PUBLIC CASE REPORT Use of the GeoGebra software at upper secondary school Linked to the pedagogical activity: Use of the GeoGebra software at upper secondary school Written by: Philippe Leclère, Cyrille Raymond, INPL, France On the 6 October 2010 1. General information 2 1.1. Project information 2 1.2. Background information about the school 3 1.3. Participating teachers 4 1.4. The pedagogical material 4 2. Documenting the activities 4 2.1. The tutoring process 4 2.1.1. Detailed summary 4 2.1.2. Similarities and differences between the proposed tutoring model and the process observed 6 2.2. Activities in class 6 2.2.1. Detailed summary 6 2.2.2. The similarities and differences compared to the example scenario proposed by the ET 8 3. Lessons learnt with a view to improving the materials and the tutoring model 8 3.1. Suggestions for using and improving the materials 8 3.2. Suggestions for applying and developing the tutoring model 9 3.3. Other suggestions and ideas 10 1
1. General information This report describes the organisation of ICT-related class work by a novice teacher who was willing to be helped by an experienced teacher in the field. 1.1. Project information The report has been produced within the framework of the FICTUP project, which involves four countries (Finland, France, Hungary and Italy). FICTUP s objective is to develop innovative training material describing specific pedagogical activities entailing the use of information and communication technologies (ICTs), combined with a closely-directed tutoring process, and to test the impact of both the material and personal support on teachers who are novices as far as ICTs are concerned. The training material devised for each case includes a report describing the activities in detail: the topic, the objectives, students outputs, the material required (software, worksheets to be completed by the students, etc.), the different pedagogical stages, and for each of these a description of the role of the teacher and the tasks of the students, etc. Each case report is accompanied by three short training videos. During the first year of the project, this training material was jointly designed and developed by a teacher experienced in using ICTs in teaching and another who had never taught using them, to ensure it could be easily used by others. During the second year, the material was tested in the classroom by a teacher who was a novice as far as ICTs were concerned. She was tutored by the expert teacher who had designed the material. This phase was observed (and filmed), analysed and evaluated by the partner researchers. The ultimate objective is to draw on the experience of the project in order to adapt and improve the training methodology tested (organisation of the tutoring, specifications for the content of the training material, etc.) and to offer it for future use in educational institutions. Each country s researchers had the following material for each case: - the report on the pedagogical sequence and the three related videos; - reports (notes and/or videos) on the meetings between the expert teacher and the novice teacher during the tutoring process (the two meetings prior to the experiment, and the meetings between the expert and the novice between each session); - the answers to a short questionnaire given to the novice teacher before and after each class, asking her what she felt about the session and what she planned to do in the next one; - the video recordings and/or observations of the researchers for at least three class sessions; - the novice teacher s activity book; 2
- the final review meetings with the novice and expert teachers following the experiment; - evaluation reports for materials that have been subject the interim evaluation by other teachers and trainers. 1.2. Background information about the school The report and the videos were produced and tested the previous year by the experienced teacher (ET) in his class in the same school and classroom. The software used for the activities was the same (GeoGebra). Please refer to the report for further details about these aspects. The Lycée Varoquaux is an upper secondary school in one of the eastern suburbs of Nancy (greater urban area population: 300,000). The school website (http://www.ac-nancymetz.fr/pres-etab/varoq/accueil.htm) states that it was established 35 years ago and currently has about 1,680 students and trainees on continuing education courses, of whom 250 are accommodated on site. The Lycée offers the range of General Baccalaureate courses as well as management, health, social work and laboratory technology courses. 11 Baccalaureate courses are offered in all. Two-year post-baccalaureate courses are offered in advanced technical subjects. The Lycée has a well-established ICT culture. It is relatively well-equipped, and an increasing number of teachers use ICTs on a regular basis. Teachers have been consulted in order to improve equipment and organise the layout of the IT Room. The overall approach is to try to make the set-up as effective as possible. 3
