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The first year of the MOTIVATE program, 1999-2000Marilyn Nickson Contents of this page:Introduction
IntroductionThe purpose of this evaluation is to assess the extent to which the first objective of the project has been achieved. This objective states the following: To enrich the mathematical experience of school students, to broaden their mathematical horizons, to give them an experience of collaborative working on mathematical tasks and of presenting reports of their work to an audience, to raise aspirations and to improve mathematical thinking and communication skills. Questionnaires have been designed for students and teachers in an attempt to asses these aspects of the project. The mathematical topic is presented during the first video-conference and the questionnaires are completed by students and teacher after the second video-conference which takes place approximately four weeks later. At this point, students will have completed the tasks set on the relevant topic and presented their results at the second seminar. The questionnaires are followed up by interviews with a sample of students and one teacher from each of the participating schools for each unit of the project. Both questionnaires are divided in two sections. The aim of first section of the student questionnaire is to gain feedback about the initial mathematics input by the presenter. The second section sets out to probe the attitudes of students in relation to aspects of the project objective quoted above and to assess the impact of their participation in the project on their mathematical experience generally. The purpose of the first part of the teacher questionnaire is to obtain feedback from teachers about the initial presentation of the topic and information about their students’ mathematics experience in the classroom. The second part is primarily to determine how teachers considered their students’ approach to mathematics may have changed as a result of being involved in the project The results of the analysis of questionnaires and interviews carried out with respect to each topic are presented separately below.
QuestionnairesTopic: Fractals.Questionnaires were completed by 25 Year 10 students from the following schools: John Kelly Girls’ Technology College, John Kelly Boys’ Technology College, Camden School for Girls, Elizabeth Garret Anderson School and Sarah Bonnell School. Student responsesThe analysis of the questionnaires indicated that most students (75%) were able to relate at least some of the mathematics in the topic to their previous mathematical experience. The language level appeared to be about right and a majority (62.5%) considered their ability to see the relevance of mathematics to the real world had improved as a result of doing this topic. Just over half indicated that sharing mathematics in the project work had increased their interest in mathematics. There was a general acknowledgment of the benefits of sharing mathematics through discussion (74%) and collaboration with peers (70.8%). About half the students appeared to feel more confident in their ability to do mathematics as a result of their project work and a majority agreed that they had coped well with the mathematics over the weeks of their involvement. Teacher responsesOf the 7 teachers responding, 4 thought the mathematical topic was ‘quite easy’. Most were able to link it to work they were undertaking in the classroom and 3 reported that they had worked on related topics with classes in Years 7, 8, 9 or 10. The language level of the presentation was considered ‘a bit difficult’ by 4 of the teachers. Teachers indicated that some group work was the norm for their classes and that students frequently discuss their work in class. Three of the 6 teachers completing the second section of the questionnaire felt that their students were able to cope with a new mathematical problem more readily than might have been expected. However, there was no consensus amongst the teachers concerning any perceived increase in students’ confidence in their mathematical ability. Teachers agreed that their own personal experience of the project had been a positive one.
Topic: The SunQuestionnaires were completed by 23 Sixth Form students and 5 teachers. The schools involved were Woodhouse College, Hampstead School, Camden Sixth Form College, St Charles Sixth Form College and John Kelly Girls’ Technology College. Student responsesAnalysis of the results indicated an overall positive response to the project. The level at which the topic was presented appeared to be about right although a a majority (60.9%) found the language level somewhat difficult. Most (82.5%) found the topic improved their ability to see the relevance of mathematics to the real world and that sharing mathematics in this way increased their interest in mathematics. There was a general acknowledgment of the benefit of sharing mathematics through discussion and collaboration with peers and with this, a change in their perception of themselves as learners. About half of the students appeared to feel more confident in their ability to do mathematics as a result of their project work and almost three quarters of them felt they had coped well with the mathematics over the weeks of their involvement. Teacher responsesThree of the five teachers considered the mathematical content of this unit to be difficult. While they could link the content with other mathematics the students were doing in some way, only one teacher said the topic was touched upon within the curriculum and this was in Year 12. Teachers considered the language level of the presentation was difficult and three of the five thought there were not enough examples given. Most of the teachers said their students work in groups occasionally and discuss mathematics frequently in class. Teachers did not see that participation in the project had had very much effect on their students although there was some indication that students were more ready to discuss their mathematics. On the whole, the teachers saw their own experience of participating in the project as a positive one.
