So, another good day of discussion at day2. We touched on the topic of homework--how much, late policies and such.
We also did some more activities that tie to Calculus--I love them and so far everything has been appropriate for even a regular Algebra classroom. I can't say too much how much I appreciate our facilitator and group. It's so nice to be young and lower on the experience ladder myself, and yet still feel that my thoughts and opinions are appreciated and valid. I'm having lots of fun and it's nice to realize I can still remember some of my calculus basics.
Anyways, here's an interesting problem I ran across a few months ago that came back to me today when we were discussing 0 as an exponent and 0 as a divisor.
When we teach rules of exponents in Algebra, we usually give them problems where they are told to simplify and than substitute numbers in for the variables. So here's one of the problems I ran across on a worksheet that stumped me as to what would be technically correct :
Evaluate for x = 0: (3x^5)/(x^2)
Is the answer 0, or undefined?
We've had so much fun discussing technicalities and such. We were talking about "no real solutions" and such and the thought struck me that when one is looking at the graph of a quadratic function that has no real solutions, and you ask for the "zeros"--saying that they don't exist isn't technically correct because they do exist on the imaginary plane. I guess it would be still correct to say that x-intercepts do not exist because the graph does not cross the x-axis....I guess it depends on how you define "zeros" and "roots" then........ I usually see roots equated with solutions, thus you have imaginary roots sometimes, and zeros equated with the x-intercepts--but I think that zeros might be defined the points where y=0. Quadratic Roots/Solutions/Zeros/X-intercepts has been one of the things recently discussed for clarification because solutions don't have to be x-intercepts--but happen to be when we solve by setting an equation equal to 0. I guess I'll finish this post and do a bit of research. I also need to stop and try and think of something that I do that I can share with other teachers that they may not already have thoughts of...
WEll, today was my first day of the PreAp Institute hosted by my alma mater. While I was disappointed with breakfast....(donuts and coffee....at least they had blueberry donuts...) I really enjoy the class so far. The facilitator is awesome and doesn't mind too many bunny trails and we have a great group for discussion. Small, yet familiar. We shared horror stories and ideas already and discussing different strategies. So far, I haven't learned anything that I can't use in my low-level classes...
It's great being back with my two fellow coworkers too. We just click so well...
It was also quite shocking to hear of someone who said that number lines aren't really in the math curriculum past 3rd grade... I'm all for teaching abstract thinking and such...but that's a bit early considering some of the later things you learn. It explains why so many of my students have a conceptual struggle with basic things like negatives. We also enjoyed a decent discussion of "Don't teach tricks; TEACH CONCEPTS". Please, please don't teach "Keep it change it change it" (for subtracting negatives...). Show them on a number line or use basic life psychology:
For adding a negative= punishment by spanking
Subtracting a positive = punishment by grounding or taking away cell phone
Adding a positive = reward by giving something good
Subtracting a Negative = Reward by taking away something bad (removing restrictions)
Just to show how +- is the same as -+ and ++ and - - are also equivalent
I'm going to check our state standards for the elementary grades in math to get a better feel for what is supposed to be taught--although that doesn't necessarily dictate how.
We also discussed what different schools do with their PreAP programs--how do students get signed up, athletic eligibility waivers and such. Many schools with open enrollment policies have faced problems of parents who want their students in the classes so that if the student fails an advanced class, it doesn't count against extracurricular eligibility.....If the district has a policy of waiving grades as such. Also how to make sure students are prepared to take grade level TAKS while on an advanced curriculum--key being the 8th graders where the state test standards are very different from Algebra--so when do they learn this material? What do you do for students who decide later on in their education--such as 9th grade to try and "catch" them up in a PreAP program?
Anyways, it's a lot of funning seeing some of the LU peeps who are still around there too. Lunch at the cafeteria wasn't too bad....the spaghetti sauce wasn't watered down (by much) and the salad bar had FRESH fruit and veggies. and the really yummy cookies for dessert...mmm Oh, and they had really fresh french bread too..... Have they ever gone wrong with the baking...???
Well, my blog was looking a bit bare, so I thought I'd share the happenings.
