Fluency or Complexity

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I am very proud of my 6-year old and the math discoveries he makes. Two days ago he came up with a proof that zero is an even number. Yesterday he built something he called “a square that has volume” (a cube), then connected 4 of them into a larger cube. And today, well before I had time to drink my morning tea, he shared his new discovery – turns out, Russian nesting dolls are fractal!

Nested Doll X-ray

I am very concerned about my 6-year old’s  struggles with math. He still gets mixed up counting past 10. He is shaky with his math facts. He still needs to use fingers, counting bears or abacus a lot.

Where am I going with this? At the last Inspired by Calculus math circle, the kids were building LEGO towers so that the number of blocks in each tower was double the number in the previous tower – 1, 2, 4, 8, 16… It seemed that most of the kids, including my son, struggled with the doubling part. Whether they multiplied or added, they kept making mistakes. The goal of this building activity, by the way, was to check whether such doubling function would be linear or non-linear.  Which got me wondering whether I am putting the proverbial carriage ahead of the proverbial horse when it comes to my child’s math education.

doubling towers

When I talk to friends about advanced math for very young kids, one of the first reactions I get is, “This is cool and I’d like to try it with my child just as soon as he learns to count/add/multiply.” When I say that many of the activities can be done with kids who don’t know any of these things yet, or are not fluent yet, the question I get most often is not, “How does it work.” It is, “Wouldn’t it be better to build up their arithmetic skills first?” And frankly, I ask myself this same question whenever I see my child stumbling with his “required skills” work.

Does it really have to be one or another? Is it possible to really understand complex mathematical ideas without firm grounding in basic arithmetic?

Right now, for my son and I it’s a question of enjoyment. He loves going to math circles and problem-solving with friends. I love that he notices math all around him now. He loves that doing math can be funny. (Cats need meat for breakfast, lunch and dinner. Grandpa says he needs meat for breakfast, lunch and dinner. Grandpa is a cat.) I love that he uses math to communicate complex ideas and deep observations.  He loves watching Fractal Cows, Infinity Elephants and Sierpinski Dream videos. I love watching these with him.

What do you think? Does exploring deep math very early helps to “get” the fundamentals?

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