The development of prospective teachers ideas in designing lesson plans in Mathematics

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1 Paper *** (oral presentation) Main theme: Technology / Technology Based Educational Systems Secondary theme: teachers education The development of prospective teachers ideas in designing lesson plans in Mathematics Charalampos Lemonidis, University of West Macedonia, Greece. lemonidi@auth.gr and Euterpe Theodorou, University of West Macedonia, Greece. efterpith@yahoo.gr Abstract This paper presents the effect of an experimental intervention in prospective teachers education, concerning lesson planning in math. A digital laboratory was used to enrich student teachers background knowledge with examples of experiencebased lessons. The results indicated that there are changes in students who participated in this experimental teaching regarding their ability to plan an experienced based lesson. 1. Introduction There is a debate about the education of prospective primary school teachers and many researches have been conducted about the issue. (Ball, 1993 Fennema et al., 1996 Lampert & Ball, 1998). Students initially have their own teachers at school as models of teaching and this previous experience is been seen as an obstacle they should overcome in order to be then able to develop their own effective practices (Masingila and Doerr, 2002). Moreover, student teachers are usually expected to develop teaching skills in conventional ways like attending lectures and studying textbooks. These kinds of activities, however, promote abstract, academic and theoretical analyses, often far from the activities that actually happen in a classroom (Herrington et al., 1998, Lemonidis et al., 2003) where the student -now as well as in the future- will face a variety of pedagogic, teaching and learning issues. In the laboratory of the didactics of Mathematics in University of West Macedonia we hold the belief that mathematics instruction should be connected to everyday life situations and pupils experience. In accordance with this belief we think that prospective primary school teachers of Mathematics, apart from gaining the knowledge of mathematical concepts should practice in finding such a context of everyday life situations where these concepts apply. The prospective teachers do not initially know these everyday life situations and appropriate examples that will lead to the concepts, through decontextualization, and therefore a special training on this skill is needed. We developed a digital laboratory, using new information technologies, to offer the student teachers the opportunity to practice in mathematics teaching. In this laboratory we present examples of lessons and a variety of everyday life contexts where mathematical concepts lie. The prospective teachers, practicing in this

2 laboratory, enrich their experience and meet many new ideas about life situations connected with mathematics. In this paper we present the development process of 35 student teachers that practiced in designing a lesson plan during academic year , using our digital laboratory. 2. Research method The participants in our research 35 students in the last two years (university course lasts 4 years) participated in our research. 10 students (28,5%) had never planned and carried out a lesson while the rest 25 (71,5%) had already planned lessons and projects and had taught experimentally in schools the previous year. Stages of the research Students were divided in groups of 4-5 people. Their assignment was to create a lesson plan for the 3 rd grade of primary school. They chose one of the two proposed subjects: 1 a lesson about multidigit numbers. 2. A lesson about multiplication tables. 1 st stage: group work without any intervention. Students worked in this stage for two weeks. Without any intervention at first the students were asked to create and write down their lesson plans. They planned their lesson and hand them over. They presented their work to their classmates and the whole class discussed about each plan. 2 nd stage: practice in digital laboratory Students practiced then for two weeks in our digital laboratory using the university s computer laboratory. They studied lots of applications of the subjects they were working on in everyday life, as well as examples of lessons that promote learning based on experience. 3 rd stage: reviewing lesson plans. Questionnaire After digital laboratory practicing students were asked to improve their original lesson plans and to re-organize them. These lesson plans were once again presented in class and commented. Finally the students answered a questionnaire, where they reflected on the process and made remarks and comments on their experience of changing during this experiment. 3. Results 3.1 students views about the experimental process and difficulties they encounter. Generally speaking, students claim that they think that the way they practiced was good. In a 5 grade Likert scale (very good (5), good (4), indifferently (3), bad (2),

