On Layers, Sides, or Facets of Knowing

He knows it and he doesn’t know it.  Twelve months of the year.  Robert knows them and lists them one by one in a proper order. He knows a month before and a month after each one of the twelve.  He hesitates with naming month after December or month before January, but only hesitates.

When he has to change number of years into a number of months, he doesn’t have problems. And easily, since multiplying by 12 is not difficult for him, he tells the number of months in two, three, or more years.

And yet…When I slightly change the circumstance in which Robert has to demonstrate the same (?) knowledge, he is lost.  He doesn’t know. He forgets. He cannot connect his knowledge with the question being asked.  He cannot apply  what he knows when the problem sets his mind to solve another problem first.

Just yesterday, there was a problem in the lesson 23 of Saxon Math that Robert couldn’t solve. There was a circle divided into 12 sections.  Each part had a name of one month written in it.  Robert was supposed to do two things:

First, he should color the spaces with those months which have 31 days.  With the help of his knuckles, and two cues from me, he managed to do it right.

Next, he should answer the question, “What fractional part of the 12 months make the months with 31 days?”  He was lost.

Yes, there was time in the past, that the word “fractional” confused him.  Not this time.  As soon as he read “fractional” he drew a fraction line.  He put 7 in the numerator.  He did not know what to put in the denominator.

Why?

He knew how to tell what fraction of a figure or a set had been colored. Without any prompting, he counted all the pieces needed for the denominator and all the colored pieces for the numerator. In this problem, he could do exactly that, but he did not.

He knew that each year had 12 months.  He demonstrated that knowledge when he had to change units of time from weeks to days, days to hours, and months to years or vice versa. But when I asked, “How many month in a year?” He did not know what to say.

Was that because of the complexity of the problem that required Robert to use a few facts in a sequence?

It might be that the process of finding the number of the days in given months tainted his ability to tell the numbers of all months as if his brain went on a different chain of thoughts and couldn’t find his way back.

Maybe, each information (fraction, and months)  was preserved in a different part of his “brain” and Robert  couldn’t access them both at the same time to make connection.

Were Robert’s difficulties a consequence of a lack of ability to generalize?

What does it exactly mean to “generalize” , and what EXACTLY impedes that ability?

What does this  mean for Robert, for me, and for  ways we both learn?

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