Student Work Post 2

This is a paper that my mentor teacher had me grade while she was out at recess with the students last week. It is a simple division practice worksheet that has 100 division problems the students have been working on for a couple of weeks now. My mentor teacher used it as a review before moving on to teach the students about long division and division with remainders. In order to remember the division, I expected the students to recall the multiplication facts that they had memorized before learning the division facts, or attempt to use math families. I also thought that the students probably used their fingers to keep track of how many groups of the second number in the problem could be made. Finally, as we learned last week, the students may even think to double in order to get to the multiplication fact they don't know and solve the division problem. I expected the students to use their memorized multiplication facts to solve the problems. I just assumed that my mentor teacher had taught them how to think of the problem in terms of multiplication the way my fourth grade teacher was, which makes division very simple, given that you have your multiplication facts memorized up to 12.

However, while I was grading the papers, I came across this particular student's paper and I thought it was interesting the way that she used paper and pencil to solve the problems involving the division of 11 and 12 that she apparently did not remember. This student wrote out the number 11 or 12 as many times as she thought was the answer, then added them up to make sure that she was right. I find it particularly interesting that she did not use any form of doubling during this process. She simply counted by twos to add up the ones column and then counted the ones in the tens column to get the answer she was looking for. To me, this reveals that even though she has gotten past the more tangible items for counting such as counters or fingers, she has not quite reached the more abstract method of finding the fact family by either doubling or simply doing the two-digit multiplication. This also may have been done before the students learned how to do multiplication with one two-digit number (they just learned it recently), so I think this method would be developed for her if she were to do the worksheet again knowing how to do multiplication that way.

If I didn't already know that they have now learned it, I would suggest that the next steps for advancing her learning would be both multiplication with larger numbers and long division with remainders. However, the students have not learned long division with two-digit answers yet, and I think that will be an important step in advancing her abstract knowledge of division. I also think it might be helpful and a big time-saver for this student to scaffold for her how to do long addition problems through doubling. Maybe show her that it is an option when trying to find out an answer like that, then see if she does it on her own later.