Challenge 3

Jim- Jim tried to strategize during his testing, but ended up guessing several times. He was throwing out random numbers and not really thinking about how his answer would make sense. However, he did know at one point in the video that "3 comes before 4". As Jim's teacher, I would focus heavily on the concept of a number. I would not only re-evaluate his knowledge of what number comes in what order, but I'd also evaluate his knowledge of conservation. I would stress that he knew that the number 3 represented three (1.2.3) cookies, or three stuffed animals. After this, I would be sure that he understands what the concept of addition and subtracting is. That he knows when he sees the problem 3 + 1 that you are adding one more cookie to the 1.2.3 cookies you already have.

Lauren-Lauren recognizes patterns that she's learned before. She isn't really sure how to explain the patterns, but it's clear that she has previous knowledge of them. She also proved that she knows how to count forward and backwards. If I were Lauren's teacher, I would work really hard with reinforcing her counting skills and then show her how that relates to addition and subtraction.

Elizabeth-Elizabeth can solve most of the problems, but she can't explain how she solved them. She is able to count forwards and understands that 6 is after 7 to solve a problem. She was often confused at whether she was supposed to be adding or subtracting. As Elizabeth's teacher, I would be sure to create some sort of illustration that helps her to visualize the meaning of "subtraction" and "addition" whenever she sees the signs or hears the words "plus", "minus", "add", and "take away".

Derek-Derek is able to count forwards and backwards. As he solves problems we see that he is using his fingers as manipulatives and relies on them in order to count. He proves to be better with addition than subtraction. For Derek, I would provide him other sorts of manipulatives rather than his fingers so that he can learn to count objects and be knowledgeable about conservation. I would also reinforce addition and subtraction with smaller numbers before challenging him with harder larger number problems.