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.
Yesterday I spent some time in a second grade classroom helping students who were adding double digit numbers. When working with one student, I realized he didn’t know he had ten fingers on his hand, and he didn’t know that four fingers on one hand and five fingers on another made one less than ten–nine. While at a CGI (Cognitively Guided Instruction) training today (I am in Year 2 of the training), some things dawned on me about this children. Children do not innately know that they have 10 fingers, nor do they necessarily discover this on their own. With that said, the CGI trainer today told us that she knew of a teacher that has students do finger flashes. She calls out numbers and the students hold up that many fingers. I had never thought to do something so simplistic. I know that in kindergarten we do such activities with dot cards, but I had never thought of finger flashes–WOW!
In this same second grade classroom, I moved on to another little girl who had difficulty counting on from the larger number. Even after I showed this student how to count on, I noticed that when looking at the problem she didn’t know where to get the other number to count on with her fingers. I showed her how to look at the problem to find the number. Again at the CGI training I realized for students to develop the number sense they need to count on, the teacher can push students toward counting on by posing a very large number in a word problem followed by a much smaller number. For example, with the problem 62 + 3, 62 would be easier to start from and just count up 3 more. Once a child is counting up just 3 more, the second number could be increased. As my mentor always used to tell me–You know better, then you do better. That is me.
Another math coach related to me today the story of how a student she taught had named fingers sections as something that comes in groups of threes. She took this concept and helped students use this to develop multiplication strategies to learn their threes multiplication tables. Fours multiplication tables can be learned as well if students include counting the top part of their palm. See the pictures below for more clarification.