You Can Learn Something From a First Grader…

This past week I was asking a first grader how she had solved a math problem.  When she showed me how she had used her fingers, I realized something amazing.  She actually saw doubles on her fingers.  I had never paid attention to exactly how students had used their fingers to solve problems.  She used each hand as the separate addends in a problem, but more specifically she used each hand as the addends of an addition problem with doubles.  So for example, she was easily able to see that 4 and 4 make 8 and that two more fingers (doubles plus 2) make 10– put one more finger up on each hand to make five fingers on each hand or ten fingers altogether.  She used this strategy fluently, but it had never dawned on me to see patterns with doubles on two hands.  I had always thought of the number four as just four fingers on one hand alone–not as two fingers on two different hands.