The students were given a math message on the board to start off the lesson. The questions on the board were 10, 12, 14, _, _, _.& 34, 36, 38,_,_,_. & 124, 126, 128,_,_,_. I walked around and observed the students. One girl, Maya, was crying and so upset that she didn't know what to do. I helped her to notice what the numbers were doing from each one to the next. She looked at the number grid at the front of the classroom and was able to figure out that the numbers were counting by two. I noticed that she was fine with the first two problems, but struggled with the third problem. She wrote down: 124, 126, 128, 129, 130, 131. I assume that she had a harder time with this problem because the number grid only goes up to 100. I believe that Maya still knows how to count up, however counting by twos was a struggle for her.
To advance Maya's thinking I would circle a grouping of even numbers on the number grid (2,4,6,8). I would ask her to tell me all of the things in common with those numbers. She will get to the fact that they are all even numbers. I will tell her that when we count by twos, the numbers can only be even, so to check our problems, if the number is odd, then we messed up along the way.
Another way to further her thinking would be to give her manipulatives and have her group them in two. Then I would have her tell me to count the whole group of items, by twos. This would help her practice counting by twos while having something concrete to use as a guide.
This is a great example. It seems very simple, yet might reduce students to tears. Also, even though the student understands part of this problem, other variations result in misunderstandings.
ReplyDeleteI think that it is very clear that the student simply does not appreciate the artificiality of the problem that is presented, even though the student may know how to count. One way in which I would try to advance the students understanding is to ask her to create her own number pattern (and then to create a similar number pattern: e.g., 1, 2, 3 & 8, 9, 10, or 6, 8, 10 & 30, 32, 34). Students could compare number patterns and test to see whether the two patterns are identical. This would have students defend their thinking to one another and indeed result in a high level of cognitive engagement. I love this example because the same concept / procedure when presented as "fill in the blank" leads the student not towards cognitive engagement but towards an emotional breakdown.