NAEP Reflection

 Based on the seven pieces of student work on the gumball problem, I learned that this problem shouldn't be assessed or graded as just right or wrong. To properly assess student learning or student knowledge using this problem, teachers need to understand the student’s thinking. If they got the right answer, teachers need to determine if the student actually understood what the problem was asking and how to use probability to get that answer, or if they just guessed. That is important in this problem specifically, because the problem basically asked the student to give an answer that was an integer between 1 and 10 and the correct answers were 4-6 so if a student guessed, they still had a 30% chance of getting it right even without understanding the problem or the concept of probability. If the student got the wrong answer, it is also important to understand the student’s thinking. Some of the students got the wrong answer because they really didn't understand probability. Some also got the problem wrong because they didn't understand what the problem was asking, but it is possible they understand probability and were just rushing and didn’t fully read the problem. It is also possible that the student is struggling in reading but is very strong in math and would have gotten the correct answer if the problem was read aloud to them.

Based on the work presented by other groups in the class, I learned how creative kids can be when trying to solve math problems or trying to show their work. In the other videos my classmates made of their problems, I saw a wide variety of students using words and pictures to express their thoughts or try to work through the problems. In the problem about the rectangle and the parallelogram, students used a variety of different ways to describe the similarities and differences between the two shapes even if they don’t know the technical terms for what they are describing. I also liked the pictures drawn in the pizza problem when the student was trying to say that the pizzas could have been different sizes when each person ate half.

Based on the student work feedback I came up with, I learned how much scaffolding is needed in math, how beneficial small group instruction can be in mathematics, and how difficult it could be to scaffold students when doing full-class instruction. When thinking of the feedback I would give to each of the three students, I originally assumed I would be giving them the feedback while working one on one with them. Then when I continued on with part two of the project, the directions asked what I would do for the next steps of instruction for the whole class, which made giving students feedback significantly more difficult. I decided I would touch on the things that multiple students in the class didn't understand and things that could be quick fixes, such as students not reading the problem. Even with this idea, there would still be students who got the problem right and don’t need further help with this concept but I didn’t know how to give them extra work while also incorporating the rest of the class.