Modeling with Sketchpad to enrich students' conception of a derivative

My teaching philosophy is socio-constructivist in many ways. First and foremost, I recognise that students are cognizing agents that construct new meanings according to prior understandings. Secondly, all students can learn mathematics, even though there may be individual differences. Thirdly, mathematics learning takes place as an individual experience as students make sense of their environment. The learning of mathematics is primarily a process of making sense of the world mathematically. Fourthly, whereas many learners can learn individually (subjectively), there is a greater benefit for a greater range of learners when learning takes place collaboratively (intersubjectively) to arrive at taken-to-be shared understandings in a socio-constructivist sense. I therefore subscribe to a view of learning as (co-)participation in a local socio-cultural setting - a form of situated cognition. Fifthly, teaching should facilitation of learning rather than transmission of knowledge. Finally, learners should be given a fair opportunities to develop 21st century skills such as critical thinking, problem solving using the new digital tools, including dynamic mathematics learning technologies.