Student Work #5

            The purpose of this worksheet was to see the student’s level of understanding on the concept of joining numbers (addition). This follows under the standard “N.MR.00.07 Compose and decompose numbers from 2 to 10, e.g., 5 = 4 + 1 = 2 + 3, with attention to the additive structure of number systems, e.g., 6 is one more than 5, 7 is one more than 6.”  It is designed to elicit student thinking because students are supposed to individually count the animals and then join the two sets together. This is intended to help students understand how addition “number sentences” are formed and that the numbers represent actual things.

            This worksheet had the student write the number of animals under each group that was shown and then combine them and write the total. There are not multiple ways the student could approach this problem. There are directions given which state to “write a number for each group then have them circle to join the groups and write how many there are in all.” This is the first indicator that this is not a high level task for the student to solve. As a result of this, I could only anticipate that the student was going to do what it says. The only possible errors the student could make would be counting the wrong number of animals, resulting in him recording the wrong number, therefore getting the wrong total.

Steps taken to approach the problem:

(Student counts 2 ducks and writes 2 below them, then counts 5 ducks and writes 5 below them. The student goes back to the first group of ducks, counts them, and then continues counting on, going to the next group to add the 5 other ducks. He writes 7 for the total.)

Me: (first problem) “How did you know how to do that?”

*Mitch: “I just counted quietly.”

(Student solves the second problem just like the first problem)

Me: (second problem) “How did you do this one? Any different from the first one?”

*Mitch: “Well I just kinda actually counted in my brain actually. My brain whispered it to me.”

Me: “Oh. Can you show me how you counted in your brain?”

(Student whispers as he counts off each rooster, starting with the first group and continuing to the second group)

Me: (third problem) “I noticed you were covering up some of the ducks when you were counting. Why did you do that?”

*Mitch: “That’s what my dad does when he is counting a lot of things on the page. I just covered 4 and then I see what it like was. You cover the rest of them, and you have to count all of them, and there’s a lot, and then I can’t remember which ones…if I counted it already or not.

Me: “Oh, I see. So you covered the ducks up as you counted so you wouldn’t accidentally count one again?”

*Mitch: “Yep, that’s what my Daddy does and he showed me that.”

            Something I found interesting that *Mitch did with these problems was that he would write the number for each group, and then instead of looking back at the numbers he had and combining them, he went all the way back to the beginning and recounted all of the animals together. So, for the first problem, he counted 2 ducks, then 5 ducks, and then went back and started counting from 1, touching each of the ducks. I thought he would just look at the numbers he had written and add them. Based on *Mitch’s mathematical thinking, I can hypothesize that, *Mitch can solve addition problems with the numbers 1-10 by counting drawings.

            To advance *Mitch’s thinking, I could ask him to make different groups of animals to represent the total amount. For example, in the second problem, the answer was 9. So, I could ask him to show me how he many ways he could group the roosters to make 9 altogether. I could also add an unknown group into one of the problems and put the total number, asking the student how many roosters would have to go in this group to make the total. For example, there would be the group of 1, the group of 8, the unknown group, and then the total 12. The student would have to figure out that there would be 3 roosters in the unknown group. This is not as high of a task as the other possible question, but would change up what he was doing instead of the same procedure over and over.