Post # 28 What Role Skip Counting

I have had a recent reason to review the role of skip counting and its relationship to multiplication.  The standards suggest that in second grade, teachers begin skip counting by 2’s and 3’s to lay the foundation for the concept of multiplication.  And which one of us could not skip count by 5’s at an early age. The problem I see is that many teachers believe that one teaches or reviews multiplication facts  by skip counting. 

Let us examine first what multiplication is:  making many of the same quantity…like repeated addition of the same quantity. The goal of multiplication fluency though is automatic retrieval of an individual product in isolation.  Using skip counting to locate a specific product in response to a prompt by going through a string of numbers every time would be highly inefficient.  In many children it might also be inaccurate.

So what is the proper role of skip counting then?  It does help us to recognize patterns. It familiarizes us with the specific products in a set of products.  It trains the ear, so that if our retrieval fails us, we might self-correct because we know that a specific number is not part of that set.  With many of my students who have dyslexia, I will hear them say the algorithm and a product they retrieve rapidly, only to follow with “no, no….” and then the correct solution. 

I write this in response to some lesson plans I received as assignments.  More than one teacher wrote of skip counting by several different numbers in the counting section of the lesson plan.  This was not counting by 3’s that day and then using the facts in all work to provide repetitive practice as I often advocate.

No these teachers suggested skip counting first by 3’s, then 4’s, then 6’s, then 8’s…all in the same day, as if that would be reviewing multiplication facts.  I found this troubling on so many levels. 

For students with language based learning disabilities, multiplication is a major hurdle.  They have no visual or quantitative reference. This is one reason I invented the Strings with Wings.  I don’t make the strings for all times tables though we certainly could.  I usually reserve them for the upper times tables. 

There is another possible use for skip counting which I feel is necessary but must be judiciously used.  I have had older students with undiagnosed LD who are not permitted to use calculators on standardized tests. Without fluency support, these students would perform miserably if not simply give up and not try.  This is the “mark answer ‘b’ and move on” crowd.

I will teach these students to create a partial multiplication chart quickly using skip counting: 2, 3, 5, 9 plus the special patterned products in the upper times table.  From these brief answers they can reason others. This allows the students to perform better and it encourages them to keep trying.  It allows them not to feel like abject failures. 

Ultimately, I feel very strongly that we must shift to a concept based approach to math for in class work which allows students to use friendly number facts for group work.  I advocate having students create their own near point references to use during class and for teachers to offer sufficient practice with a limited set of facts at a time to develop automaticity.  We must continue to work on fluency development for all students. For independent work, homework and tests appropriate  challenges for more rigor or accommodations could be used. 

The point is, that we must take the time to build fluency and reasoning capacity in our students so that the mind can be free to do the math. Students who exclusively use calculators often do not understand the underlying concepts.  They may be pushing numbers around according to that unit’s procedures. The learning doesn’t last and they lose the ability to apply.

In other words, do not think that by skip counting with older students that you are teaching multiplication facts. You are not reviewing them or practicing using them.  You are, according to the standards, laying the foundation only.