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Sumary of Project Year 3Section 2B - Overall Description of the Project 1. ObjectivesThe aim of the Project was 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 main goal of the Project was to initiate teachers into the constructivist method of teaching mathematics. The constructivist type of educational approach requires the teacher to be the motivator and organiser of class discussions, setter of challenging situations and of enhancing the intellectual self-confidence of the students. The students gain knowledge through problem solving and communication with each other and the teacher. The main objective of year three of the Project was to organise two seven-day pilot courses which would attract teachers from the whole of the European community and the associated countries and to evaluate them in terms of our objectives, e.g. if the courses contribute to the teacher's applying new approaches to specific topics, new teaching strategies, towards becoming a reflective teacher, etc. The courses took place and there were participants from 16 European countries. They followed constructivist teaching strategies using workshop and group-work creating a supporting and collaborative climate among participants. Special attention was given to how the work done in the course influences those pupils who are under-achieving in mathematics in schools. A very friendly and supporting climate prevailed during the courses. Following the courses, participants were expected to use the methodology and ideas gained from the course in their classrooms. They have been submitting reports of this work which, among others, enable the tutors to evaluate the effectiveness of the course and see if the course contributed to the change in the teacher's practices. After each course, the work was evaluated (see below) and where necessary, modifications to modules and the administration were made for the benefit of the next course. Considerable efforts have been made to evaluate the courses at all possible points. Participants were given questionnaires at the outset to ascertain their objectives and again at the end to determine whether these had been achieved. Each session was evaluated by the participants and they were asked to keep a diary of the work done. Tutors sat in on each others modules and evaluated the work seen and they also gave an overall evaluation of their modules both verbally and in writing. An external evaluator not only evaluated the evaluations of participants and tutors but also sat in on the work of the modules and made his own evaluation of the work done. The partners also aimed to produce a comprehensive publication which would include the description of the four modules and which could be used not only by tutors in future courses but also by other professionals. The publication has been produced and is enclosed with other products of the Project. Priorities: From the above, it can be seen that the project matched most of the priorities for SOCRATES action. The participants of the courses were trans-european, many languages used, the content was aimed at getting students to reach their mathematical potential, whatever the level and to ensure they would enjoy their mathematics and wish to study it further and there were no restrictions from the point of view of disability, ethnicity or religion placed on the applicants. The course concentrated on developing constructivist teaching strategies which the teams' research has proved to help pupils learn mathematics. The participants were taught by these strategies so that they can experience the deeper understanding of the mathematical concepts which such methods produce. Although the course was taught basically in English, other languages were used which helped 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 was 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.
2. Organisational Aspects The four modules which form the course were divided among partners: 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 project and the content developed during the second year of the project. Each partner was also responsible for their share of the final publication. All partners were asked to evaluate each others module not only during the pilot courses but also afterwards when the courses were modified. The co-ordinating institution, Charles University, Prague was responsible for the communication with participants and the organisation of the second run of the course held in January 2002 in Prague. The third time the course was offered, the partner, University of Derby, was responsible for communication with participants and the organisation. 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 new version of the CD-ROM for the course participants, while the partners prepared materials for their respective modules and submitted material for the CD-ROM. The co-ordinating institution was responsible for the overall steering of the project and disseminating information among partners. The agendas and minutes of the meetings were done by the co-ordinating institution. 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 Bruxelles and partner institutions communicated with their national agencies. The partners were responsible for their chapter of the final publication, while the co-ordinating institution was responsible for its whole production and print. 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 and needs. 3. Methodology, tools and technology used3.1 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 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 given 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. However, from the first participants' reports we can judge the effectiveness of our efforts during the course. It is also hoped that via the participants of the course and their modified teaching strategies towards the constructivistic approaches, the teaching strategies of their colleagues at school will be positively influenced, too. 3.2 Open and distance learning Participants use e-mail to keep in contact with tutors during the semester work which they are doing in their schools. From the survey among the past participants it is known that some informal discussion groups have been set up among the course participants who took part in the same module to discuss their projects. 3.3 Tools and technology The 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 are maintained with partners by means of electronic mail during the rest of the programme. 