Colorado was great. It was a nice change of pace and was just right in length and rest--even if I did have a horrible attack of the allergies due to "summer snow", a.k.a. cottonwood.
We got back, unpacked, cleaned up and than had a fabulous time--mini-reunion of sorts with the TSF which Jared describes very well. We had decided just to buy one copy from last year and picked "Harvey", but immediately after watching Much Ado about Nothing, we put in an order for that too because it was just that wonderful. I loved the stage version of Amadeus and seeing Man of La Mancha live! Othello was good too.
Then, after everyone left, i rested from people and read books, lazed around, and generally enjoyed solitude. Although I really should have been productive--organizing the many boxes brought from Colorado and the stuff that I just didn't get at the end of the school year. But hey, I have another month :-)
This last weekend was spent sleeping and reading Harry Potter 7--and I was satisfied. It was quite the shift in style for the series in terms of writing, but it felt right and in the end, it was a children's series again. I found the first six books in a nice boxed set at Hastings that was a good buy with my happy teacher discount--it saved me about $13-14. I've also been reading Wheel of Time series courtesy of Josh who gave the first book for Christmas. I'm not sure how this stretches out into 11 and then some books...but I guess I'll see. I've started to get into it a whole lot more with book 2.
Otherwise, I go to Bible Study which proves for lots of interesting discussion, especially as we have begun to not the like the book quite as much as we did at first. The author gets a bit fundamental with some things and maybe too....petty? It's hard to describe. She does have a lots of good points still. But hey, the only book I'd probably ever agree 100% with that isn't the Bible would be a book I write myself.--and then who knows what I'd think a few years down the line. But the study is good in that we are all thinking, discussing and learning. Sometimes i feel quite at odds with the group--I'm the youngest by a margin and have a very different perspective. I'm, believe it or not, probably have one of the more conservative viewpoints--but it's friendly disagreement. I just have a different appreciation for doctrines. It's a struggle sometimes--as I mentally cringe as a few things I hear in discussion--because I begin to struggle with pride from what I learned through my Biblical Studies minor--studying doctrines and studying how to study God's word.
For example, one lady was explaining how she wishes the church was doing a better job of teaching--especially younger ones--how salvation isn't just a one time thing--how it's a process of living out your salvation. I replied in agreement that I think we need to teach teenagers more of the biblical doctrines. She disagreed and continued to explain how so many people don't have a real good understanding of what salvation and being a Christian is...when she was done, I pointed out that we said the same thing-what she described is the doctrine of salvation--but she doesn't like the word doctrine. A few ladies are touchy about "Christianese" words. So I go, okay then--what the Bible teaches about salvation.
At any rate, it's usually a good time and the ladies seemed to like my first try at fruit pizza although I need to work on my dough still. I think adding extra butter trying to make it chewy may have been a bad idea--and using part wheat flour shouldn't have made a difference. It's also funny because I've been told by one of these ladies that I should consider going to seminary one day...it does provide an interesting thought.
As I consider what I'd like to do--since I don't see myself just teaching my entire life--seminary is an interesting consideration. But more and more I find that I want to focus my later studies on curriculum and mathematic pedagogy. I still would love one day to travel around the world and visit schools to compare how math is taught differently in different cultures, countries.
So, that's my rambling for tonight.
Well, in an effort to make uploading pictures speedier on my part, I've started a picasa gallery since it's free and easy to work with. It also makes it easier to upload the pictures in original size and easy to uploads lots of large photos in a smaller size, because uploading a bunch of pictures to here gets really annoying and I get to the point where I hate having to pick and choose.
so, whenever something fun happens, or maybe when i get out and start playing with "learn how to use manual setting", my photos will now be posted to
Enjoy! My CO pictures are up along with a few i took at the Shakespeare Garden this last weekend. I was playing around with my manual settings to get a feel for what the different things do.
I'll try and post when I've updated things.
Doesn't get much better. I'll try and post some pictures soon of our Alpine Loop tour today...hehehe, it was quite the adventure... I just have to downsize them from 4 megs or something like that...
The community service on Sunday was wonderful--I love how churches get together and celebrate as one.
and chillin' around town and eating the good foods of parents and local restaurant fare has been a nice break from pretending to diet. I'll get back to that next week.