Amy Gaisser
Dr. Bloom
ED 316
Reflective Writing About Session #1 on September 13, 2011
Yadira and I first met in the morning, when she was working on a worksheet in Mrs.
Harden’s class. This worksheet had 10 x 10 squares (meaning that there were 100 squares total in each of the big squares). These 10 x 10 squares represented the block manipulatives that the kids use. Yadira was to add the big square blocks that were pictured together. For example, one 10 x
10 square + one 10 x 10 square = two 10 x 10 squares = 200. What I observed, however, was that
Yadira thought of the 10 x 10 squares as representing 10, rather than 100. Thus, she arrived at the answer of 20 for that problem. I think the concept of multiplication (i.e., 10 x 10) was new to her. She seemed most used to the base-ten blocks that had ten little squares arranged in a column.
In an effort to help her understand the value of the 10 x 10 square, I tried to break it down by first asking Yadira how many little squares were in the base-ten block pictured on her paper. I noticed she counted by ones starting with the first square. (This showed me she was confident in her ability to count by ones.) She said, “ten,” demonstrating her understanding of hierarchical inclusion. Then, I pointed to another base-ten block and asked, “How many squares does this one have?” I wanted to see if she saw that they represented the same value, and she did. So I asked how many squares we would have if we added those two base-ten blocks together, and then we added another, and another… up to ten times (for a total of 100). Although Yadira started by recounting all the squares in the first one and counting one-by-one in the second, she eventually switched to the more efficient method of skip counting by tens. Yadira then used her knowledge of part-whole relationships to realize that, since these base-ten blocks made up one 10 x 10

square, that 10 x 10 square must also equal 100. After this realization, she was able to calculate this and other problems (still with some support) that involved 10 x 10 squares.
What was most important about that initial time I met her, however, was not the value of the
10 x 10 square, but the knowledge I gained about the math concepts that she already knew
(counting by ones, skip counting, hierarchical inclusion). Additionally, I gained some knowledge about her as a person when we worked together later on in the day, and the get-to-know-you activity we did really helped provide a way for me to start to build rapport with her. This was crucial, because, as I noticed very quickly, Yadira was quite shy. Building that rapport was going to help her feel more comfortable sharing her mathematical ideas with me (and others).
For our get-to-know-you activity, I had Yadira work with me to create a Double Bubble graphic organizer, so that we could learn what things we had in common and what made us unique. I had written on the posterboard some topics that could get our conversation started, such as “interests,” “colors,” “food,” “subjects in school,” and “animals.” Yadira and I ended up finding out that we had a lot in common. For example, we both liked pasta, fruit, the colors blue and green, art, computers, puppies and Princess Belle. Some things that were unique to Yadira were her love for pizza, Barbies and the color pink. Also, a significant thing that was unique to me was that I like math. Thus, I found out that Yadira’s disposition toward math, for whatever reason, was not particularly enthusiastic. Perhaps, I could help her to enjoy it a little more.
After the activity, I conducted an interview with Yadira. I asked her if she had any siblings, and she said she had four sisters. When I questioned what their names and ages were, she said that Jennifer was 13, another sister was named Carmen, and that she did not know any more information about the others because she had not met them all. This surprised me and I decided

to not ask any additional questions that were related to her family, just in case there was information that should remain confidential. (However, I did later come to find out from
Cassandra Faulkner, a secretary at Central Elementary, that Yadira comes from a great and very supportive parental background.) Yadira had a long list of friends! I stopped her after she named six of them, but she could have kept going. Their names were (pardon my spelling) Aristóle,
Vanessa, Ashanti, Emily, Taisha, and Leila. With these friends, Yadira likes to play tag and chase boys. I used this information to personalize the mathematical questions I asked her next.
From the mathematical component of the interview process, I found, once again, evidence to support the fact that Yadira is very confident about her abilities to count. When I asked her how high she could count, she said, “900!” Though I stopped her at 36, she certainly could have kept on counting. I found she knew a lot about number order. The only unorthodox answer she gave me was that 200 came after 100, which could actually be correct, since the question does not specify the next whole number after 100. Yadira had difficulty explaining her thinking to me when I asked about that answer. She just smiled and waited for me to move on. I am not sure she knew how to think about her thinking (or use metacognition). Or, maybe she was not sure how to put her thinking into words in order to explain it. I found that Yadira was not as confident about the concept of skip counting, even though she skip counted by ten earlier. She did know how to skip count, but was reluctant at first to do so for me. She seemed unsure of her ability to skip count. Despite the high “affective filter” she had for this concept, she did well with skip counting by 2’s, 5’s and 10’s. 100’s were tougher: she went by 1’s instead (i.e., 100, 101, 102, etc.). I really took note of her concept understanding and her confidence level with the various concepts.
Finally, we had time left for three story/word problems. The first was “Jennifer has 5 apples. Her mom gives her 3 more apples. How many apples does she have altogether?” Yadira’s

answer was 6. She either did not choose or know how to explain her thinking to me for how she arrived at this answer (or the answers from the other story problems). I did notice, though, that she gravitated toward making pictorial representations of the problem with markers and paper. In this case, she made dots and added them together. I think, to get 6, she must have just lost track of the numbers she heard me say or how many dots she had made on the paper. The second problem was “Carmen has 4 pizzas. Her friend gives her 5 more pizzas. How many pizzas does
Carmen have altogether?” Yadira said 9. Her pictorial representation is of 4 triangles, a plus (+) sign, and then 5 triangles. She clearly showed her thinking through that representation. The third problem was “Ashanti has 9 toy cars. She gives 5 toy cars to her friend. How many toy cars does
Ashanti have left?” Yadira said 5. Again, I think she just lost track of the number of tallies (or lines) she had put in her pictorial representation. But she sure had a great strategy: draw 9 tally marks (she actually made 10 of these), and cross out 5 of them. I really learned a lot on this day about Yadira’s strengths and areas for growth as a mathematician, and about her as a person.