Challenge 3

Each child went through the same basic pattern of explaining their thoughts: they began by saying they "just knew how" or they guessed, then would say they counted or used their fingers.

Derek: In the beginning, when asked how he knew the answer, he said he "just did." When prompted to explain further, he said he decides to stop when he gets to big numbers, so he stopped at 14. Derek said he used his fingers to count up from 7 to 15, and he got the correct answer.

Elizabeth: When doing addition with fictitious apples, Elizabeth always reached the correct answer but her explanation was lacking; she would say she didn't know how she got her answer, she just guessed. Toward the end of the video, she would either say that she reached her answer by "counting in her mind" or "counting up."

Jim: Jim always said "I just thought about it for a minute." In the beginning, he said he didn't count, he just saw it in his mind. When doing subtraction with apples (6-2) he said he thought about it for a minute then took away Five and Six, as if they were proper nouns. When completing a different problem, he said that he knew if there were 4 cows and he took away 1, there were 3 left because 3 comes just before 4. Jim had trouble with larger numbers because he did all of his math in his mind.

Lauren: In the beginning, Lauren used the dots on the dominos to count up. She was not always accurate, but she used the patterns on the dominos to help her. Even if there wasn't a tangible domino there, she imagined it, suggesting she was good at abstract thinking. Throughout the video, she would explain her answers by using her fingers and counting backwards in her mind. When Lauren understood and came up with the correct answer she could always verbalize it.