4. Products and results, their dissemination4.1 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 requires time for this to be achieved and partners can only see the first effects of this when they are receiving the reports of the teachers' classroom projects which are based on these strategies. Some positive results can already be seen in publications which resulted from the participants' reports (see part 2c). The discussion of two participants' reports is also given in the final publication of the Project (chapter on module A and B). An important product of year 3 was running two pilot courses during which the partners implemented their ideas towards reaching the objectives of the Project and could see their effectiveness. Two different organisations of the course have been trialed, during the first of them the participants went through two modules only and spent a greater length of time on them, while in the second they experienced all four modules. The experience from these two courses together with the local trials of the modules in partners' countries contributed to the final modification of the modules which became more flexible and can now be adjusted to different situations. A book has been published under the title 'EMTISM - a Course on Constructivist Teaching Approaches, Theory and Practice' which is a joint publication of the partners and which gives the philosophy of the Project, detailed descriptions of all four modules, participants' handouts and examples of participants' reports and their reviews from the course. The book is to be used in future courses but also by other professionals who wish to use our methodology for promoting constructivist approaches at school. The individual project products are described in more detail in part 2c, and their copies (where applicable) are appended to this report. 4.2 Intellectual property rights, copyrights. The individual partners who produced the modules, their philosophy, and the associated materials hold the copyright. The copyright of the book to be published in paper and CD-ROM form is shared between the Prague and Derby partners except for module descriptions, for which the first statement above holds. Any examples used from project reports within the book are the property of the individual participants concerned. 4.3 Dissemination Participants of the course although only taking two modules (in the second run of the course) have information concerning all four modules offered on CD-ROM therefore they have the facility to use work from modules which they did not undertake within their classroom. The work of the course has and 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. Tutors from the course have given workshops to teachers and teacher-education students and taught classes both primary and secondary in several countries to promote the teaching approaches and content of the project. Course participants generally intend to share their new experiences with their colleagues at the school and some of them have already published the results 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 2c) (both in their presentations and through course leaflets). Information about the course and its content has been published in the proceedings of the above events. Partners regularly organise or take part in regional in-service courses for both primary and secondary teachers and parts of their modules have been piloted through these workshops. The content of the modules has also been used in teacher-education courses in the partners institutions. The effects of the project have been exceedingly wide. A participant has decided to continue her studies to PhD level in didactics of mathematics; several have given papers on their work following the course at in-service courses; some have attended further in-service courses offered by the partners. The long-term collaboration between the UK and CZ partners has been one of the most influential reasons for inviting a Derby University professor to undertake the position of Visiting Professor to Charles University, Prague for the Autumn semester 2002. Two tutors from the course have been asked to prepare a series of articles for publication in the Swedish Mathematics journal 'Namnaren' following invitations for them to offer in-service courses and teach in schools in Sweden. 4.4 Commercialism The articles produced for 'Namnaren' will be published under the commercial system operated by the Journal.
5. Transversal Issues In all modules particular attention was given to individual teaching approaches, namely to motivation, affective work with under-achieving pupils. The material used had no gender-bias. All applicants for the courses were accepted without discrimination.
6. Evaluation 6.1 Formative evaluation of the project work and organisation All partners kept diaries. Agendas and 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 evaluation of meeting the goals set up previously was part of each partner meeting. The main partner meetings were evaluated by each partner by filling in the questionnaire. 6.2 Formative evaluation of the course External evaluation by course participants (questionnaires, observations): A comprehensible battery of questionnaires (see the external evaluation by Mr Je?ík attached) which had been designed specifically for the teacher participants of the course was evaluated. An external consultant who specialises in constructing questionnaires prepared this. 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. The second questionnaire concentrated on the long-term impact of the course on the course participants. It has been distributed for completion after their work in school. 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 classrooms. The participants' own experimental work and its success serve as a kind of test if the above aims have been achieved. This is being assessed by partners via the participants' reports. External evaluation by an external consultant (observations, analysis of the questionnaires): Two external evaluators (one for each trial course) analysed the participants' questionnaires together with their own observations and have produced critical evaluations of the whole course which are enclosed with this report (the evaluation of Mr Je?ík and Ms Polechová). 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.
7. Feedback on the project One of the original partners withdrew in year 2 of the Project because the philosophy of the course did not match his expectations. Otherwise aims, objectives programme and budget have been as originally envisaged. Difficulties have arisen mainly in administrative matters. The changes of financial year and lateness of receipt of finances have caused particular problems for the coordinating University. The lateness by which the applicants are informed of getting financial support makes organisation of the courses more difficult than necessary. The benefits of this course are long term. Our experience has shown that the effort of keeping personal contact with the participants for half a year whilst they were working in school influences their way of teaching much more deeply than in those cases were there was little contact.
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