Searching for a model for learning with technology

It is tempting but futile to try to answer questions on educational technology just by looking at the latest technology available. Equally, it is futile to keep doing the same things (buying the same things) - see my earlier post on the Capital Budget.
How should we be using technology in learning and teaching?
What models of learning with (through? assisted by?) technology exist?

In 1986 Lee Shulman introduced the idea of considering the teacher's SUBJECT knowledge (the content) and the teacher's PEDAGOGICAL tool kit (my terms) together, and not as separate entities. He illustrated it thus:

He stated that these areas were treated as mutually exclusive entities in research and in training teachers. The crucial intersection, that of Pedagogical Content Knowledge (PCK), is often ignored:
"This knowledge includes knowing what teaching approaches fit the content, and likewise, knowing how elements of the content can be arranged for better teaching. This knowledge is different from the knowledge of a disciplinary expert and also from the general pedagogical knowledge shared by teachers across disciplines. PCK is concerned with the representation and formulation of concepts, pedagogical techniques, knowledge of what makes concepts difficult or easy to learn, knowledge of students’ prior knowledge and theories of epistemology. It also involves knowledge of teaching strategies that incorporate appropriate conceptual representations, to address learner difficulties and misconceptions and foster meaningful understanding. It also includes knowledge of what the students bring to the learning situation, knowledge that might be either facilitative or dysfunctional for the particular learning task at hand. This knowledge of students includes their strategies, prior conceptions (both “naïve” and instructionally produced); misconceptions students are likely to have about a particular domain and potential misapplications of prior knowledge." (from pck.org, accessed 29Dec10)

This makes perfect sense and it is how we think about preparing learning in schools. As a mathematics teacher I consider the content knowledge of what I am about to teach, the pedagogical knowledge in its broader sense AND the specific teaching knowledge regarding the mathematical content. This latter, often gained by experience over time in an iterative process each time I prepare to teach it.

The same type of model exists for technology, introducing Technology as a new interacting domain.

Here is the diagram now that we include Technology: (diagram from TPCK)
The point is that each intersection deserves attention. An excellent presentation about this is done by Ruben Puentedura - it is worth listening to on I-Tunes -  "As We May Teach: Educational Technology, Maine Uni". He does this as the introduction to SAMR - an item for my next post.