First Evaluation Reportof the CALGEO project
( first meeting)
External evaluator: Despina Potari, University of Patras
The aim of the evaluation
The evaluation is of a formative nature. Its main aim is to identify the strong and the weak points of the program as it is developing. Its ultimate goal is to contribute to the improvement of the project by helping the coordinators and the other members of the team to examine critically their planning and development.
More specifically, the evaluation investigated:
a) Whether the aims and goal of the project were reached and the expected products were developed as it was planned
b) The quality of the products
c) The expectations and the goals of the participants in the project
d) The interaction – cooperation between the participants
Methodology
The evaluator based this report on the analysis of the products that were developed during the first year; on her field notes and audio- recorded discussions during the first meeting (May 16-19, 2005, Nicosia, Cyprus); on the analysis of a questionnaire that was developed and given to the participants (see appendix ); on informal discussions with the participants.The products that were developed were:report on the existing curricula on teaching calculus in the four participated countries,a literature review on research concerning learning and teaching calculus and a work plan for the second phase of the program (until the second meeting, December 14-15, 2005, Athens, Greece).
Results
In this section, the four points that have been investigated are discussed in reference to the products, the observation of the first meetingand the questionnaire
The report on existing curricula in each country
This report came out from the analysis of the responses of each country’s coordinator on a questionnaire that was developed by the program coordinator and the Cypriot participants. The questionnaire focused on the identification of the intended curriculum in each country and not of the hidden curriculum as the questions about the actual teaching practice were very few. Issues explored were the content of the calculus curriculum, the order that it was taught, the grades where the content was introduced, the current curriculum innovations, the use of technology, the teachers’ qualifications and training. As it was also proved in the first meeting, it was very difficult to get an accurate description of the calculus curriculum in each country only from the questionnaire. The main reason was that the different educational context in each country had as a result each participant to attribute different meaning to the same question. Moreover, some of the terms used were not very clear as the participants had different experiences and backgrounds. An example was the meaning of “intuitive” or “graphical” understanding and in what ways these were different.
These weaknesses of the questionnaire were overcome in the discussion where many of the misunderstandings were clarified. The group decided to improve the report by taking into account the discussion in the meeting. In the planning of the second meeting the reporting of the actual teaching approaches in calculus was one of the goals.
The literature review
The literature review was very detailed and a large number of research examples mostly on calculus learning was sited. This information is very useful for the development of materials for calculus teaching and teachers’ training as teaching is based on learning. However, I summarize below how the report can be improved.
- By including research examples about calculus teaching by the use of technology.
- By focusing on teachers’ development and identify professional programmmes that have been reported as “effective”
- By defining a framework under which the literature review could be structured.
These points were discussed in the meeting and it was decided the report to be improved and presented again in the second meeting. It was also decided to produce a relevant list of references that could be included in the project’s web-site.
The first meeting
The meeting was very well organized. All the country’s coordinators and other members of the project from Cyprus and Greece participated in the meeting and exchanged ideas on different issues concerning the teaching and learning of calculus. Many issues were clarified about the role of each coordinator and a specific work plan until the second meeting was also decided. The focus for the second meeting would be to go more deeply to actual teaching practices by taking in to account both the use of history and technology. The group decided to move according to the project planning to curriculum development. The first steps were to collect classroom problems, to experiment with the technology and to examine the possibilities of using or designing specific software.
Overall, the cooperation among the different group members was excellent and by the end of the meeting the work was distributed to the different members.
The questionnaire
The questionnaire was given to all participants in the meeting but only fiveout of eleven completed it. The points that emerged from the questionnaires are summarized below.
The four participants are university teachers who have done research in the area of Mathematical analysis and who teach calculus for 15-30 years and the last
Expectations from their participation in the project: They are all interested in the improvement of calculus teaching in their country through the development of innovative materials, tools and alternative teaching approaches. They see the project as an opportunity to develop research activities on the area of Mathematics Education. They expect to improve their knowledge about teaching calculus in high school in other countries, to interact with colleagues from mathematics education and improve their own teaching at the university, to explore how they can develop teaching approaches in calculus based on geometrical models and finally to study what is the teachers’ pedagogical and mathematical knowledge and how it can be developed. They expect that the results of the program can influence the educational policy of their country and improve both the teachers’ training programmes and the teaching of calculus. They also believe that the project will support the development of calculus teaching towards students’ conceptual understanding.
