Insegel till dialog. Skolans matematikutbildning – en studie i fyra praktiker

Mathematics education in Swedish schools is the subject of constant debate which seeks to improve and change school practice. This is, however, often undertaken without sufficient attention to or understanding of the practices that shape mathematics education on a daily basis. The purpose of this thesis is to reach a better understanding of how school mathematics education is formed by examining four different practices; the curriculum developer’s, the mathematician’s, the teacher’s and the school principal’s. The investigation involves formulating knowledge ‐ often tacit and unformulated – developed in the four practices, three of which make up my own professional experience. The work is grounded in the epistemological claim that practical knowledge denotes an unique species of knowing which cannot, without further ado, be reduced to applied theory, but must be developed and communicated in its own way. The work is also based on an insight drawn from discussions in the philosophy of language perspective; namely, that it is through our actions that language receives its meaning, and that even theoretically formulated knowledge is constituted by the unsaid as much as by the said. The Dialogue Seminar Method, developed at KTH Royal Institute of Technology in the subject of Skill and Technology, has been used, with the help of the philosophy of science and art, to find a language to convey practical knowledge. The method has been used partly on my own professional experience, and partly on the professional experience of a group of school principals. Furthermore, the method has resulted in texts produced between 2004 and 2011. These texts have been interpreted in light of the phenomenological and hermeneutical traditions, in accordance with the tradition of the subject Studies of Professional Practice at the University of Nordland. In addition, an epistemological investigation has been made of the concept of knowledge that the Swedish school has been based on since 1994. The thesis provides three contributions. The first is a theoretical contribution where three shortcomings are highlighted in the concept of knowledge that the Swedish school rests on, where knowledge is seen as consisting of facts, understanding, skills and familiarity: i) tacit knowledge is not only found in familiarity but cuts across all four knowledge forms; ii) understanding is not only associated with facts but also with skills; iii) the language that understanding can be conveyed through is not only in terms of defined concepts, but also in the form of metaphors, analogies and stories. The second contribution is a portrayal of the four practices in the form of stories. The hermeneutical and phenomenological work on the stories provides the third contribution in the form of a deepened understanding of six phenomena that practitioners manage in their work life: i)0 problem and solution; ii) non‐existence, solitude and community; iii) concern about the unforeseen and human ignorance; iv) the relationship between school mathematics and usefulness; v) the curriculum ‐ text, interpretation and action; vi) reactions from pupils on their activities. The constitution of these phenomena is analysed and their mutual influence on each other is discussed, as well as how a view on knowledge that equates practical knowledge with applied theory affects the phenomena. The three contributions of the thesis show that it is a fundamentally practical knowledge to understand and use mathematics. This gives a different and deeper understanding of how mathematics education is formed than the one that dominates public debate. Based on the three contributions conclusions are drawn for the further development of mathematics education. Practical knowledge and its tacit elements in mathematics education exist and need to be addressed. The habit of discussing mathematics education in the form of problem and solution, where metaphorically this is seen as a puzzle to be solved, means that we are concentrating too much on trying to manage an unpredictable reality by predicting – because mathematics education can metaphorically also be regarded as a living being that is dependent on its heredity and environment, and on recurring natural needs. The thesis is a seal to enhance the quality and continuity of the dialogue we conduct on mathematics education, by making visible the complexity of knowledge, and our disagreements, thus going from many monologues to a genuine dialogue – from school for Bildung to the Bildung of the school.