Post # 20 The Importance of Sub-Skills

I sometimes work with schools for at risk students.  These students come in all categories imaginable but with one common denominator.  Many of them are below grade level in skills not only math, but reading, writing and critical thinking.  They are still required to pass state mandated tests and exit exams.  This includes algebra I.  I have students who are not allowed to use calculators on these tests and are still counting on fingers and ignoring all word problems.  They guess at random or simply put their heads down in defeat.

I see teachers trying to teach content for which the students are wholly unprepared.  I see them feeling frustrated because they feel they do not have time to teach content deeply and must take short cuts.  They throw their hands up and teach procedures hoping they will stick for the week or so until the testing is done. They practice random sample test prep questions, public release items which cover a year's worth of content in random order, one problem isolated from the next as if it all makes perfect sense.

In this type of school there is frequently high turnover in both students and teachers.  There are often students who enter the week before the tests.  Their skills are a patchwork of misunderstood procedures and a lack of numeracy is almost a given.  The students push numbers around with no meaning.

Throughout the year I refer to the What Works Clearinghouse suggestions and Universal Design for Learning.  I strongly suggest numeracy activities at all levels of math.  I mandate teaching some facts to mastery and using those facts for all new introductions.  We use linkages and emphasize practice in sub-skills before embedding those subs-kills in larger a context.  

I will give one example I used recently.  The object of the lesson was simplifying radicals for an upcoming algebra 1 exit exam.  I began with multiplication.  We constructed perfect squares using simple cubes to demonstrate square numbers.  We placed them on a multiplication chart to illustrate the products growing diagonally down the page.  I only constructed the first few, to make the point of perfect squares and then transitioned to the representational level.  We inserted the meaning of the square root and began choral recitation of the facts.  Two squared is four and the square root of four is two.  Three squared is nine and the square root of nine is three.  We counted by perfect squares to one hundred sixty nine and back by squares to one.  We alternated using the meaning of "squared" occasionally asking "what number times itself is forty-nine?" They did not use calculators.

We discussed why other radicals are irrational and how the most accurate way to write them was with the radical.  Finally I introduced the concept that the square root could be simplified by factoring out a perfect square and "pulling out its root."  Within the hour these remedial students were factoring radicals and simplifying them.

The process:  Begin with something they know, link it to something they can relate to and learn quickly, use visual representations and manipulatives conceptually,  teach incrementally in logical steps using repetitive procedures that make sense and relate to the final solution, teach the sub-skills and integrate them into the final skill set, solidify learning with practice and problem solving.   Time:  one class 50 minutes to one hour.

And at the end, the students were leaving for the day.  One rather tall young man hung back as they exited and said,"I just wanted to thank you lady, for teaching me that today.  I got it.  I got it really fast."    Priceless.