Variables:
-- knowledge and skills
-- self-efficacy
-- pedagogical preference
-- school culture

For a recent article exploring the relationship between the P and the C, see "Building a Better Teacher" from the New York Times (3/2/10). The article make reference to "Mathematical Knowledge for Teaching", a special kind of knowledge of math that makes for effective math teaching.

See also: Wikipedia entry on Technological Pedagogical Content Knowledge
tpack.org: A site devoted to TPCK
TPCK Radio/Video Show: Cute video on TPCK, prepared for the 2010 ISTE conference

What is TPCK?
Technology Pedagogical Content Knowledge
This knowledge attempts to capture some of the essential qualities of knowledge required by teachers for technology integration in their teaching.
TPCK is combing the three primary forms of knowledge:
  1. Pedagogical Knowledge (PK) is deep knowledge about the processes and practices or methods of teaching and learning.
  2. Content Knowledge (CK) is knowledge about the actual subject matter that is to be learned or taught.
  3. Technological Knowledge (TK) is knowledge about standard technology such as books and chalk and blackboards, as well as more advanced technologies such as Internet and digital video.
When we combine Pedagogical Knowledge (PK) and Content Knowledge as a product we have a new type of knowledge Pedagogical Content Knowledge (PCK).This knowledge includes what teaching approaches fit the content, and knowing how elements of the content can be arranged for better teaching.
If we look in this new type of knowledge PCK and we add the Technology Knowledge(TK) to it, as a product we have Technology Pedagogical Content Knowledge TPCK.
  1. TPCK is the basis of good teaching with technology and requires an understanding of the representation of concepts using technologies;
  2. Pedagogical techniques that use technologies in constructive ways to teach content;
  3. Knowledge of what makes concepts difficult or easy to learn and how technology can help solve the problems that students face;
  4. Knowledge of how technologies can be used to build on existing knowledge.
  5. Teachers need to know not just the subject matter they teach but also the manner in which the subject matter can be changed by the application of technology.


More visual representation of this concept is the graph below:

tpck.jpg

On this graph TPCK is represented as a overlaying area of the three knowledge.


The Perfect Teacher

Works Cited:
http://www.tpck.org/tpck/index.php?title=Main_Page
http://www.tpck.org/tpck/index.php?title=Pedagogical_Content_Knowledge_%28PCK%29
http://www.tpck.org/tpck/index.php?title=Technological_Content_Knowledge_%28TCK%29
http://www.tpck.org/tpck/index.php?title=Technological_Pedagogical_Knowledge_%28TPK%29
http://punya.educ.msu.edu/2011/01/19/harris-mishra-koehler-republished/
www.ascue.org/files/proceedings/2009/p162.pdf