Mathematics Teachers and Their Conceptual Models - A New Field of Research

• Swedish mathematics teachers’ knowledge for conceptual teaching is the issue of the present study. Anglo-American research in this field shows that teachers lack this particular knowledge to a high degree. The aim was to study firstly, a number of mathematics teachers’ conceptual understanding, secondly, their knowledge of pupils’ conceptual understanding, thirdly, a number of their pupils’ conceptual understanding and fourthly, to try to develop a comprehensive theory of conceptual understanding for school mathematics. The fourteen interviewed teachers were selected by means of theoretical sampling in order to reach theoretical saturation. The data were transcribed and analysed within an extended Phenomenographic framework. By comparing the teachers’ own understanding with their knowledge of pupils’ understanding of the concepts of variable and proportionality, the variation consisted in two principally dissimilar patterns. Characteristic of the first pattern was that the teachers’ own understanding coincided with their knowledge of pupils’ understanding. Typical of the second pattern was that the teachers not only exposed mathematically qualitatively well-developed ways of understanding the concepts but also an awareness of pupils’ less developed ways of understanding. In order to compare teachers’ predictions of pupils’ understanding of the two concepts, variable and proportionality some of the teachers and a number of their pupils were interviewed altogether 15 persons. The teachers’ predictions displayed a high precision. It was shown that a decisive influence on the pupils’ ways of understanding the fraction concept was exerted by the conceptual models of vulgar fractions applied by the teachers in their instructional practice. It was possible to characterise each individuals’ conceptual understanding by taking the descriptive categories on group-level as a point of departure and by using each individual’s data. Whether or not a certain way of understanding will be exposed is determined by the powerfulness of the experiment problem. The results suggest that not all teachers have the necessary knowledge for conceptual teaching. Subsequently, the aim is reached. With few exceptions, the categories of conceptual understanding are in harmony with research. Since conceptual models were proved to influence pupils’ conceptual understanding, it would be fruitful to study how teachers apply the models in their teaching and how they are understood by pupils. Therefore, there are reasons for putting forward the role of conceptual models in school mathematics as a new field of research.

Ämnesord

SAMHÄLLSVETENSKAP  -- Utbildningsvetenskap -- Didaktik (hsv//swe)

SOCIAL SCIENCES  -- Educational Sciences -- Didactics (hsv//eng)

SAMHÄLLSVETENSKAP  -- Annan samhällsvetenskap -- Övrig annan samhällsvetenskap (hsv//swe)

SOCIAL SCIENCES  -- Other Social Sciences -- Other Social Sciences not elsewhere specified (hsv//eng)

Nyckelord

Conceptual teaching

Undersatnding Mathematics

Teacher Knowledge

Experiment Problems

Conceptual models

Education

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vet (ämneskategori)

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