Guided reflection - math strategies
1. and 2.: Collect stories/What happened? – Miranda helped Omar do his math homework
Once again, we had more volunteers than students at tutoring. Mariah – the director of Wordsmiths – asked Miranda and I to work with Omar. He had not been in school that day, so he needed to do both his schoolwork and some homework, which had been compiled into a packet. Since Miranda had worked with him before, I let her lead; so, for the most part, I just watched. Omar said he already knew how to do this, and that they didn’t need to work on it today. Miranda said that he needed to finish as much as possible, since there wouldn’t be tutoring tomorrow or the next day. She repeated that he had to do it today.
Omar started with the first page, which was 3 columns of basic addition (ex: 1 +2 = ?; 3 +7 = ?). For the first few questions on the first column, Omar used one of two strategies: he wrote tally marks for each number and counted up the total (ex: I II = 3; III IIIIIII = 7), or he used his fingers and counted from left to right (ex: 1 finger on one hand next to 2 fingers on the other hand). When the numbers were too big to fit on one hand (ex: 7), he used tallies. Miranda and I both watched him. For some of the equations that Omar was going to use fingers for, Miranda held up her own fingers and told Omar to look up. He counted her fingers and used that number. He said the answer out loud before writing it; when the answer was wrong, Miranda asked, “Are you sure?” or said, “Check that again.”
Omar started saying the equations out loud more often. On the third column of the page, Omar noticed that he had already done some of the problems – and could use his previous answers to help him solve the repeated questions. He was reading an equation out loud when he said that the answer must be 10. Miranda asked him to explain – he said that if 1 + 8 = 9, then 2 +8 = 10. She exclaimed and told him, yes, that it was right. He tried using this strategy a couple more times, and Miranda pointed out equations where this strategy would work.
I sat next to Miranda on the train on the way back. I asked her what she thought of the day. She commented on Omar – “he’s so smart!” and then elaborated on how he came up with his own strategies for doing the work (“If 1 + 8 = 9, then 2 +8 = 10”). She said that he gets picked on a lot – “Did you see how scared he was when Jamal came in?” Amanda told me that Jamal usually bullies Ahmir. She says that his sister does too – both because he has trouble doing his work, and because he is overweight. Miranda also noted that Omar was, for the most part, able to do his homework without stopping – the part that got him really confused and frustrated was coloring in the spots on the giraffe’s neck. The answers to various numbered equations corresponded with a color (ex: answers ranging from 30-55 were one color). Omar had a hard time with this; Miranda said that he didn’t recognize when one number was higher than another. She said that she tried to explain this with money – asking Omar which of two amounts he would prefer. He did not consistently ask for the higher number.
3. Why did it happen? – Omar is 7 years old, but he is repeating 1st grade. I was surprised that he seemed to have so much trouble with basic addition. He seemed very dependent on the fingers- or tally- strategies for getting through that entire page. Miranda was supportive of these strategies, but I wonder why he hasn’t been able to internalize other ways of conceptualizing numbers (ex: for 7 +3, counting from 7 8 9 10).
4. What might it mean? – I wonder how much time Omar has spent on math in school. Has he been going over this particular topic for a long time? Why is he still dependent on these strategies? Since he also had trouble telling what number was bigger (ex: 57 vs. 64) on another page, I wonder whether he might be dealing with some learning disabilities.
5. What are the implications for practice? – I thought that Miranda’s approach here was really useful – validating what Omar already knows, and then suggesting strategies that built off of those practices. Establishing a level of comfort with math as a language is crucial. At this point, I think a confidence boost is definitely useful for him; but it seems that he is also really benefitting from consistent one-on-one attention.