In one of the previous posts I wrote about three steps in teaching Robert a skill.  The first step is the hardest to explain.  I don’t expect Robert to learn the skill.  I lead him step by step through the procedure, I talk to him knowing that he doesn’t understand most of what I am saying, no matter how simple they seem to me.  It is as if I asked him to look through the window of a moving train and notice an object we were passing by.  I wouldn’t expect Robert to notice any of the specific features of that object.  For now a realization that there is something out there will suffice. We will study it intensively another time.  That would be a second step. Next we would proceed to finding the same object in its different manifestations and various environments… In other words Robert  would generalize the skill.

When I described those steps  I omitted the most important function of the first step. Besides exposing Robert to an existence of something new, this step is for me to learn how to teach Robert. I observe Robert to know  which of the steps I am leading him through he can climb on his own, which words he recognizes, which he doesn’t, and what other support I will need to provide to assure learning.

There were times when  I skipped this first step.  I jumped into intensive teaching without strategic reconnaissance.  I expected Robert to learn something I didn’t know how to teach.  I was putting pressure on Robert not on myself.

What I am writing is not about a teacher being prepared  for a lesson (for instance by writing a lesson plan).  The lesson plan is an important tool, but for children like Robert it is just  like a hypothesis.  It doesn’t assure learning.  It only sets the stage for testing of the hypothesis.  The first step, as I understand it, is about checking the hypothesis. You don’t know how to teach before you start to teach and analyze responses – good and bad, complete and partial. The teacher has to learn from those responses and then develop  proper strategies, check them again, revise them again until he or she finds the best approach to teaching this specific skill to this specific student.

Just yesterday I tried to teach Robert to divide fractions. I had a lesson plan.  I had already practiced with Robert prerequisite skills like finding reciprocals.   I used simple words.  The words he knew – multiply , divide, flip the fraction over, reciprocal, reciprocal..

He couldn’t grasp the division.  That should be fine. The mistake was that I expected him to learn and consequently subjected him to the same method over and over.  That lead to more errors and repeated failures.  The failures lead to frustration and learned helplessness…

I shouldn’t pressure Robert  to learn during that phase.  I should be the one who was supposed to learn during that time. I had to take a breath and think about this failed attempt.

When I did,  I noticed  that although Robert understands when I say, “Multiply four by seven.  Divide 42 by six”  he doesn’t understand me when I say, “multiply instead of dividing”.  I observed that for Robert finding reciprocal to the separately standing fraction is not the same as finding reciprocal during division. I came to a conclusion that relying on language concepts that Robert used only in limited numbers of applications was not working. I understood that I would have to to experiment with different methods of presenting the new information.

In the end  I used abstract algebraic formula: “a/b : m/n = a/b * n/m .  This approach I would use with “typical” students. It seemed much too abstract for  Robert.  But since  I was only experimenting it was no harm in trying it. I introduced this formula not expecting Robert to learn it and use it.  I pointed it to him as if that was that object we had  seen from the passing train.  Somehow this formula seemed for Robert easy to follow.  Much easier than my verbal directions. I found a way to teach.  The phase one was over. Let’s move to the next.

One might point out to me, that even during a failed phase of intensive teaching I  was still learning how to teach.  That is true.  Yet I was also subjecting Robert and myself to unnecessary frustration by rigidly sticking to one approach instead of investigating its effects and being ready to flexibly adjust it.  I should have taken a breath, led Robert through the activity (just stopping it without finishing would leave negative residues which also should be avoided) as calmly as possible.  Then, I should have taken time and rethink the whole process in connection with everything I knew about Robert and started over.