Elementary does not mean easy

Our tutor confronts a challenge.

Our tutoring consultant, handling mathematics and science as well as some languages and other subjects at the High School level, plus college prep, is in an unusual situation.  He has four students to whom he is teaching the basics of handling fractions.  Now, it is not unusual for a student at that level to be uncomfortable with fractions.  They look more complicated than straight numbers, even numbers with variables in them, and details of how to work with them can get fuzzy.  Maybe part of the cause is that calculators are not good at handling fractions as fractions, and most students now are far too dependent on electronic help.

But these four students were completely lost, having no idea what to do.  They were quite unable to add or multiply fractions, and mixed numbers were a particular puzzle.  Why High School students, several of them, lack an Elementary School skill is a separate question.  The task is to teach it.

This is not easy.  It involves some very basic operations, things our tutor is used to doing automatically; he has to explain things he doesn’t think about and correct errors he would never make.  It means looking explicitly at steps he last wrote out decades ago.  It’s not that he is above such elementary things; it’s that he lacks the background and skills to be an Elementary teacher, which are different from those needed in secondary school or beyond.

And these rather basic operations require even more basic skills.  Simplifying a fraction or finding a common denominator involve factoring numbers, that is, reducing them to a product of prime numbers.  One of the students remembered nothing of this, and the others were weak on it.  That meant another lesson to shore up the weakness.  Converting to a mixed number means carrying out long division.  Three students did not know what this was (or had forgotten).  For one of them, our tutor has not yet managed to get the technique across, in spite of spending quite a bit of time trying to explain it.  A particular accomplishment our tutor treasures is teaching that student how to properly multiply decimals.

Well, there is something to be said for being forced beyond one’s comfort zone (as the cliché has it), or receiving a lesson in humility.  And, as a teacher, learning something about the craft.  But our tutor would really rather that High School students had mastered Elementary School skills.