Topic: ChaosQuestionnaires were received from 13 Sixth Form students and four teachers who were involved in this unit of work. They came from the following schools: Woodhouse College, John Kelly Girls’ Technology College, Camden Sixth Form College and Hampstead School. Student responsesMost of the students (92.3%) were able to link the mathematics of the topic with some of the mathematics they already knew and found the topic accessible. A majority (69.2%) found the language level about right but approximately a third of the students would have liked more examples given in the presentation. Over half thought the topic had helped them to relate mathematics to the real world and had increased their interest in mathematics to some extent. About three quarters of the students thought discussing mathematics helped them to understand it better and increased their confidence in their own ability to do the subject. There was some evidence that students found that explaining mathematics to others improved their ability to do the subject. Over half agreed that presenting mathematics to people outside their class was a worthwhile experience but answering questions from outsiders about their work was not viewed in such a positive light. Although half the students felt they had performed well on the work set in the topic over the weeks, only 31.3% agreed that the experience had encouraged them to study mathematics at a higher educational level. Teacher responsesThe four teachers agreed that the mathematics presented was ‘quite easy’ for the students to understand and three were able to link it, to some extent, to work they had previously done with their students. They considered the number of examples given was right but three felt the language level was difficult. Three teachers also indicated that they did ‘a lot’ of group work in class and discussion took place frequently in all four of their classrooms. Two teachers found that their students were more able to tackle a new mathematics problem than they had expected. Two found that students appeared to be more confident since working in the project and that participation in classroom discussion had increased. Three of the four teachers agreed that their personal experience in the project had been positive.
Topic: Taking chancesQuestionnaires were received from 19 Year 8 students and three teachers. They came from the following schools: Elizabeth Garrett Anderson School and Sarah Bonnell in London, and from Pinelands High School and Grassy Park High School in Cape Town, South Africa. Student responsesMost (78.9%) students were able to relate the content of the topic to some of their past mathematical experience. About two thirds considered the level of difficulty about right while one third found the language used a bit difficult. Just over half (57.9%) thought the topic had increased their appreciation of the relevance of mathematics to the real world and almost three quarters indicated that sharing the experience with other students had increased their interest in mathematics to some extent. There was a strong indication of the value students placed on talk and discussion in helping them understand mathematics better and to a slightly lesser extent, on the way in which it increased their confidence in their own ability to do mathematics. Group work was considered beneficial with about two thirds indicating that it both changed their perception of themselves as learners and helped them to think about mathematics differently. Almost half (47.4%) strongly agreed that taking part in the project had made them feel more confident about their mathematical ability while about one fifth did not consider this to be the case. Most considered they had done progressively well in the topic over the weeks and over half (57.9%) strongly agreed that they now felt encouraged to study mathematics at a higher educational level. Teacher responsesThere was no agreement amongst teachers about the level of difficulty of this topic for their students but all three were able to link the topic to their mathematics scheme to some extent. Group work was done in all three classrooms and teachers indicated that discussion plays a large part in their mathematics lessons. There was some indication that teachers felt students who took part in the project were more ready to discuss mathematics and that their own perception of students’ ability had changed as a result of their students’ work during the project.
Topic: Mathematical surprises.Completed questionnaires were received from 35 Year 9 students from the following schools: St. Bernard’s, Herschel and The Westgate schools in Slough and John Kelly Girls’ Technology College, John Kelly Boys’ Technology College, Sarah Bonnell, Hampstead and Elizabeth Garrett Anderson schools in London. One teacher from each of the 8 schools also completed questionnaires. Student responsesWell over half the students could make links with the topic and 85.7% found the level of difficulty about right. Most thought the presentation was at the right level in terms of language (88.6%) and examples (74.3%) used. The topic increased an appreciation of the relevance of mathematics to the real world for a majority of students (60%) and over a third (37.1%) thought that sharing mathematics with others in the project had increased their interest in the subject. There was a clear indication that students felt that discussion increased their understanding of mathematics with 68.6% of them agreeing strongly that this was the case. There was also agreement that they thought both discussing and explaining mathematics increased their confidence in their own ability to do mathematics and that group work had changed their perceptions of themselves as learners of mathematics. Overall experience in the project had been positive with respect to presenting mathematics to others (in particular, answering live questions) and generally increasing their confidence in their own mathematical ability. More than three quarters felt they had done progressively well in the topic throughout their engagement in the project and that they had been encouraged by this experience to study mathematics at higher education level. Students’ comments added to questionnairesSeveral students added personal comments about their experience of the project at the end of their questionnaires, most of which were wholly positive. They describe it as a ‘good experience’ and mention that they ‘were made to think’. Several said that their self-confidence had improved. Another said that ‘overall the experience was great and really enjoyable’ but they thought, in some cases, too much time was given to solve some of the problems. In one case, the experience was described as ‘a challenging task’ and the result was that they felt more confident about mathematics. A criticism in one case was that it ‘would have been better if the schools had contacted each other’ about the tasks they were involved with and another said that ‘the problems should have been harder’. Finally, one said ‘I think the communication was brilliant and it was a very good experience.’ and that ‘this should increase mathematics and make it more enjoyable’. Teacher responsesTeachers were able to link the content of the topic to other classroom mathematics at least to some extent and most (5 of the 8 teachers) thought the content was easy for students to understand. All indicated that their students did group work in the classroom and that discussion plays a strong part in classroom work. Only 2 teachers agreed that their students appeared more confident as a result of working in the project and that student participation in class had increased. However, they all agreed that their own involvement in the project had been a positive experience.