The group cooperation and the first meeting: The participants felt that the first meeting was successful as the quality of the discussions and the cooperation was very good. The fact also that the group members were coming from different countries and had different educational and research interests seemed to be one of the strong points of the team. However, the project coordinator and a group member from Cyprus suggested that the cooperation needs to be more active throughout the project. This would certainly help the group to pose new goals, to take into account the experience of the other participants and as a result to improve the quality of the products.One suggestion was to have some intermediate meetings, to set intermediate goals and deadlines.
Concluding remarks
The project in its first year seems to fulfill its initial aims and goals. The products are those that had been planned in the proposal and the deadlines were followed. Moreover, there is a flexibility and openness to integrate new ideas that emerge during the group interactions.
In my opinion, one very strong point of the project is the composition of the research and development group. Different research and teaching experiences of the group members can lead to consider the process of development from different lenses. For example, among the different experiences are: research in Mathematical Analysis; research in Mathematics Education with an emphasis on geometry education, on calculus education, on teacher education and on the use of computers; curriculum development with an emphasis on software tools, textbbooks; teaching calculus at the university level.
Another strong point is the process of interaction in the meeting. There is willingness to exchange ideas and work together. However, at the moment the cooperation among the different countries needs to be developed further during the whole period of the project. At the moment, the model of cooperation that seems to apply in the project is the division of the work in smaller teams usually from the same country. This type of coordination seems appropriate in this phase as the project is still at the level of exchanging experiences. However, a more interactive approach among different countries is needed in the process of developing teaching materials so that to meet the cultural and educational differences of the participated countries.
Appendix
Evaluation of the fist phase of the CALGEO programme
Name:
Participating country:
- What is your role in the project?
Project coordinator
Country coordinator
Member of the research team
- What is your previous experience related to the CALGEO programme (tick where appropriate)
Teaching calculus at the university
Teaching calculus at school
A mathematics researcher in the area of mathematical analysis
A mathematics researcher in other areas of mathematics
A researcher in mathematics education in the area of calculus
A researcher in mathematics education in other areas
Other
Give more information about your research interests and teaching experience.
- Have you participated in other similar projects? Specify.
- What are the reasons that you participate in the CALGEO programme? (Grade from 0 -5 according to the importance you attribute to the following reasons)
Exchange ideas with other researchers concerning calculus education
Learn about particular difficulties that students face in learning Calculus
Develop approaches that will improve teaching calculus in your country
Develop research on learning and teaching calculus
Other (specify)
- In what research or development areas of CALGEO are you interested in working?
- Describe your involvement (up to now) in the project. Specify the kind of activities that you have undertaken in CALGEO?
- Did you have the opportunity to cooperate with the other participants?
The programme coordinator
The other countries’ coordinators (specify)
Your country’s research team
Comment on this cooperation.
- What do you think that you are going to gain from your participation in CALGEO?
- What do you think that your country is going to gain from your involvement in CALGEO?
- In what ways do you think the CALGEO will contribute to the research and development in the area of Mathematics Education at the international level?
- Was the coordination of the programme close to your expectations? Describe any problems you had and make suggestions about improvements.
- Evaluate the first meeting of the programme (Grade from 1 – 5) in terms of
The presentations
The products
The quality of the issues discussed
The cooperation of the participants
The organization
Explain your grading and comment on any other issue related to the meeting.
- What in your opinion was the strongest part of the first meeting and which one was the weakest?
- Suggest ways that in your opinion would lead to the improvement of the future meetings.
- What do you think that is the contribution of the programme (up to now) to your own understanding of teaching and learning calculus?
- Describe particular areas (content, approaches, perspectives, etc) that in your opinion need to be stressed in the future in order the programme to fulfill its overall aims.
- Write any other comments or suggestions you would like to make that are not included to the previous questions.