Entry 2 week 3

What We did This Week.
This week was actually kind of slow. We didn't do any labs but went over one packet that we got last week. This was supposed to only take a day and a half, however, this ended up taking the whole week. This was mainly due to the fact that we could not for the life of us focus on the task at hand. The fact that we are left to our own devices at the beginning of class didn't help, or having some kids go off on random tangents (drawing winter in Hawaii for example) especially when there are few kids wanting order.

Day 1
On the first day it was a standard day, we got in, settled down after a long while and started to discuss the packet. I of course was very nervous because I hadn't fully understood the packet but tried to do it anyways. We discussed the topics in small groups with the people at our table, and from the looks of things, no one else understood what to do either. No one else even completed the packet. The only reason I even guessed was because I remembered some of the things from Algebra 1. This caused major confusion and some heads being butted. Like when the teacher said to talk about the characteristics of a directly proportional line and I said it must go through the origin, while one person disagreed. That was not fun. I believe the teacher could see this confusion because the next day all we did was talk about those equations and their characteristics.

Day 2

On day two the teacher decided to do a type of Socratic Circle, only with a few catches. For instance, there were two different circles and each of them were having a different conversation. One circle was actually talking and the other was communicating via a type of texting website. There were many problems that came with this. For instance, trying to picture the tables in our heads was impossible, trying to keep up with the conversation was difficult, trying to multi-task between texting and listening caused people to get lost, and trying to make connections/ comments about the things being said was just not possible (except in a few places). Although, the conversation that happened during this new experience suggested that most people had the same issue that I did, not understanding. Next is what the first group talked about. They were charged with explaining what would happen in the equation y=a/(bx^2) if each of the variables were doubled while the other two stayed constant. For instance changing a but leaving b and c the same. What they decided would happen is if a doubled so would y, if b doubled then the equation would be halved, and if x was doubled then it would be cut into fourths. The first group explained this in three ways, one was with math and logic, another involved using actual numbers, and finally there were people that just used common sense. The group that explained this stuff was very good because there were no real dominators, they also got the idea to use white boards to show the math, and there was even a girl that after every point explained the concept. Then there was my group. My group was tasked with explaining the equations y=kx, y=k/x, and y=k/x^2. However, instead of all of the wonderful things that the first group did we did the exact opposite. We moved fast and almost the whole conversation was ran by three people. We did however use white boards and tried to explain why did what we did (even though later we would discover that was wrong). Our findings was that the first equation would start at the origin and be linear, the second equation would be doubling, and the last equation would be decreasing by a factor of 4. It was a very confusing time for the whole class. We ended the day by explaining what directly proportional, inverse, direct, and indirect. These would be further explained the next day.

Day 3
On this day we would go even further into the parent equations of direct, indirect, inverse, and proportional functions along with there qualities. We decided that in order for a function to be proportional it would need to go through the origin and go up at a constant rate. We also discovered that this equation can also go under the category as a direct variation, however, this can not be reversed. In addition to those findings we also discovered that direct variation means that an equation goes up on both axis or down on both axis, this can be compared an indirect equation where each axis varies in which way it goes. We also discovered that direct/ indirect equations don't have to be just linear, they can inverse, quadratic, and exponential too. This was a huge change from what I originally thought.  Then with inverse we discovered that they will never touch an axis but each axis will be the inverse of the other, so instead of being divided by 3 the other would be times 3. However, these findings were after much debate and a lot of being off topic. We finally ended this day with creating white boards for the rest of the labs in the lab-o-rama. We however did not get to talk about them.


Final Thoughts
To begin with, I liked the fact that we did go so much into detail about these issues because for me it did clear up some of my questions. I also liked how it was run by the class and we ultimately created a set list of criteria for each of the graphs. Then, some of the things that could be improved upon is the having us stay on task more so. I also believe that the texting portion of the second day needs to either be really reformed or gotten rid of completely. Finally, I believe we could have had some more background information on the first day about the packet or maybe filled it in as we went through the week instead of having us try to do it before hand.