Skip Counting’s Importance to Arithmetic

I am currently assisting in a research project with faculty and staff from the University of Ottawa. The project will teach tutors to provide effective reading and math programs to approximately 80 foster children who are wards of two Children’s Aid Societies.  This work is a replication of a previous, successful research project led by Dr. Bob Flynn, in which we taught foster parents to effectively tutor their foster children.

Yesterday I was training tutors in the programs that they will use in these one-on-one tutorial sessions. When we got to the math program I asked the group to count aloud by 5s. They did so easily at 150 counts per minute with no errors. I then asked them to do the same task with 6s. They were fine up to 30, but then their behavior became ragged, slowed appreciably and had more errors. Their response simply petered out as we advanced. Only one member, a former secondary math teacher, was able to count by 6s fluently.

When I asked the group to explain their lack of performance, I got all kinds of insights – mostly they had never been taught or given practice in counting by any numbers other than five, ten, or one.  Why should they care?  What possible difference does it make?

Well, they are going to teach these foster children how to do division as one of the four fundamental arithmetic operations.  How do you divide a large group of items in groups of six if you cannot count by 6’s?

If you cannot count by 6’s, or any number other than 1 for that matter, you are robbed of the easiest way to solve division problems. You are restricted to either sorting the large group into sets of 6 physically and then counting the sets by 1, or by representing the large group as tallies in sets of 6 and then adding up the sets. These are time consuming, error–prone alternatives to simply being able to count by 6’s from 6 to 120.

As a precursor to learning arithmetic operations, learning to skip count by any and all numbers up to at least 12 is a useful skill for children to learn fluently. As an exercise, it should take no more than 3-5 minutes a day of instruction and practice.

There are a couple of hints to help you in my next blog.

Note: Interestingly enough, all of these new tutors had arts or social science degrees or diplomas. No math, business, or science degrees in the room. None of these bright, young people had registered for an elective math course at college or university, except for the math teacher. Hmmm – Is there any kind of connection here – between basic building blocks for math and later career choices?  I wonder.