation of the course and their modules and the external assessor who provided an overall evaluation (see below Evaluation). The main changes following the review of the course was a re-organisation of the programme of the course and minor modifications to the modules. Stress was placed on the importance of making sure that there was no overlap in the work done in each module. Organisational approach and structure developed within the partnership 1. Course Four modules which form the course were divided among partners like this: module A - UK, module B - CZ, module C - SE, module D - CZ. Each partner was responsible for the design of their module(s) within the framework of the whole course set up at the beginning of the course and put more specifically during the second year of the project. All partners were asked to evaluate all other modules. The co-ordinating institution was responsible for the communication with participants and the organisation of the first run of the course held in August 2001 in Prague. The programme of the course and its evaluation was the joint responsibility of all the partners. Partners were responsible for the organisation of the work within their respective modules. The co-ordinating institution was responsible for the preparation of the CD-ROM for the course participants (see part 3, table 2 for more detail), while the partners prepared materials for their respective modules. 2. Project management The co-ordinating institution was responsible for the overall steering of the project and disseminating information among partners. The partners were responsible for the organisation and programme of the partner meeting in their respective countries. The co-ordinating institution was responsible for the communication with the Socrates office in the Netherlands. The general organisational approach to running the project and the course has proved efficient and served our purposes well. The communication via e-mail between partner meetings and the exchange of materials in an electronic format was appropriate to match our aims. Educational and teaching approaches Our educational teaching approaches have been from a constructivist standpoint and we have expected participants of the course to take the part of members of a class, to enable them to experience the teaching approaches which we used. The tutors tried to present new ideas in such a way so as to use as much as possible the participants' existing educational experiences. They proceeded from the assumption that general didactic situations can be fully understood only if they are seen in mutual relationships with one's own teaching practice. The general approach to teaching has been through workshops in which the participants have been encouraged to contribute and assess the work that has been given. During the course the participants were encouraged to prepare their own teaching projects which they will use in their classrooms. Both individual and group work was undertaken within the modules. Much emphasis has been put to enable participants to share their practical experiences from the classroom with others which contributed to the international flavour of the course. It is hoped that the influence of the course will be felt within the classrooms and demonstrated by the types of teaching approaches that will be used to complete the projects, which are an integral part of the course. The effects of these approaches will not be apparent in the short term. It is also hoped that via the participants of the course and their modified teaching strategies towards the counstructivistic approaches, the teaching strategies of their colleagues at school will be positively influenced, too. Priorities The aims of the project were to bring together teachers from different European countries, to enable them to discuss and share problems in mathematics teaching within their institutions and to take part in a quality in-service education course which is intended to influence, sensitise, motivate and enhance the teaching of mathematics within their schools. The course will concentrate on developing constructivist teaching strategies which the teams' research has proved to help pupils learn mathematics. The participants will be taught by these strategies so that they can experience the deeper understanding of the mathematical concepts which such methods produce. Although the course is taught basically in English, other languages are used which helps to foster language development among the participants. All participants are encouraged to inform other members of the course about the particular mathematical educational systems in their countries. This latter process is intended to broaden all the participants' viewpoints into a European awareness of mathematical education. The first experience of our course has shown that participants are encouraged to and wished to collaborate with colleagues in other countries in the school based projects. Open and distance learning Participants will use e-mail to keep in contact with tutors during the semester work which they will be doing in their school. It is hoped that an informal discussion group will be set up among the course participants who took part in the same module to discuss their projects. Tools and technology Course partners produced and brought materials which could be used within the workshop situations and which were new to many participants, e.g. mathematical games, dice, tangrams, pentominoes and manipulative material. In addition, written material was provided. A video of work in progress during the course has been transposed onto CD-ROM format for all participants. Contact will be maintained with partners by means of electronic mail during the rest of the programme. Evaluation 1. Formative evaluation of the project work and organisation All partners kept diaries with the information of partner meetings, stage of work on their respective modules, seminars and conferences where they piloted parts of the modules. Minutes of the meetings were kept to record: the state of work on individual modules, the experiences of partners with the piloting of the modules, the plan of work for the next period, the important deadlines, the decisions taken, the result of "brainstorming" of partners when working on some topic, the overall feelings of the partners (their satisfaction and dissatisfaction). Group discussion: At each meeting, the partners were specifically asked to comment on the following aspects of the project: the working plan (the deadlines for the individual stages of the projects), the task division among partners and division of responsibilities, information dissemination, the budget, the philosophy of the course ("Will your module fit in?"), the educational approaches of modules (constructivist) ("How will you incorporate it in your module?"), piloting of their modules, 2. Formative evaluation of the course External evaluation by course participants (questionnaires, observations): A comprehensible questionnaire (see part 3 table 2) which had been designed specifically for the teacher participants of the course was evaluated and modified at the partners' meeting in Sweden. Its purpose is to get as much information and feedback from the participants of the course as possible. It was prepared by an external consultant who specialises in constructing questionnaires. It mainly consists of closed questions with some open ones for people to comment freely on their experiences. The first questionnaire was given out at the beginning of the course to all