3 very bad (1)) 17% of students answered 5 very good, 71,5% good and 11,5% so and so. (Mean 4,05) Moreover they said that designing these lessons was useful. In a 5 grade scale (very useful (5), useful (4), indifferent (3), not so useful (2), not useful at all (1)) mean is 4,22. As far as the difficulties they faced in designing the lessons are concerned, students generally claim that they found it quite difficult. In a 5 grade scale (very easy (5), easy (4), moderate (3), difficult (2), very difficult (1) Mean is 2,74. The difficulties they came across when they worked on the lessons seem to be the following: Quite a lot of students (28,5%) mention that they had trouble to choose or to create the appropriate activities or exercises to include in their lesson. Many students (25,5%) also said that their difficulty was that they didn t know the cognitive background of third graders and they ways children at this age understand things. A student wrote: What I found particularly difficult was that we had to keep in mind students ideas, their ability to understand things and organize our lesson in accordance with these Another area a large number of students (31,5%) had difficulties in was to find the right order of activities, the connection between them and generally to organize a lesson in stages following a reasonable structure and to pick activities in accordance to the lesson objectives Two students wrote: What I found particularly difficult was to organize ideas in an order that would be appropriate for lesson objectives, rejecting ideas that seemed good to me but were inappropriate for students needs and needs of the lesson. What I found particularly difficult was to decide which idea to follow and how this would serve lesson objectives and would lead to these objectives. I mean, a complete design in accordance with the objectives It is also interesting that some students (17%) mention group working as the main difficulty in designing their lessons. Most of them said that the actual difficulty was to find time for meetings that was convenient to every member of the group. There are some of them, however, that said that opposing views of group members caused problems. It s worthwhile mentioning that a student strongly denied to work in a group and insisted on working on her own. 3.2 changes that students identified in themselves. Students were asked if their views about lesson planning changed after having practiced in the digital laboratory and having got feedback from their classmates. They stated that, generally speaking, their views changed. 57% of students said that they changed a lot, 20% that they changed quite a lot, 17% that they changed a little and only 5,5, % said that they didn t change at all. More precise questions were posed in order for us to understand certain aspects of the change mentioned by the students. The aspects were the following: - Ideas about everyday life context where mathematics occur.

4 - The selection (among the variety of ideas) of the suitable examples for teaching. - Teaching methodology. - The organization of a lesson plan. Students seem to believe that after practicing they have changed a lot or fairly regarding the ideas about everyday life context where mathematics occur. 5,5% of them stated that they changed totally, 54,5% that they changed a lot, 14,5% that they changed fairly, 20% a little and finally 5,5% not at all. A student that says she have changed a lot wrote: "As a student, I thought that mathematics was something far away from everyday life. I considered math - as the teachers in the school did merely as a school subject. After practicing in this course I understood that mathematics exists everywhere in our life and that by using examples from everyday life, children s stress is restricted and learning as a natural not a formal process is promoted.» Concerning the choice of suitable examples for teaching among the wide range of ideas, the majority of students claims that they have changed a lot or fairly. In particular 3% of students mentioned that they changed totally, 54,5% that they changed a lot, the 28,5% that they changed fairly, 8,5% that they changed a little and finally 5,5% said that they have not changed at all. " A lot of ideas about the subject of the lesson I had to teach existed in my mind. However, after this course, where the advantages and disadvantages of each idea had been clarified we managed to select the suitable context to the age and children s preexisting knowledge.» The answers about the changes that occurred in methodological approach varied. The majority believes that there were changes. (5,5% of students claimed that they totally changed, 43% that they changed a lot and 25,5% that they changed fairly). There also a few students who stated they changed a little or not at all. (8,5% of students stated that they changed a little and 17% not at all). It is worth noting that the majority of students already have some kind of teaching experience. Thus they are able to follow a teaching methodology or to distinguish it. That s what a student who stated that she fairly changed: I had already known about the effective social and education results of group work teaching. Because of my inexperience, I was uncertain about implementing this method in classroom. After teaching math during this course in this way I decided to use this method for other lessons two. By practicing during this course, I succeeded in interrelating theory and practice. The majority of students stated that their views about lesson organization also changed. More precisely 11,5% of students stated that they changed totally, 37% that they changed a lot, 25,5% that they changed fairly, 20% a little and 5,5% not at all. Some students mention that they realized that lessons should be based on pupils pre-existing knowledge or that an introductive activity based on experience is of great importance. Two students stated:

