In the past, I taught math by:
1) Put the steps on the board, for which the students will need to know to solve a problem
2) Complete questions of increasing difficulty.
3) Complete a word problem.
4) assign the odds on page XX; next year it would be the evens (my attempt at differentiated assessment)
I found it very strange that I would actually give steps before I have shown the students WHY they would require the steps, or even given them a chance to CREATE the steps themselves.
Here is how I have changed.
These are the steps I took to teach "How to graph a function from an equation"
1) To start, my class and I had a discussion about the importance of seeing a graph of a function.
2) While my students sat in groups of 4, I gave them the following question, “If I gave you a function, what would you need to graph the function?”
3) I gave them 5 minutes to brainstorm all the information needed.
4) We then compiled all the information on the board, and determined whether we would use the function, the 1st derivative, or the 2nd derivative for each information.
5) In each group, students then graphed functions that we created as a class.
6) Finally, in groups of 2, each student had to illustrate they understood the steps required to graph a function.
Here is an example of one of the “illustrations”.
I truly believe my students can call this learning their own, as they were the ones who CREATED the learning in their mind, as opposed to sitting there and being TOLD what to do.