The paper reports on the qualitative results of the experimental phase of a study to examine the links between children's learning experiences associated with two digit division and the transactional analysis concept of drivers. The author presents results obtained from a process that used a questionnaire developed during a prior heuristic phase of research, combined with undergraduate student observations of the children, drawings produced by the children, and teacher observations on permission transactions used. Examples are provided for each of the five drivers. KeywordsMathematical learning environment; procedures for calculation of two digit division; drivers; permission transactions Study ObjectivesThe aims of the research were to: investigate how different mathematical calculation procedures for two digit division, with increasing levels of difficulty, might activate drivers (Kahler 1975) with different levels of intensity; to explore the impact on the children's learning results of permission transactions (1966) used by teachers. The Research ContextThis paper reports on one part of a research process that has been developed over a period of about 7 years and will conclude in 2010. The heuristic phase ran from 2003 -2005 and involved development of a questionnaire, originating with one devised by Klein (1984), and including pictures and a structured interview guide, plus a grid and associated training in direct observation of driver behaviour. In the heuristic phase, four 4 th year Primary school classes (98 children) and two 3 rd year Primary school classes (46 children) were involved.The Experimental Phase, which is the focus for this paper, ran from 2005 to 2007. During this phase, experiments were carried out according to the following procedures: 1.Administering evaluation entry tests. 2.Administering driver questionnaires 3.Starting up the didactic interventions, which included 5 activities in sequence; these were courses in class and study of drivers in action by means of the observation grid for: division with successive subtraction; division with the repeated addition method; division with the traditional method; division with simplified traditional method; division with traditional method. 4.Administration of final examinations and production by each child of a drawing of themselves during the test. 5.Organisation of recordings and observations in order to indentify suitable describers and relations between the data.In the experimental phase, four 4 th year primary school classes were involved with a total of 93 children.The Diffusion phase is now running from 2008 to 2010 and relates to the presentation of the first qualitative results and diffusion of the research. The theoretical backgroundWe may consider predominantly the structural characteristics of mathematics learning such as the processes of 1 (1), [30][31][32][33][34][35][36][37][38][39]
Life-long learning is an increasingly relevant need of our time. Educational perspectives currently tend to focus - beside the single subjects (Foreign Languages, Maths, History) - on how, while learning, you can learn to learn. Considering this perspective, we have been integrating Transactional Analysis in the training for future Primary School Teachers. Our objectives are both more traditional applications intended to improve the relationship between teachers and teachers, teachers and families, and to observe, study and intervene in the relationship which children create with their learning process. The writing on emotional drivers, which we presented on IJTAR – International Journal of TA Research - for didactics of Mathematics, has proved very helpful for other subjects and in learning how to learn. Our experimentation involved 10 classes of a primary school, and enabled us to create several tools (interviews to identify drivers, egogram interview, check lists for the observation of transactions during the lessons). The learning outcomes have been analysed by the teachers according to some against indicators of learning and didactic objectives established within a systematic frame of reference. This model for didactics in TA clearly contributes to the construction of a learning environment, enhancing both the expression of the Free Child and Self-efficacy.
This chapter introduces the transcoding pattern, used in simulation games, to organize the language, the setting and the learning environment, defining the course of learning on various levels of abstraction. The aim is to facilitate the construction of a language that can be used in the processes of the mathematicization of reality and in math teaching in general. In order to give the reader a better understanding of the ideas and components of this process, an example of the transcoding pattern is provided before going on to describe the objective of our research the simulation game.
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