1.3. Participating teachers The experienced teacher (ET) has been an agrégé mathematics teacher. He has been teaching for 12 years (6 years in lower and 6 years in upper secondary school). This was the first time he had supervised a trainee teacher on practical training. He is acknowledged as an accomplished user of ICTs and their applications in class and regularly participates in staff development courses. The novice teacher (NT) is 22 years old. She is a trainee teacher and has passed the CAPES secondary school teaching theory exam. She is doing practical training during which she is in charge of a class from the beginning of the school year. She has been doing real teaching for seven months. She has a good knowledge of IT, which she has been using for 12 years. She started using it in class four months ago but was unfamiliar with the GeoGebra software. 1.4. The pedagogical material The material given to the NT comprised the report written by the ET giving a detailed description of the pedagogical activities he had already organised in class. There were three videos illustrating ICT skills at a technical and a pedagogical level, which were deemed useful for this pedagogical activity: - one video examined the benefits of using the geometry software. This consisted in giving an overview of the GeoGebra, its specific characteristics and some examples of its pedagogical use in class. It was a fairly technical presentation of the software with some simple applications giving an insight into the general approach (MicroWorlds); - another one showed how the teacher structured work in the IT Room by alternating students individual work with collective work. It offered a pedagogical model tailored for sessions entailing work with ICTs; - the third video presented some examples of ICT use with a video projector in a room with no computer, to respond to specific and occasional needs. The purpose was to demonstrate the use of ICTs in a traditional classroom situation. 2. Documenting the activities 2.1. The tutoring process 2.1.1. Detailed summary 4
The tutoring/support of the NT by the ET took place as follows. The NT was given the pedagogical material (the report and three videos), and then met the ET twice before implementing her own sequence in class. After each session, the ET and the NT systematically had a face-to-face meeting to discuss it and prepare the next one. The ET attended all of the sessions organised by the NT. He sometimes intervened during the sessions in order to join in with the students activities. In no circumstances was this to make up for any shortcomings in the NT s work, as he felt the classes were very well run. The purpose was to offer an additional pedagogical input. Type of activity Date Duration Location Participants Remarks Examination of the pedagogical material 20 March 2:50 At home EN The case study and the three videos Design of plan for the sequence and the 1st activity 21/22 March 1:45 At home NT None Meeting 1 22 March 0:50 At the Lycée NT, ET Discussions on the material and the use of ICTs in class in Detailed design of the 1st activity, send to ET 25 March 2:50 At home NT None Formatting/correction of the 1st activity and design of 27 March the following sessions 3:10 At home NT None Meeting 2 29 March 0:50 At the Lycée NT, ET Some days before the start of the pedagogical sequence, the NT presents the pedagogical structure she is proposing by outlining the first session in detail. The ET asks her to explain certain points and puts it into the context of the example Final correction of the first activity 6 April 1:45 At home NT None Pre-session questionnaire 6 April 0:15 At the Lycée NT Just before the session is organised Organisation of session 1 6 April 0:55 At the Lycée NT, ET With the ET attending Post-session and pre-session 2 questionnaire 19 April 1:10 At home NT By email Final correction of the 2nd activity, send to ET 25 April 0:40 At home NT By email Meeting with ET 27 April 0:40 At the Lycée NT, ET Just before the session is organised Organisation of session 2 27 April 0:55 At the Lycée NT, ET Post session 2 and pre-session 3 questionnaire 28 April 1:00 At home NT By email Final correction of 3rd activity, send to ET 28 April 1:35 At home NT None Meeting, discussion with the tutor 4 May 0:40 At the Lycée NT, ET Just before the session is organised Organisation of session 3 4 May 0:50 At the Lycée NT, ET Post-session 3 and pre-session 4 questionnaire 6 May 1:00 At home NT None Design of the 4th activity, correction, send to ET 8 May 1:55 At home NT None Meeting with ET 11 May 0:30 Au lycée NT, ET None Organisation session 4 11 May 0:55 Au lycée NT, ET Post-session 4 questionnaire 12 May 1:00 At home NT None Interviews 18 June 1:00 At the Lycée NT With the ET attending Total hours spent by the NT NT 29:00 At the Lycée 08:20 Total hours spent by the NT with the ET ET 07:05 At home 20:40 Total hours spent by the NT on her own NT alone 21:55 5
