addition assesment

The first time i went to Lorri's class I noticed one student who was having difficulty with her self start math facts. She (BC) usually finishes all of the problems, but has few of them correct. They were working on addition facts, adding 1,2, and 3. When I noticed this I asked her to show me how she new the answer and indicated one that was correct. She showed me on her fingers and counted all. When I asked the same question about one that was incorrect she used the number line, put her finger on the first number and began counting up. However she began her count on the first number instead of the next number and many of her answers were one less than the correct answer. I worked with her to fix a couple of her answers, but she tired of it quickly and I didn't persist.
So I knew she was using the number line incorrectly, but it also seemed like she sometimes just put any number so she could be done quickly. I knew from our math methods text book that number line strategies are more difficult. I talked with Dr. Tuft and she said BK probably need more addition practice that is contextual and that possibly she just needed a little one on one instruction.
The next time I talked with Lorri she said I could plan a one on one or small group math activity(this activity was conducted on Fri, Oct 2).
I studied from the text more about developing meaning for the operations. I decided that a math story, or story problem could serve as an assessment and a learning activity. From the text book I chose, "Sandra had 5 pennies. George gave her 3 more. How many pennies does Sandra have altogether?"
I wrote this at the top of a scrap paper for each student and provided pennies and small round counters. Lorri selected four children who she is least unsure of their addition understanding. The students were excited to come to the back table with me. I told them we were going to read a math story and work on the answer. I gave them their papers and read the problem out loud. Almost before I was finished they were counting on their fingers and raising their hands, anxious to tell the answer. I told them i wasn't ready to hear the answer. I wanted them to think about how they could teach a kindergartner to figure out the answer. I also wanted them to write or draw on their paper how to teach someone else to figure out the answer.

MK drew a picture of his family and wrote, "I culd teach my little brothre and hes in kidnergarden." When i asked, "how would you teach him?" He replied, "I would teach him to be good." He did eventually count out pennies but when he counted the initial sets of 5 and three an extra was hiding under his sleeve and he didn't notice when he slid the piles together, so he had 9 pennies. HY helped him separate them into 5 and 3, and identify the extra, then he counted 8.

HY talked to an imaginary kindergartner as she counted out pennies. She drew five ooooo, added three more ooo, next to them. She counted them all to make eight then said, "then add 2 more." She drew 2 more to complete a ten frame pattern and indicated that there were ten.

RC wrote on her paper. "you can cat the pienes (count the pennies)" Her drawing shows 7 dots. When I asked her to show us how to teach a kindergartner how to figure out the answer she indicated her counters (5 pennies, 2 red counters, 1 blue counter) and counted up, "5,6,7,8"

HL wrote, "I wunbe hlep theym doow mathe and a storey(I would help them do math and a story)." Her drawing shows us at the table. One figure has a speech bubble: "I wunt to do math." On the table is a group of 5 dots, a group of 3, and the number 8. She chose to represent Sandra's pennies with red and blue counters. She used 5 red, line them up and continued the row with 3 blue. When I asked her why she did it that way she said it made more sense. I wish I had been better at helping her define why it makes more sense, but I felt a little stuck about how to go about helping her with out giving her my words.

What I learned:
MK's paper shows the least understanding of the concept. His work with the manipulatives does show that he understands the story is a joining of 2 sets, and that he can find the "altogether" amount by counting out the two sets and counting all. If i have a chance to work with him one on one I'd do several more stories like this having him show the story with the counters and I would model some ways to represent his work on paper. Then ask him to show how he knows the answer by drawing a picture.

HY's work with the story suggests she is verbal and social. I'm not quite sure what to do next. Possible a few more stories and an assessment of her understanding of these symbols +, =. I'd like to ask her if she can show what she did using them in her drawing.

BC I was surprised to notice her count up as i hadn't seen her use this strategy on her fact sheet. I think she could benefit from the same activity as suggested for MK. This would improve her communication about what she knows and give her contextual practice. I'd also like to work with her to represent joining stories using a ten frame. To strengthen her understanding of the relationship of other numbers to ten.

HL's counters show a strong understanding of joining two sets. I think she could Join HY in the suggested activity.

I repeated the same activity with 5 more students. Most of this group traced or drew circles and made them into number sentences: ooooo + ooo = oooooooo (or 8). TL and ML possible used the + and = sign when they saw their neighbor use them.

SN drew two boxes with a set in each. Then she wrote the fact family for 5,3,and 8.
AN finished before most of the group and asked now what do I do. I remembered HL adding 2 more to get 10 and asked AN, "How much more does Sandra need to buy a candy that costs $.10?" He wrote, "3+8=10" When I asked him to show me how he knows he used the pennies and discovered his error.

I think the whole class could benefit from a math story instead, or alternating with, fact practice each morning.

I tried to scan their papers but couldn't get the scanners in the labs to work :(. I will try one more time. Sucess with the scanner! Student papers added.
The next Friday I spent in Lorri's class I taught a math lesson in the launch, explore, explain format. I'm anxious to blog about it but this blog has taken me awhile, so I think it will have to wait :(.