A Socratic Circle Order Share Thingamabob

Alright, I'm back!

Yesterday, in our physics class, we did a sort of inner circle outer circle thing, where we were divided into two groups and one went in the middle of the room, set up chairs in a circle, and discussed a problem referring to direct and inverse relationships while the outer circle used this very cool site in which we could comment our thoughts on what was being discussed. (That had to be THE longest run on sentence. Ever.) At first, I was in the outer circle. We were saying that we were kind of on lost on what they were saying, which mostly focused on the method of substitution they used. We thought we offered good, constructive criticism. Then- it was our turn to go in the circle. These were the main topics we discussed.

• "Multiple x's"- This was something we wanted to clarify as discussed by the first group. There was some confusion for them when given a problem such as "When given a/(bx^2), double x," whether they should double the x before squaring it or after. We quickly cleared that up by verifying, Manipulate the variable as instructed in directions FIRST, before following Order of Operations. 
• We also discussed the values of substitution versus theoretical mathematics. Which is to say- plug numbers in for the variables as an example, or just apply the instructions to the variables and try to solve. Using the example I mentioned earlier: substitution would be 8/(4 x 2^2) = 1/2 and 8/(4 x 4^2) = 1/8, so therefore the answer is divided by four. Whereas theoretical would be a/(bx^2) = y and a/(b2x^2) = y and trying to decipher it from there. I've known for a while that substitution is definitely the easier way for me (as you can see, I have trouble even explaining the alternative) but some had yet to decide their method of choice, so we tried many different presentations of how to do it. 
• When using substitution, we talked about which numbers to avoid plugging in, as they can make your answers all crazy-like, therefore leading you in the wrong direction. For instance, if we had used zero in my apparently favorite example ever, we would have gotten the same answer, as zero times two is...well, still zero. So we decided that zero should forever be avoided, and had a lengthy discussion about using 1 which basically resulted in us coming to the conclusion of Feel free to use 1, because sometimes it works, but sometimes it doesn't, so you have to be careful, because it doesn't always work, except for most of the time in multiplication, and almost always division, but sometimes it doesn't work for multiplication and messes up your results in division, but sometimes it'll work but just be tough to deal with, so only use 1 sometimes. Yeah. 

If you remember from the beginning, the topic was direct and inverse relationships.

As you can see, our class is currently suffering from communication issues. I'm finding myself exclaiming the very title of this blog! (If you don't understand, its because... just leave me a comment. I'll get back to you.) I'll save that post for another time in the near future! I know, I know... She's leaving us hanging?! Shirley that can't be the end of the post!