Hopscotch Math

The disoriented author and his wife are home school parents. Actually we have tried and continue to take advantage of a variety of educational opportunities for our children. We have had children homeschooled independently, homeschooled through a district sponsored  homeschool program, in public school, parochial school and this year our daughter was a Congressional Page and attended the Page Boarding School in the Library of Congress.

Each year we look at each child and try to choose the best educational opportunity for them. Next year we are planning a combination of public and home schooling for our remaining children at home.

Yesterday when I came home from running errands, I noticed that our kindergartner was drawing chalk numbers on the different squares on our front sidewalk. Generally she draws pictures and recently she wrote "I love you Daddy".

Today she had written numbers. As I got closer, I saw that she had written:

-2  -1  0  1  2  3  4

As a parent, with a mathematics degree, I was thrilled.

While Babylonian mathematicians had the concept of zero two centuries before Christ, it would take Western mathematics until the 15th century AD to fully realize negative numbers. And my six year old had drawn them on the sidewalk.

I was in a hurry and I  had my hands full of groceries. I set them down and asked her to show me the numbers. I then showed her how I could add 2 + 2 by standing on the 2 and hopping twice to the 3 and 4 respectively. We played this game happily for a while and then extended it to include the negative numbers and zero. Soon we started hopping backwards and doing subtraction.

I am sure that my daughter will only remember playing hopscotch with Dad. But somewhere under the surface I saw a bit of a mathematician poking through. When my father saw that in me, he encouraged it and nurtured it. He bought me books on math and talked to me about the math he was doing as a geographer. He explained trigonometry to me on the back of a napkin in a restaurant. Later he introduced me to basic statistics the same way.

As we both got older, the roles sometimes reversed. Later I sketched Göedel's Incompleteness Theorem for him on a napkin. We marveled together over the proof that the cardinality of the  Integers and Rational Numbers is the same while the Real Numbers have a higher cardinality. My father has since passed away but these are some of my fondest memories of him. I may have attended public school but I was also homeschooled.

I wish he were here to share these moments with my daughter but having learned from him,  I would not miss them for the world.