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# Guided Reflection, Field Notes 2/15

What Happened?

When I arrived at my field placement last Friday, the class was just finishing a math lesson on solving two-step stroy problems involving subtraction and addition. As is their routine, after the class was finished with the lesson, they played a math game independently. Today's game was called "Spin-and-Add"-Each student was given a spinner with a series of three-digit numbers, and they were supposed to spin the needle and add the first two numbers that it landed on. My cooperating teacher, Mrs. Dolly, asked me to work with two stundents, Wendy and Joel, both of whom do not have the "number sense" that their peers do. Their spinners were only numbered 1 through 9. For Wendy and Joel the goal of "Spin-and-Add" was to practice "counting on" using their fingers.

Although I was working with both students, I found myself having to focus primarily on Wendy. Although Joel occasionally had trouble understanding that each finger he put up corresponded to one number, it seemed that he began to realize the process the more that he practiced. In contrast, Wendy did not seem to be understanding at all. She could add numbers that totaled less than 10, but struggled with anything that required more than two hands to visualize. For instance, on one of her spins, Wendy got a 4 and a 7. Our conversation was as follows,

Me: "So what two numbers are we adding?"

Wendy: "4 and 7."

Me: "What is 4+7?"

Wendy: "Um, 6?" (she did not even attempt to use the counting on strategy that we had been practicing)

Me: "Let's use our fingers to help" (I tried to demonstrate "counting on" and when we reached 10 and still needed one finger, I put my own finger next to her 10 to represent the last 1)

Me: (looking at our fingers) "So do we know what 4+7 is?"

Wendy: "6" (looking me directly in the eye and not looking at our fingers)

Me: "But is 7 bigger or less than 6?"

Wendy: "Bigger."

Me: "So can 4+7 be 6?"

Wendy: "No."

I then counted the fingers that we had put up with her and we determined that 4 fingers, plus 7 more fingers is 11 fingers.

Why Did It Happen?

Initially, when I saw that Wendy was struggling to add, I assumed that she was guessing the answers rather than trying to figure it out using the "counting on" strategy. I was frustrated because it seemed as though she was not even trying to understand when I explained how she should be using her fingers. I thought she was not listening because she would be looking at me as I explained, but she would be looking me in the eyes rather than looking at what I was demonstrating. However, toward the end of the activity, I began to notice a pattern; Wendy was having the most trouble with problems that could not be represented with just her two hands, such as 4+7 which equals 11. This made more sense to me, especially when I watched her try to figure out what to do when she reached 10 and ran out of fingers. Not having enough room to do the problem on her fingers, immediately confused her; she forgot what number she was on as she tried to go back and re-use fingers.

While I initially assumed that she was not listening because she was looking me in the eyes, instead of at my fingers, while I was trying to demonstrate "counting on", I now realize that this should not have been interpreted as a sign that she was distracted. Rather, she was confused and was still trying to respectfully listen, even though she did not understand.

What Might It Mean?

This experience reinforced that teachers need to be flexible in the way that they explain things. Although the class had been using their fingers to learn the "counting on" strategy, the same number concepts could be taught using manipulatives. This would have eliminated the confusion that comes with running out of fingers when the sum is too large. Although I am only a teacher's assistant and did not feel comfortable changing the strategy that the students had been taught, in my own classroom, this would have been a situation in which I would have altered the way that I explained the concept.

What Are The Implications for Practice?

In conjunction with being a flexible teacher, this exchange with Wendy reflected that students learn in different ways and teaching methods should reflect this. While "counting on" using his fingers was effective for Joel, Wendy struggled with this strategy. Although I was able to manage two students who required different types of attention, this experience caused me to think about how I will handle a classroom in which there will be more students who are not understanding, and who may not be understanding for a variety of reasons. This is why I will need to incorporate activities and strategies that appeal to different kinds of learners. This way, students will have a bank of resources and strategies that they can use to critically think and solve problems.

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