participants (in English and Czech) and collected at the end. The questionnaire was anonymous and responses were sent directly to the external evaluator. It has been decided that this first questionnaire will be followed by the second questionnaire which will concentrate on the long-term impact of the course on the course participants. It will be distributed to them after they have defended their projects. The main purpose of the second questionnaire will be to see the extent to which their teaching strategies have been influenced both by the course and by their own experimental work in their classroom. The participants own experimental work and its success will serve as a kind of test if the above aims have been achieved. Other formal and informal evaluations took place during in-course and out of course meetings and where suggested changes were practical, these were incorporated into the course. External evaluation by an external consultant (observations, analysis of the questionnaires): An external evaluator visited and observed all modules during the time of the course. From the analysis of the participants questionnaires together with his own observations the external evaluator has produced a critical evaluation of the whole course which is enclosed to this report. Self evaluation (group discussions): Partners met regularly both formally and informally to evaluate their work as the course progressed. The partners evaluation which was summarised at the end of the course has resulted in a modification of the programme for the next course. Consequences of the evaluation: The evaluation of the course participants elaborated in the evaluation report by the external evaluator has brought up the following changes in the course:
It has been noted that participants were satisfied with the preliminary information of the course and its modules, the communication with the organisers, the emphasis on the school practice rather than theory, the timetable of the course and the organisational and educational approaches within the modules. Some participants felt that they would have liked to take part in all four modules of the course, however, from the standpoint of organisation, it is impossible. Dissemination Participants of the course although only taking two modules will have information concerning all four modules offered on CD-ROM therefore they will have the facility to use work from modules which they did not undertake within their classroom. The CD-ROM also includes video sequences from the course which it is hoped will serve as a means of promoting the project work. The work of the course will be disseminated by the course participants both within their classroom and to other teachers in their schools and in certain cases through in-service centres. Course participants intend to publish the results of some of their work on the course in local and national mathematical publications. Descriptors of the modules making up the course together with the philosophies on which they have been based are located on our website - http://www.pedf.cuni.cz/kmdm/index.htm. Partners have been diligent in their dissemination of the project's work together with the in-service course provided whenever they attended conferences and gave and attended seminars both in their countries and abroad (see part 3, table 1) (both in their presentations and through course leaflets). Information about the course and its content have been published in the proceedings from the above events. Partners regularly organise or take part in in-service courses for both primary and secondary teachers and parts of their modules have been piloted there through workshops. A qualitative description of the project products Because the rationale for the course is to enable and in certain cases change teaching strategies of the participants from transmissive to constructivist methods, it will require time for this to be achieved and partners will see the first effects of this when they receive the reports of the teachers' classroom projects which it is hoped will be based on these strategies and when the second questionnaire is distributed to them and then evaluated. The CD-ROM with the materials from all four modules and the video record of work in progress will be available to course participants only. Four modules have been completed and can be accessed through Darina Jirotkova, Universita Karlova v Praze, Pedagogicka Fakulta, M. D. Rettigove 4, 116 39 Praha, CZ. The individual project products are described in more detail in part 3, table 2, and their copies (where applicable) are appended to this report.
2.3 Evaluation of the work undertaken Difficulties There were some problems with arranging times for partners to meet because of teaching commitments in their own countries and different arrangements of the school year in participating countries. There was a change in membership of a national team due to unforeseen circumstances. Outcomes
Elements of good practice, by-products, discoveries
Divergence from the original conception of the project Change of partnership: The partners in the original group knew of each others work, prior to submitting our bid for the project and held it in high regard. At the preliminary meeting the intense discussions indicated that the partners were very enthused by the general ideas which were put forward for how an in-service course would be developed for the benefit of mathematics teachers. However, when the drafts of the modules were circulated as per our detailed programme, it was obvious that there were great philosophical differences between the methodologies which the German team wish to employ and those of the rest of the partners. As we had gained approval for our project on the grounds that we would be both teaching the students in an open constructivist method and expected them to do the same once they were back in their classrooms, the formal methods which the German module implied countered the underpinning philosophy of all the remaining modules. Our German colleagues did not wish to change their methods and so asked if they could withdraw from the project. Reluctantly the rest of the partners agreed to this. Additional comments For many teachers our philosophy implies a considerable change in their teaching strategies. (The traditional transmissive approach with a teacher as a producer and a student as a consumer of the knowledge should be changed into the constructivist approach with a teacher as a motivating agent and a student as a creator of his/her own knowledge.) This cannot be achieved by simple information but requires practice within their classrooms and for them to give their partner tutors feedback. Our initial planning required a further residential week working with participants, some six months after the first meeting with the group to enable them to give the partners progress reports concerning their work in schools and to discuss successes and problems encountered in this. The EU funding, as we understand it, would not allow such a course to be undertaken and we feel that this is a regrettable decision. All the participants asked for a follow-up session at the end of this course but we were unable to agree to this because of EU funding restrictions. We had to overcome this problem by asking the participants to send their projects and have tutorial discussions by electronic mail. A full address list was given to all partners and participants to enable free discussion between all members of the course.
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