### Article: Ball, Thames, Phelps

Ball, Thames, Phelps: Content Knowledge for Teaching - What Makes It Special?

What I particularly like about this article, is how convincingly it shows that there exists some "special" mathematical knowledge that teachers have (and need) that other professions do not. In discussions about teacher education, people often say that mathematics teachers need to know "the mathematics" and they need to now pedagogy, and often "the mathematics" is thought of as the same mathematics as their pupils are to learn, only more.

The authors gives the example that many professions need to be able to subtract two numbers, and some professions need to be able to check a subtraction to see if the answer is correct. However, only teachers need to be able to see or investigate whether the method used is valid in general or to pinpoint the error in the algorithm.

This is *not* pedagogical content knowledge, because this is not, in itself, concerned with students or learning. It is pure mathematics, but mathematics of a different kind than what is normally taught in universities. In addition to this (which the authors call "specialized content knowledge") comes pedagogical content knowledge, which is concerned with students and learning - for instance knowledge of which typical misconceptions students may have, knowledge of different ways of representing a certain mathematical idea, knowledge of how to choose examples that provide exactly the right progression etc.

I think the concepts "common content knowledge", "specialized content knowledge" and "pedagogical content knowledge" will be useful in further discussions on what we should teach in our teacher education courses.

What I particularly like about this article, is how convincingly it shows that there exists some "special" mathematical knowledge that teachers have (and need) that other professions do not. In discussions about teacher education, people often say that mathematics teachers need to know "the mathematics" and they need to now pedagogy, and often "the mathematics" is thought of as the same mathematics as their pupils are to learn, only more.

The authors gives the example that many professions need to be able to subtract two numbers, and some professions need to be able to check a subtraction to see if the answer is correct. However, only teachers need to be able to see or investigate whether the method used is valid in general or to pinpoint the error in the algorithm.

This is *not* pedagogical content knowledge, because this is not, in itself, concerned with students or learning. It is pure mathematics, but mathematics of a different kind than what is normally taught in universities. In addition to this (which the authors call "specialized content knowledge") comes pedagogical content knowledge, which is concerned with students and learning - for instance knowledge of which typical misconceptions students may have, knowledge of different ways of representing a certain mathematical idea, knowledge of how to choose examples that provide exactly the right progression etc.

I think the concepts "common content knowledge", "specialized content knowledge" and "pedagogical content knowledge" will be useful in further discussions on what we should teach in our teacher education courses.

Labels: knowledge, mathematics, teacher education

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