Amy Gaisser
Dr. Bloom
ED 316
Reflective Writing About Session #6 on October 25, 2011
In the previous lesson, Yadira and I had arrived at the solution to a problem multiple times
by using a variety of strategies. Yadira seemed to really benefit from using these strategies, even
though we had only planned to focus on subtracting by “adding on” in that lesson. Thus, in this
lesson, I wanted to reflect with Yadira on the strategies we had used last time. I planned for us to
describe what they were at first, but also (as we got further into the lesson) to think about when it
was most effective or helpful to use each strategy.
We started off by trying to remember the different strategies we used last time. The first
strategy that came to mind for Yadira was counting by fives, which she used when we grouped
the pizza toppings in a way that would help us to figure out how many were left. I had her write
this strategy down on a piece of paper, so that she could remember later. She seemed hesitant to
write at first, because she was not sure how to spell “counting.” I guided her in thinking about
how to spell it. Then, as we continued to write more strategies, she seemed to become more
comfortable with writing. She did not ask me for help and I was happy about that, because I did
not want her to think she had to write with perfection! I was hoping she would realize that these
notes about strategies were just for her, and that her spelling did not matter. She needed to know
that it was okay to use approximations when writing. I have seen some students who are so afraid
of making a mistake that they will not even try to write, but that did not seem to bother Yadira.
The next strategy she remembered using was counting by tens. Apparently, the grouping
and counting by groups of numbers had really stuck with her! I had her write this also. She did
not automatically remember using the number line, so I took it out to see if that would bring it to
mind for her. We also started looking at the book I had made for her about “adding on,” to try to
remember how we figured out those problems. With some prompting, Yadira did remember
“removing” by going backwards on the number line. She decided to call that strategy “number
line.” However, we might have to return to that later and name it something else, because we
have also been using the number line for subtracting by “adding on.”
Yadira did not remember the strategy of “adding on” at all. We looked through the pages of
the book that we had considered last week, trying to remember how that strategy worked.
However, I ended up showing Yadira again, because she said she still did not know. I was
surprised she had not connected with this strategy, given how strong she is with addition! I also
had her add this to the strategy list before we moved on.
We picked up where we had left off in the “adding on” book. The problem posed was the
following: “There are 11 computers. The teacher gives away 7 computers. ______ computers are
left.” Yadira loves computers, which is why I had created this problem. I thought she would
connect with it. I had drawn eleven computers on the page, and eleven in a row (as if on a
number line) on the page below. First, I asked Yadira to tell me in her own words what we were
trying to figure out. I was going to ask her next what strategy might work the best to help us to
do that, but instead, I saw her looking at the page. What she said to me was, “Four.” She had
completely moved on past thinking about how to do the problem: she had found the answer. So,
naturally, my next question was, “How did you get four? Tell me about your thinking.” I had
noticed that Yadira had been looking at the computers on the page, and I wondered if she had
visually counted how many would be left. As it turns out, she had done just that. We decided to
call this “looking at what is there,” and Yadira added it to her list of strategies.
I asked Yadira if there were any other strategies on her list that we could use. She did not
think of “adding on.” She did think of “removing” and we did that on the number line, starting at
eleven and counting seven to the left. Then, I suggested we try “adding on.” I guided Yadira in
how to use this strategy on the number line, by starting at seven and counting up to eleven to see
how many were left. Nevertheless, she did not really connect with it. We talked about how we
might represent what we did with this strategy in the book. Yadira drew some arrows to show
that she counted up (to the right on the number line) from seven to eleven.
The next problem posed (and the last in the book) said the following: “The teacher has 20
pencils. The teacher gives away 15 pencils. The teacher has ____ pencils left.” I chose to involve
pencils in this problem, because I was thinking Yadira might represent those with lines (or tally
marks). I had seen her do that before. She could not remember how to use the strategy of “adding
on,” so we talked through it and tried it on the number line. Then, I asked Yadira how she
thought she would represent that in the book. She and I worked through this together and decided
that she could draw a number line. She did this, with boxes and numbers in them, and she made
arrows to show how she counted up from 15. Nevertheless, she still did not seem to connect with
this strategy. She had not yet grasped how to use it on her own, or why it worked.
Although we did not get to finish the pizza business or connect with the “adding on”
strategy in this lesson, I can see that it is time to move on and try something new. Since Yadira
seems to connect so well with counting by fives and tens and, in fact, told me this time that those
were her favorite strategies to use, I think it makes sense to try subtracting by making jumps of
ten backwards. On another note, Yadira made me a picture again today! We are building more
rapport each time we work together, and I want to also help Yadira to build rapport with math. I
believe this new strategy will help. It could help her to experience more success with subtraction.