I've been doing a lot of thinking about math recently and you can expect to read about it fairly often on this page. Teaching math can feel like a balancing act. On the one hand, computational skills are vital to math literacy. They must be taught and practiced. On the other hand, the beauty of the mathematics and its connection to the natural world is also crucial. Without exploring the wonder of math, it is dull and lifeless. Without knowing some foundational pieces, one is blind to the wonder.
The lessons of the past two days illustrate how we try to nurture both elements in our students. Yesterday, we did a pretty straight forward lesson on place value. We looked at how our place value system works and why it is an efficient system that had advantages over abandoned systems like Roman numerals and Egyptian glyphs. We briefly hypothesized why Base10 might be so popular with humans (10 fingers?). We practiced reading big numbers. We learned how to place commas in numbers. We used place value to easily add large numbers together.
Today, based on a brief conversation yesterday with G.S., I asked the class how a creature, say a T-rex would count. After all, it has only 3 fingers. I'll admit to a lot of roaring and stomping as I, the T-rex, became more and more frustrated trying to write a note to my mother in which I wanted to tell her that I had eaten four velociraptors. The only digits I had were 0,1,2,3. How could I write the quantity four? Suggestions abounded and eventually, we hit upon a place value system but, instead of a group of ten being the next place value, four would be. At this point, about 10% of the class was really understanding what was going on. I added 13 more velociraptors to the original 4. Now how could I tell my mom? A new place value was needed, four groups of four. We practiced with a few more values and more heads started to nod. The dinosaur was feeling pretty good about things.
Another student then pondered, "What if you had a different number of fingers?" Instantly, I announced that we had landed in Hexadeciland -- home of a species with 16 fingers. They, of course, had a system with 16 digits -- 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F. Kids giggled as they announced, "I'm going to be A this year!" "My brother just turned F!!!" Someone asked, "How old would my Dad be in Hexadeciland -- he's 54" We figured it out and then figured out his age in Dinosaur Base4. Students were howling to discover that I would be 203 in Dinosaur. More hands shot up and we figured out ages for siblings, grand parents, great grandparents. At one point, a student was jumping up and down saying, "I get it! I get it!"
We ended by imagining what Gourdland would count in. After all, they just have one stalk -- so it must be Base2! (That makes me 100011, by the way.)
At different points, I re-assured students that they should feel very confused. Everything they had learned since pre-school was based on their ten fingers, after all. I also assured them that we were just playing and that they weren't responsible for being able to do this by themselves. But they left the room laughing and imagining different people they'd want to figure out in dinosaur. It was all just a little bit crazy -- and wonderful. Our goal for the day was accomplished.
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