### Article: Lee S. Shulman

For some reason, I haven't read anything by Lee Shulman before reading his short 1985 article "Those Who Understand: Knowledge Growth in Teaching" today. This does not mean that his thoughts haven't influenced me, however - last year I even wrote a short paper (for a course I'm taking) partly based on some of the ideas.

The main point in this article is perhaps distinguishing "among three categories of content knowledge":

(a) subject matter content knowledge

(b) pedagogical content knowledge

(c) curricular knowledge

There is a tension even in the Norwegian mathematics education field between people focussing on the mathematics and other focussing on the pedagogy. Shulman's categories introduced more nuances into that discussion.

An example of "pedagogical content knowledge" that I teach in my courses in mathematics in teacher education is students' typical misconceptions and how to overcome them. Another example is which bits of history of mathematics are useful to motivate students in particular parts of the curriculum. Examples of particular methods of teaching should also be included here.

"Curricular knowledge" includes both knowledge of different materials available (including digitally) and when they can usefully be used. Knowledge of what goes on in other subjects in the same grade or in mathematics in other grades are also included.

These three categories will probably prove to be useful for forming the discussions we will have now that the curriculum (in teacher education) will be changed again.

Shulman's article is written as an answer to George Bernard Shaw's "He who can, does. He who cannot, teaches." Shulman's version is: "Those who can, do. Those who understand, teach."

The main point in this article is perhaps distinguishing "among three categories of content knowledge":

(a) subject matter content knowledge

(b) pedagogical content knowledge

(c) curricular knowledge

There is a tension even in the Norwegian mathematics education field between people focussing on the mathematics and other focussing on the pedagogy. Shulman's categories introduced more nuances into that discussion.

An example of "pedagogical content knowledge" that I teach in my courses in mathematics in teacher education is students' typical misconceptions and how to overcome them. Another example is which bits of history of mathematics are useful to motivate students in particular parts of the curriculum. Examples of particular methods of teaching should also be included here.

"Curricular knowledge" includes both knowledge of different materials available (including digitally) and when they can usefully be used. Knowledge of what goes on in other subjects in the same grade or in mathematics in other grades are also included.

These three categories will probably prove to be useful for forming the discussions we will have now that the curriculum (in teacher education) will be changed again.

Shulman's article is written as an answer to George Bernard Shaw's "He who can, does. He who cannot, teaches." Shulman's version is: "Those who can, do. Those who understand, teach."

Labels: teacher education

## 3 Comments:

yeah, the best way of learning is teaching!

would you like to say more about PCK? In your opinion,what is the definition of PCK ? How many elements dose it cover? I'm very interest in that.

Shulman's article has had a big impact on the field of mathematics education. Since writing this blog post, I have read an article by Deborah Ball (which I will blog about shortly) which tries to define PCK more clearly for mathematics (as well as telling a bit of what has happened since Shulman's article).

In my opinion, some key aspects of PCK for mathematics are

- knowledge of how pupils typically think

- knowledge of different ways of teaching a topic

- knowledge of the history of the topic

- knowledge of what constitutes good examples/tasks

and so on.

Deborah Ball's article is, however, particularly interesting in discussing what is Content Knowledge in mathematics - that teachers need to know some particular pieces of mathematics that other professions don't. Her example in that particular article: While most other professions only need to be able to find the answer in one way, a teacher needs to be able to see a method she has never seen before, and figure out whether it is sound.

(I'll come back to this in later posts.)

Bjorn, I'm also finding myself coming across more and more information regarding Shulman's work. Including TPACK which is an extension of his work that includes the essential qualities of knowledge required by teachers for technology integration in their teaching: http://punya.educ.msu.edu/research/tpck/

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