InterviewsInterviews have been held with students from five schools: John Kelly Girls Technology College, Camden Sixth Form College, Woodhouse College, Sarah Bonnell School and Hampstead. Five open-ended questions (see below) were asked and a summary of responses is given here. Question 1. Tell me what you think has been the most worthwhile aspect for you of taking part in this project.Answers ranged from the change from ‘being told things’ by the teacher and being more actively involved in the learning process, to the benefits of making links with other subjects (science in particular). While the experience of carrying out independent research was seen to be valuable, some concern was expressed about putting the rest of their mathematics ‘on hold’ for awhile. Mixing with other schools was seen as a good experience and one person identified participating in the conferencing as ‘making me feel better about myself’ and another of their self-esteem being increased. Working in the project was seen to provide them with an accessible way of experiencing the sorts of things they would do if they chose to do mathematics at university level. One person expressed pride in being chosen to participate. One of the strongest feelings expressed was that the project had facilitated collaborative learning which involved them in developing enough confidence about some aspect of the subject to explain it to others. This approach was viewed as a welcome change from working through textbooks. The opportunities provided by the use of technology were also considered very worthwhile by some, especially involvement in the video-conferencing and presentation of their results. Some students had taught themselves how to use Power Point and now felt that they would be capable of making similar presentations in the future. Some also identified how worthwhile the input from Cambridge academics had been. Question 2. Do you think taking part in the project will have a long term effect on your attitude to learning mathematics?Participation in the project was seen as a ‘one off’ event in their mathematics education and they did not anticipate it would make much difference to their long term attitudes towards learning mathematics. However, they felt they were now more confident about their ability to take on challenges in mathematics and independent research and the nature of the tasks and topics covered made them realise the breadth of the kinds of mathematical content that exist. They suggested that they had been given too much time to complete the tasks they were set to do. Some students said the experience had strengthened their enthusiasm for mathematics and were impressed by the possibilities that were opened up when several minds were focused on one topic. The challenge of achieving the right balance between putting their findings across to an audience of other students who might not have the same level of understanding, and at the same time answering questions from academics, was a real challenge which they had enjoyed. The links forged between mathematics and science had an impact on their attitudes towards learning mathematics and in the long term it was integration of mathematics with other subjects that interested them the most. Question 3. Have you any ideas about how the approach to learning mathematics in the project may be more or less effective than everyday classroom teaching?They considered the approach made mathematics more ‘real’ and was more interesting than normal teaching. It was good for finding out how to learn independently and how to go about finding out about new things; it was seen to ‘push them a bit further’. It had helped them to develop their research skills. Some students identified the new challenges presented them as a result of using the technology involved in the project although they questioned whether it would be so effective across all mathematical topics. In some instances, the project had brought the class together even though not all had been involved in the video presentation. Question 4. Have you used the e-mail question and answer service built into the project?For one group of students, this part of the project was the least used although they recognised that it had potential. Not many had used the facility and some said they would have used it more if they had had a computer at home. Another group of students had all used the website extensively during their investigations although they did not e-mail questions directly to Cambridge because they preferred to use the Internet to find their own solutions. Question 5. What other kinds of transferable skills have you developed as a result of being involved in this project?The list of skills identified by the students included the following: technology skills; research skills; independent learning; organisational skills (especially time management); presentational skills; group working skills; communication skills (particularly verbal skills); confidence in their own ability; team work, self-esteem, the ability to work at university level, assertiveness and self-motivation.
General discussionThe students were generally very positive about the use of technology in learning mathematics. However, one group was a bit critical of the breakdowns that occurred in the initial session which appeared to frustrate them somewhat. They felt that technology should be exploited even further in teaching the subject. This group expressed some concern about the dullness of the setting for the conferencing and the image of mathematics that it projected. They suggested that presentations by the academics could be shorter. Students felt that contacts between schools need to be encouraged more in order to obtain maximum benefit from their participation in the project.
ConclusionsThe following general conclusions may be drawn from the evaluation as a whole: 1. Students have valued their participation in the project and in particular:
2. The topics chosen have, on the whole, been presented at a level that is accessible to the students and appear to have captured their interest.
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