…the same thing that Arkansas!

That was my CT’s non-math question of the day for W/U; an oldie but goody. The math in today’s W/U consisted of finding: 1) the domain of a rational function y = (8+x)/((2x-3)(4x-1)) and 2) the value for x if the distance between the points (x,11) and (5,-4) is 17. Most students found the first one with ease, while others tripped up, like I did initially, on the second. When solving the problem, the best approach is to leave (x-5)^2, as is, on one side of the equality with 64 (= 17^2 – 15^2 = 289-225) on the other then take the square root of each side to yield x = 5 + 8 = 13 and x = 5 – 8 = -3; as opposed to squaring (x-5) then combining like terms; I’m a little rusty on optimal math approaches. BTW, I wonder if one can be rusty at something they were never good at in the first place (optimal math, that is)??

Things came together between my CT and I today, too. The timing could not have been more perfect. At practicum yesterday, I was asked how things were at my placement and my honest answer was “it is too early to tell but that I thought it would in time.” Well, time wasted no time, and here I sit, happy that my CT and I finally clicked and I’m off and running as a TC with my CT.

It all came together just before the end of my day when my CT and I had a nice chat about my time in front of the class today as well as a plan for the next two days where I will lead a lesson on standard position and co-terminal angles generating a worksheet and homework problems to reinforce the lesson.

As mentioned, I had my first chance to spend an extended period of time “teaching” the entire class today where I reviewed seven homework problems for which the students in P2 requested help. These problems consisted of graphing various functions and relations (linear, quadratic, rational, square root, circle, semi-circle) as well as determining: a) whether each was a function, b) the domain and c) range.

Net net, it went well with much room for improvement, but hey, it was my first day in front of these students and I did not choke, trip, or die of a heart attack, which at my age, and going forward, is something I need to take preventive measures against. Something I do not share with my fellow TCs…fortunately for them!

Looking back on the 15-20 minutes spent in front of the class today, and reflecting on my CT’s feedback, I feel satisfied with my contributions and know specific areas I need to improve upon: 1) write a little neater (this requires me to “slow down” a little – my writing cannot keep up with my thinking…my CT was OK with my writing though so I should table this for the time being), 2) do not introduce new concepts in the middle of others (e.g., I introduced “set-builder notation” while also providing the answer in interval notation – my CT felt this could confuse students or they might overlook it), 3) ensure I engage with the entire class and not just the side to my right and in the middle, 4) learn students names!, 5) compliment them / affirm them more consistently when they respond to a question, and 6) think about what I might say when explaining a problem before I am actually up in front – this will take some time since I am more of an extemporaneous speaker…so if I stick with that approach, which is likely, I need to develop consistent approaches to explaining how to work problems.

Today was a good day, indeed. Glad Tennessee saw what Arkansas!

I’m glad you had a good day, Dave. I think that optimal ways of solving problems are really nice, and I love to see students do it, but it shouldn’t be expected unless it is the explicit goal of the lesson. I don’t even think I’d think to get every term under a square and cancel the exponent out. I’m not even sure if the students would know that technique. Though it makes sense intuitively, I would be hesitant to introduce that method of solving a problem without introducing logarithms first.

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Thanks for the feedback Mr. Z. It coming from you, especially, helps assuage my delicate math ego…which is ALL my issue…darn those hangups! But I shall overcome them!

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