My definition of technology would be a blend of Feenburg’s attribution of social values and Roblyer’s description of technology as our tools, methods, and creative problem solving. From this, an ideal pedagogical design of a technology-enhanced learning experience for math includes recognition of the context of scenarios, effective manipulatives and devices, and strategies, and the interconnections between these elements. For example, a word problem describing a photovoltaic cell may be unnecessarily confusing for a student with minimal electrical physics knowledge, who may then be unable to achieve the intended mathematical outcomes due simply to the disconnect between his experience and the question context. At this point, devices and strategies would likely be ineffective as he would not have enough understanding to adequately apply them.
When designing a technology-enhanced learning experience, I would account for the different backgrounds of the students by attempting to provide a variety of pathways including a variety of technology tools to hopefully engage every student in some way. Increasing student choice enables them to make the best decisions for their own learning needs, and to find their own connections between their strategies and digital devices. In my mind, choice is central to growth and learning.