The time spent by the NT (29 hours in total for four hours of lessons) is much higher than a teacher should spend (about 10 hours). This is evidently due to the experimental nature of the project and the additional work given to the NT, in particular on writing up her activity book and on analysing the existing material. The discussion hours correspond to the cost in terms of the number of hours (about seven) the ET was present. We have not calculated the time the ET spent looking at the NT s proposed sessions and preparing the meetings (six in total). 2.1.2. Similarities and differences between the proposed tutoring model and the process observed The tutoring developed fully complied with the model that had been approved by the project researchers. All of the optional suggestions were taken up, in particular concerning the ET s attendance at all sessions organised by the NT and the meetings before and after each lesson. 2.2. Activities in class 2.2.1. Detailed summary Subject(s) Class level Duration of the sequence Name Official website Tool type Objectives of the teacher Pedagogical sequence/unit Mathematics Upper secondary school, the second form (15-16 yearolds) 4 one-hour sessions spread out over a month ICT tool(s) Geogebra, open source cross-platform software http://www.geogebra.org MicroWorlds software http://en.wikipedia.org/wiki/microworlds Description of the sequence/unit - To introduce the students to the GeoGebra geometry MicroWorlds software; - To use the software and its dynamic functions for resolving open problems: conjecture, demonstration or just verification of a proposition; - To help students become autonomous. 6
Session 1 The aim was to introduce students to the GeoGebra software using simple mathematical concepts. The first exercise was to construct a rhombus and the second exercise was to formulate a conjecture on the alignment of three points using the dynamic attributes of the software. After the instructions had been read out and it had been checked that they had been understood, the students attempted to find the solution on the computer (one student per terminal) and gave their answers to the questions on a worksheet. The answers were then pooled together on the teacher s computer, which was connected to the video projector. The students then did the second exercise in the same way. At the end of the session, the students and the teacher wrote up the explanation requested. Description of the phases of the sequence Session 2 The aim was to formulate a conjecture using the software in order to answer a question on the topic of the exercise. As for each session, the teacher checked the instructions had been fully understood. The aim was to find out how to maximise the area of a triangle. The students formulated a conjecture on a computer (one per terminal) and gave their answers to the questions on a worksheet. One student worked on the teacher s computer with the video projector turned off. After a discussion and demonstration on the teacher s computer, the students sought a consensus that was then validated by the teacher. This method was adapted for the second part of the exercise. The fastest students were asked to demonstrate the results found for the previous question. Session 3 The aim was to use GeoGebra to formulate conjectures, construct a dynamic figure and solve an open problem (first part) and a directed problem (second part). The approach used was the same as for the first two sessions. The students had to find the shortest path for a farmer s wife carrying water taken from the river to the furthest stable in the farm. The second part entailed the construction of an algebraic model of the problem and thus helped to update knowledge about functions and curves. Session 4 7
The aim of this module was to identify the link between the representative curves of the square function and of a polynomial function of the second degree. The GeoGebra software was used at the beginning as a drawing tool (to do the line of a curve). The session was closely directed. It ended with several questions seeking to establish links between algebraic modelling (parameters) and drawing, and with a demonstration that students would finish writing up at home. 2.2.2. The similarities and differences compared to the example scenario proposed by the ET The sequence proposed by the NT followed a very similar course to the one outlined in the EE s case study. The intent to help students become autonomous and the means of achieving this are the same. The sequence of steps in each session was practically the same: - reading out the instructions; - reformulation of these instructions by the students to ensure that everything has been fully understood; - conjecture using the tool; - joint summing up session. GeoGebra is alternatively used as a drawing tool and as a means of formulating conjectures. The ET s report also clearly helped the NT to understand how to pace an ICT session. She adopted the same method for organising the session, alternating individual work or conjecture, rather with collaborative work, making it possible to exchange ideas and embed knowledge. However, the NT completely changed the activities and used her own exercises. 3. Lessons learnt with a view to improving the materials and the tutoring model 3.1. Suggestions for using and improving the materials With this case, the pedagogical material was mainly used in the preparatory phase. It would thus be interesting to have the pedagogical activity report list the key points the NT should pay particular attention to in order to anticipate any problems that might arise in class. This 8
