Hewitt reading reflection

Hewitt describes something as arbitrary if the information must be told by others and “without someone else, the knowledge would not exist for us.” Hewitt describes things that are necessary as things that can be worked out, things that does not need to be informed.  I think there should be different steps and levels in a lesson. First I would start with giving students arbitrary information or new information they never learned, then I would show them examples, and lastly let them try the problems on their own. I think it depends on the topic, sometimes I might let them start the exploration first then teach and show examples. I think it is important to show examples, even though it may be necessary knowledge that they may be able to figure out. Due to time constraint and various levels in the class, giving students a step-by-step solution might be the most efficient way.  For the struggling students, it is much easier for them to have a recipe to follow. For the advanced students I will have challenge problems to promote high level thinking. Most importantly, I want to give student enough time to try problems on their own and ask questions. I think students really understand the concept and understand the necessary knowledge when they try it themselves. It is important to find the right balance of how much arbitrary information and how much necessary information the teacher should give to make a smooth and productive lesson.