Let’s say a school let you teach a class the way you felt it should be. I know this is a fantastic notion, given the state of American education but stay with me here. You gave your own style of opening, you taught the concepts that you felt necessary and gave them a chance to practice the new concepts. What then? How do you know that they learned what you tried to teach them? Some mainstreamers would probably say, “I’ll check their homework the next day?” What if they don’t do the homework? What if they ignored you and just watched some YouTube videos and/or some Khan Academy videos? Yeah, it’s great that they learned, no matter how they learned. But what about your teaching? How do you know your methods were effective? And, oh yeah, what if they had their girlfriend/boyfriend/friend/sibling do the homework for them? How does this inform your teaching?

Standard application of the 4-part lesson plan (opening-instruction-practice-closing) gives that needed feedback. However, the standard closing of unsolved problems has its issues. First, it tests where the teacher feels the student should be, not where the student actually is in its knowledge base. Second, the same problem for everyone leads to an opportunity for kids to copy each others’ answers and thereby gives a false impression of knowledge. Third, the uninitiated will become bored with it and claim that they cannot do anything because they don’t understand it.

In my estimation, the solution to this issue lies in having choices. In response to that, I developed a “closing protocol” outlining 10 choices of ways to give feedback to the teacher about the students’ depth of knowledge. Of these ten, several are straightforward and logical and the rest are pretty creative. Among the creative are drawing a cartoon, creating poetry or a rhyme, telling an applicable joke, etc. The idea of these closings is to tap into what the student enjoys while giving feedback of knowledge.

These are quite useful but an idea I used for my dissertation goes a bit deeper. At the time I was choosing a topic, I was interested in bringing psychology ideas to education. One idea I was greatly impressed with was something Active Imagination (AI). AI is taking an abstract idea and having a conversation with it. The study took the step by step approach analyzing dreams (Robert Johnson’s Inner Work) and taught it to classes. One of the steps of this work is doing an AI with a character of one’s own dreams. Once the student understood AI, the student was given the option of doing an AI with a mathematical concept. The study shone a very positive light on these type of closings.

Given these positive results, the reader may be asking whether I use this idea or not. The answer is yes and no. Yes, I use the closing protocol on a daily basis. However, AI is offered in the protocol but I no longer encourage its use through dream analysis. Why not? Because it requires taking up to week of teaching dream analysis and I am afraid of being accused of “not teaching math.” (One school suspended me for several days on that charge. The school district’s decision was actually political but it hid behind that charge, in my opinion. The same school eventually allowed me to run a monthly “Dream Club,” where I taught the dream analysis steps and students analyzed each others’ dreams.)

If you would like access to any of these documents of this dissertation, please ask in the comments section.