Posted at Sep 16/2018 01:59PM by Stu 8:
From what I have read, the article talks about many of the same things I thought of when watching the videos, but in much more detail. With the context of Piaget's theory of how children develop concepts of rate, there is much more insight into what Ann may have been trying to do when using her repeated "division" in activity 1 and struggling in activity 2.

Aside from this, the article gives a lot more context for what Bill may have been thinking about and doing in the first two lessons. While I did notice that there were times when he did not ask Ann to elaborate on her calculations or clear up confusion that may have indicated Ann did not understand the concepts as well as he thought she did, it did not occur to me that Bill may have wanted Ann to "move through the tasks" in the activities. I am skeptical at this point as to whether this was Bill's intent or whether it just happened automatically, but either way, it is a good detail to notice.

On a related note, Bill did seem satisfied with Ann's calculations when they were correct; he seemed to assume that she understood the concept associated with them if she was undergoing the correct process associated with the task and finding the right answer (assuming no errors). This suggests that Bill forgot it was important to question Ann regardless of whether or not she was correct. For all he knew, she could have guessed or used some instinctive idea that seemed related to the solution of the problem; this does not mean she fully understood what (conceptually) she was doing or why.

Posted at Sep 17/2018 04:31PM by Stu 6:
I did not notice that Bill was returning to calculations because it was closely tied to his conceptual understanding of rate. Like you Stu 8, I noticed that Bill thought that Ann understood the concept of rate if she was doing the calculations. I didn't pick up the reason why.