This sample of work is the pre-assessment that I gave my students this week before planning for my GLT math unit that will focus on subtraction. The first two word problems show eraser marks that change the addition symbol to a subtraction symbol. This shows a possible misunderstanding about what each of the symbols really represents conceptually. However, this student did correct his initial errors. It is unclear whether he looked at someone else's paper, or if he re-read the problem and changed his mind. Additionally, I find his interpretation of the first word problem quite interesting. Instead of subtracting the 3 pickles that are remaining from the initial amount to determine the unknown change, he either counted backwards and found the unknown change and wrote the corresponding number sentence, or he placed the final amount of pickles on the other side of the equal sign and found out the missing number of the number sentence.
The most revealing information from this pre-assessment comes from the column subtraction problems. This student chose to use tallies to represent the minuend and then crossed off the number of tallies of the subtrahend. With all three of these problems, the student used the same approach, even though #5 was a simple subtraction problem where students could have used their fingers or just counted backwards. He miscounted his tallies and his answers were all off by 1.
One next step for working with this student would be to have a discussion with him about how we can use tallies/drawings to represent problems with smaller numbers, but when we have larger numbers, it is not only time-consuming, but also easy to lose count of so many tallies. This leads to a conversation about having a system to increase efficiency and accuracy (borrowing, working in columns). I would also like to ask him about the changes he made in #1 and #2 with his mathematical symbols to gain insight about his understanding of when to use the different symbols and their meanings.
This is a good example; again, since the child is able to do the work with his own method, but not yet with the "most efficient" method, you might give students a problem to solve; have them solve it; and then have a whole-class discussion in which students present their different methods. You might select / sequence the responses so that this student goes first, followed by the more efficient method, so that the student can make the connection: the two ways are equivalent.
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