Posted at Sep 14/2018 12:42PM by Stu 4:
I have not yet written my essay, so this is only the beginnings of an idea that I will flesh out later. I was impressed with the technicality of language as well as the sophisticated and technical vocabulary that the authors used to describe their findings.

I shared many of the same ideas and came to many of the same conclusions as the authors; however, I did not have the depth of knowledge concerning psychology, theoretical constructs, math ed jargon, etc. to be able to rigorously defend my findings.

Maybe describing this in the context of a mathematical proof will make more sense. When proving things in Real Analysis, Stu 9 and I will often try to create a picture to help us understand what is going on. Initially, this picture is incomplete and does not work for all situations required in the proof. Eventually, we work out all the kinks and have a visual created that seems to cover everything. But then we have to go back to the beginning and rigorously defend what we have done. Most of the time, understanding the picture is not enough to create a rigorous proof. I must conceptually understand the topics and the definitions of each underlying element of the picture to be able to rationally defend why the picture holds the answer for the given situation.

After reading the article, I definitely feel like I had a slight grasp on the overall picture but lacked the deep-rooted understanding of the technical details and philosophies necessary to create a coherent and rigorous argument to support my findings, as the authors have done.

Posted at Sep 15/2018 12:07PM by Stu 1:
Stu 4, I felt the exact same way. I felt that the conclusions I made in my paper were similar, but definitely not expressed in the effective manner they were in this paper. In fact that is exactly what I struggled with when writing my own analysis of the videos. I had all of these ideas, but I did not know how to put the ideas together in a cohesive piece or flow of words. I really enjoyed reading this paper, learning new terms, and trying to decipher what theoretical constructs were being used.

Posted at Sep 15/2018 12:26PM by Stu 9:
I don't think I did a great job focusing on the constructs. I think because I am still forming my own definition of a construct, I looked at the first paper as more of a summary than actually putting my own thoughts about the underlying constructs onto paper. Reading the article though helped make some clear connections I was struggling to make last week. I agree with Stu 1, I really enjoyed reading the article.

Posted at Sep 15/2018 04:45PM by Stu 7:
As an overall thought I too summarized what I thought happened in the videos rather than breaking it down by excerpts like it did in the Article. The way the article broke it down made it a lot easier for me to see all of the claims explicitly. I too really enjoyed reading it. I also think that having some background knowledge about the purpose of the videos in the article provided some clarification for why and what Bill did in the video lessons. Not having this knowledge before made me feel like I was making too many assumptions while writing our first assignment. For example, I wasn't sure where Bill's understanding was. Therefore, I couldn't speak on the reason why he was using examples as explanations of reasoning or correct answers as confirmation of moving on to the next activity.

Posted at Sep 16/2018 03:29PM by Stu 2:
Yes! To jump off of what all four of you have said, (and I know I've had this conversation with Stu 1 as well). I find myself to come to the realization that my vocabulary and knowledge these constructs and theories is my downfall in writing these papers. It is as if they simplify this long proof of what is happening to this sweet, simple coherent proof of 3 lines (hahaha)

Posted at Sep 16/2018 08:59PM by Stu 6:
The "Teaching Gap" addresses that U.S. lessons focus on learning procedures and do not focus on building deep thinking and conceptual understanding. Yet Bill's procedures are deeply connected to his conceptual understanding of rate. So which comes first? The chicken or the egg?

Posted at Sep 16/2018 09:32PM by Stu 2:
Good point Stu 6! This makes me wonder if most U.S. have a similar dilemma as Bill...

Then I asked myself a question, Do teachers believe that the conceptual understanding of some topics is embedded in the procedures? Is there this notion that the conceptual understanding of "speed" or any other mathematical topic can be learned through countless amount of procedural problems?

Posted at Sep 16/2018 09:34PM by Stu 10:
I'm still struggling not to get defensive and insecure at every juncture. Every difficulty Bill has expressing himself to Ann sounds like twenty problems I've had expressing myself to my students.

Back to comparing to my notes.

Posted at Sep 17/2018 03:47PM by Stu 7:
Stu 2, Overtime I have come to see some context behind some of the procedural problems I used to do over and over again, however, that was much later when I looked back and reflected. I am not sure how others are but I would safely assume that when going back and teaching a class, teachers have to review the material a bit. While reviewing the material, maybe it clicks for them. Then they teach the procedures because one day if students work with the material later they will have the same light bulb effect. I am not sure if this makes sense for everyone but maybe thats how some might be.