I love the idea of not giving to much information to students and getting them to notice and wonder so they can decide on a solution pathway instead of being told or outright asking for the way to solve a problem. I find many of my students give up on the logic problems that I give in class. I also find that after a while they do begin to dive into their tool bags to see if they can use something from their past experiences to help them solve the problem in front of them. My wondering is how do you do this for concepts that they have never seen before? For example, part of our curriculum has to do with teaching the pythagorean theorem. Without learning this, how do you just throw a problem at them that would normally use the pythagorean theorem to solve it? I don’t want to be the “sage on the stage” but when is the right time to give a problem to kids that you know requires more mathematical understanding then they currently have?
I like the idea of being able to let the students ‘do’ all the steps you mentioned. If we as teachers list them out.. then they are not ‘doing’ the thinking about the topic, but instead, they are just waiting for you or that ‘one student who always answers’ to do so. I wonder how long will it take for all my students to get here? Should I be expecting a few months before I can get the majority of the students involved?
I love the idea of having the students start with something that they can relate to. I am going to pull up the electronic version of my textbook right now and see if I can find a problem that I could start working with in the next topic I am going to cover. The students do already have a lot of prior knowledge and the skill is just the next step.
I think my big take away is the need to build anticipation and curiosity. I understand the need for numberless word problems, but I am still wondering how to get there and how to make it apply to whatever topic I am on.