5 It s very important for a lesson plan to be based on pupils pre-existing knowledge and to begin with this knowledge. Now I am able to use contexts from everyday life. To approach an issue interdisciplinary and to set clear objectives. 3.3 pupils attitudes regarding math and math teaching The students were asked if they liked Mathematics when they were attending school. In a 5grade scale they answered the following: 28,5% very much (5), 28,5% fairly (4), 28,5% so and so (3), 11,5% little (2), 3% not at all (1). (Mean 3,68). This shows that in general the students we examined liked math when they were pupils. In our question if they like Mathematics now that they are preparing to become teachers they also answered positively. In a 5grade scale they answered the following: 17% very much (5), 48,5% fairly (4), 34,5% so and so (3). (Mean 3,82). The crosscorrelation of answers in these two questions shows that there isn t statistic cohesion between them (X 2 =0,38, p>0,537, Φ=0,1). There are 17% of students that liked mathematics as pupils but now they don t like it anymore. 25,5% of them, on the other side, didn t like mathematics as pupils but they do like it now. Therefore one can claim that student teachers may have a different attitude towards math when at school and when at university. The students were asked to write three subjects (in order of preference) they think they would like more to teach at school. 54,3% of students includes Mathematics among the three first courses they would prefer to teach. Only 5,5% of students place mathematics as the most preferred subject, 23% as the second and 25,5% as the third. Even if they claim that they like math they do not seem to be that keen on teaching it. We compared the answers in the questions: if they like Mathematics now that are preparing to become teachers and if Mathematics are one of two subjects they would like to teach more. We found that the answers in these questions have statistical cohesion (Χ 2 =7,3, p<0,007, φ=0,457). It seems that those who like mathematics are keener on teaching it and those who don t like math do not prefer to teach maths as well. 4. Conclusion After an experimental practice in the digital laboratory, which was created to teach students better, students in general, judged this process as good and useful. However they thought it was quite difficult. Tasks they found particularly difficult were: creating their own activities and exercises, lack of knowledge about the cognitive level of children, connecting lesson objectives with the activities and generally deciding on a certain sequence of activities when planning a lesson. The majority of students stated that their ideas changed after the experimental intervention. They changed regarding using everyday life contexts for teaching mathematics, the choice of suitable examples among many contexts, teaching methodology and the organization of a lesson plan.

6 The majority of students we examined said that they liked mathematics when at school as well as now in the university. It seems however that students who liked mathematics when at school, may not still like it during their preparation as schoolteachers and vise versa. Even if students said that they generally like mathematics, only 54,3% of them mention math as one of three preferred-to-teach school subjects Of course it is noticeable that those who like teaching mathematics are those who also like it as a subject. 5. References Ball, D.L. (1993). Halves, pieces, and twoths: constructing representational contexts in teaching fractions. In Carpender T., Fennema E., & Romberg T. Rational numbers: An integration of research (pp ). Hillsdale, MJ:Erlbaum. Herrington, A, Herrington, J., Sparrow, L. & Oliver, R. (1998). Learning to teach and assess mathematics using multimedia: A teacher development project. Journal of Mathematics Teacher Education, Vol. 1, pp Fennema, L., Carpenter, T., Franke, M., Levi,M., Jacobs, V. & Empson,S. (1996). A longitudinal study of learning to use children s thinking in mathematics instruction. Journal for Research in Mathematics Education, Vol. 27, No. 4, pp Lampert, M. & Ball, D.L. (1998). Using hypermedia technology to support a new pedagogy of teacher education (ERIC No. ED ). Lemonidis Ch. (2005). Les mathématiques de la nature et de la vie: une conception pour l enseignement des mathématiques. Présentation d un exemple extrait de la formation des enseignants. Colloque COPIRELEM 30, 31- Mai, Strasbourg Lemonidis, Ch., Spanaka, A. Fahantidis, N., (2003). Postgraduate students handle teaching objectives through a multimedia application. 6th Pan-Hellenic Congress of Didactics of Mathematics and Information technology in the Education. November 2003, Volos. (In Greek) Masingila, J. & Doerr, H. (2002). Understanding pre-service teachers emerging practices through their analyses of a multimedia case study of practice. Journal of Mathematics Teacher Education, Vol. 5, pp