In the 80’s, Lee Shulman introduced the concept of pedagogical content knowledge to differentiate it from content knowledge (CK) and knowledge of general pedagogy (PK). Pedagogical content knowledge or popularly known as PCK is teachers’ knowledge of how a particular subject-matter is best taught and learned. Since Shulman introduced this concept, many others have contributed towards defining and describing it, the most important elements of its description include (1) knowledge of interpreting the content, (2) knowledge of the different ways of representing the content to the learner, and (3) knowledge of learners’ potential difficulties, misconceptions, and prior conceptions about the content and related concepts. Click here for an example of a pedagogical concept map for teaching integers.
With the increasing dependence of almost everything to ICT, it is no longer a question of whether schools should integrate these technology in its curriculum. In fact it’s been decades since courses on ICT have been offered as a subject in many schools. But how about the use of technology in teaching traditional subjects like mathematics? Does knowledge of technology equip teachers to use it to teach effectively?
Some mathematics teachers jumped to it right away, used technology in teaching. Some teachers are still in testing-the-water mode. Some, until now, are still totally in the dark, sticking to their old method despite the availability of technology, oblivious to the reality that in today’s ICT-driven world, it’s the students who are the natives and the teachers are the migrants (heard this at an APEC Conference in Tokyo). The way students learn are influenced by their experiences with many forms of technology and the way these tools think and do things.
When the pen and the printing press were invented, everybody thought that they will give an end to illiteracy (I heard this from the same conference). It didn’t take long for us to realize that it didn’t and can’t. The same can be said with computers, internet, softwares for teaching. Experience with these tools tell us that it is not enough to know how to use ICT just us it was not enough to know mathematics content to teach mathematics so that students learn it with meaning and understanding . Teachers must now be equipped not only with PCK but with TPCK – Technological Pedagogical Content Knowledge.
Punya Mishra and Matthew Koehler introduced this theoretical framework known as Technological Pedagogical Content Knowledge (TPACK) in 2005. The basic premise of TPACK is that a teacher’s knowledge regarding technology is multifaceted and that the optimal mix for the classroom is a balanced combination of technology, pedagogy, and content.
The figure at the right is popularly known as TPACK Framework (click image for source). It shows the kinds of knowledge teachers should posses. It can be used as framework for designing learning experiences for teachers and for planning, analyzing and describing the integration of technology in teaching.
is one of the most widely known irrational number. Ask a student or a teacher to give an example of an irrational number, the chances are they will give