may concern pedagogical aspects (problems that are too hard to solve, the need to reduce students degree of freedom, etc.), technical aspects (having a reserve plan if things go wrong) or the pedagogical use of ICT (its relevance). On this point, the systematic explanation of the added value of using ICT in each activity would help to counter some teachers reluctance to use them. It would also be useful to systematically append the activity documents (instructions, students worksheets, etc) to the case report. 3.2. Suggestions for applying and developing the tutoring model Preparatory meetings and the meetings between sessions As we have already mentioned, the preparatory sessions and the meetings between each lesson have played a major role in ensuring the success of the tutoring process. They enabled the NT to anticipate potential problems and, with help from the ET, pinpoint difficulties encountered and obtain advice in order to improve organisation in class. These meetings could be shorter but organised closer to the lessons to facilitate evaluation when things are fresh. Class activities organised close together As far as the scheduling of sessions is concerned, the ET recommended that a tutoring process like this should entail two to three sessions following on from one another (one per week). Support in class The ET presence at the end of the ICT sessions was reassuring. It also enabled the ET to identify some problems that the NT had not necessarily seen as she had been taken up managing the students. If the ET cannot attend the first sessions, it might be a good idea to film the entire activity in class if possible. The video would indirectly permit the ET to see what went on in class and permit a joint analysis with the NT, drawing on comparisons with his own practices. To conclude, support in class can vary widely, from joint management of the class for one or two sessions to just attendance. Varied degrees of tutoring The two teachers recommend that the ET s support (including both meetings between sessions and attendance in class) can vary. As the sessions progress, and as the NT becomes more at ease in session preparation and class management, the ET could adopt a lower 9
profile and only be available at the request of the NT. On the other hand, it would be good for the ET to observe one of the NT s ICT sessions, for example one month afterwards. In our study, the ET s presence proved to be less useful after the second session in class. To conclude, the length of support cannot be determined in advance and it depends on the degree to which the NT becomes autonomous. At the end of the period of intensive tutoring, the ET is advised to organise one or several visits to the NT s class at suitable intervals. An original activity: a lesson taught in parallel by the NT and the ET The NT in the ET could each develop an identical pedagogical activity created by the NT and then conduct a joint evaluation of the problems they each encountered, their different pedagogical approaches, etc. (this was a suggestion made by the NT). This stage could be integrated into the tutoring process so that the ET is a little less passive, or be added as a third stage, in other words as an extension of the experimental process. At the end of the process, the ET would provide the NT with some new examples of ICT usage in class for the latter s future activities. 3.3. Other suggestions and ideas A technical support person In order to address the NT s technical concerns, a support person could be identified in school, during and even after the tutoring process. This person would be available if any technical problems arise in class. Their presence would aim to help reassure the NT. A teaching support person After the tutoring process, it might be interesting for each school to have a teaching support person who is an expert in the use of ICTs in class. This person would for example have some flexible teaching hours allocated to this task every week. Their role would be to support teachers in the school in using ICT. The support would be of a more occasional nature than the tutoring tested here, but it would nevertheless help to respond to specific and very detailed queries from the teaching staff. 10