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Pedagogical content knowledge is made up of several components. In this paper we concentrate on one of these: teachers' planned presentations of the subject-matter. We deal with two main sources of this component of pedagogical content knowledge: knowledge about the subject-matter and knowledge about students. Illustrations are given in two mathematical domains: functions and undefined mathematical operations. The paper concludes with a discussion of the nature of teachers' knowledge and the interconnections between the three constructs: subject-matter knowledge, knowledge about students, and knowledge about ways of presenting the subject-matter. S u b j e c t -m a t t e rEven though it is usually assumed that teachers' subject-matter knowledge and pedagogical content knowledge are interrelated there is little evidence

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In this paper we examine the possibility of differentiating between two types of nonexamples. The first type, intuitive nonexamples, consists of nonexamples which are intuitively accepted as such. That is, children immediately identify them as nonexamples. The second type, non-intuitive nonexamples, consists of nonexamples that bear a significant similarity to valid examples of the concept, and consequently are more often mistakenly identified as examples. We describe and discuss these notions and present a study regarding kindergarten children's grasp of nonexamples of triangles.