By Helle Alrø
Discussion and studying in arithmetic schooling is anxious with conversation in arithmetic class-rooms. In a sequence of empirical reports of venture paintings, we stick to scholars' inquiry cooperation in addition to scholars' obstructions to inquiry cooperation. either are thought of very important for a concept of studying arithmetic. targeted awareness is paid to the notions of `dialogue' and `critique'. A important thought is that `dialogue' helps `critical studying of mathematics'. The hyperlink among discussion and critique is built additional via together with the notions of `intention' and `reflection'. therefore a thought of studying arithmetic is constructed that's resonant with serious arithmetic schooling.
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Extra resources for Dialogue and Learning in Mathematics Education: Intention, Reflection, Critique (Mathematics Education Library)
To show which numbers he has already used in the calculation] Tim: This is just as easy. Teacher: It isn’t always just a question of easiness. (8) Teacher: The first condition for calculating correctly is that you put it down correctly. (9) Teacher: If they made the exercise, they are the ones to decide whether it is right, aren’t they? In (7) the teacher wants a different marking of the numbers used by the student in an exercise. The student writes his proposal on the blackboard. He argues that his marking method is quite as easy, which is indirectly rejected by the teacher.
We conceive zooming-in as an interesting phenomenon that reveals structures of the actual classroom practice. It also provides elements to a discussion about the nature of learning activities. Zooming-in is not a common phenomenon. We can mention two factors that tend to eliminate a zooming-in. First, the classroom can be organised in a way that makes it clear what all tasks are about. 33 These two factors can be combined in the traditional mathematics classroom: The teacher explains the new topic, the teacher introduces which exercises to do next, the students do the exercises, and the teacher ‘ticks’ the results.
COMMUNICATION IN THE MATHEMATICS CLASSROOM Thomas: Malene: 41 page like this [Malene gets the newspaper], can’t you see? It is not at all like this, can’t you see? Right. Then we cannot measure it, can we, because they are not the same. 32 She argues and explains, but she also gives out orders: “Then fetch the newspaper,” she disciplines: “listen will you” and she asks questions, which she (partly) knows the answers to: “Which one was it we had a moment ago? ” Thus, the teacher is invisibly present in the communication, and Malene is his advocate.