OK, this is far from a revolutionary idea, but I was impressed with my eldest daughter’s approach to a subtraction problem. What I present may already be used by others, but it was new to me.
She was interested a few months ago in learning what negative numbers were and what caused them. Of course, I dove right in and explained. From time-to-time she’s asked for more, but mostly I thought it was an idea that had gone fallow. Then she wrote the following last night.
I had learned column subtraction from right to left with “borrowing.” It was an algorithm that I understood; many classmates struggled. My daughter worked left to right by column/place value. So, she computed 70-40 and wrote 30. Then she used her knowledge of negative numbers and asked me, “So 0 minus 2 is -2, right?”. She then wrote -2. The rest was easy. What impressed me was her adaptation of an algorithm she had been using for partial sums. If a student understands negative numbers, I wonder if this might be a cleaner approach. The thinking is also similar to what one might use when calculating using an abacus. Cool.