Problem solving, thinking, and some effort...

Some posts are written down on paper first, this ain't one of them.  It's really just disguised laziness.  I like the challenge of problem-solving.  I like teaching math and I liked the part about math where you work real hard to figure something out and then figure it out.  It is a special accomplishment and why people always view math as hard and a measure of intelligence.  It is often a challenge but it is not any more of a measure than any other study, we just measure it on a different part of the scale than we do other things.
I work to try and help people build their schema of math understanding and develop that part of reasoning and symbolic logic.  Unfortunately, I am not the most organized individual so I haven't refined how to best reach my goal.  My goal also involves changing others' viewpoints and that just don't always work so well.  People are a stubborn species and teenagers are a stubborn subset of people.  Getting them to buy into a different view of the world, particularly one based in the unexciting system of algebra, feels like a pointless fight at times.  My only advantage is that the students do believe that something about the subject is good for them, even though they have to ask "When will I use this?" every class.
That supremely frustrating question is why I am shifting to a class more focused on problem-solving rather than mechanical-computational skills.  I am also moving in that direction because modern students have astoundingly little space or need to recall facts and skills.  They are absorbing information at peak levels.  They know fifty times more bands that I did at the same age.  So much of the working memory I need access to for traditional learning is used up on things far more interesting to teenagers.  So....how do I teach a subject that requires a significant amount of this cognitive process? I have faith, perhaps too much, in my ability to present the information to people in way that makes sense but the same people often don't store it.  I am trying to circumvent this issue by using a problem-solving approach or a method in which I guide students to construct their understanding of mathematical systems.  Both methods require thinking and both require effort from the students.  Effort is a challenge in the subject.  Student often ask for help as soon as they read a problem. He or she may work on it for a minute or two but rarely long enough to reason through it.
I have worked on a problem-solving approach for a few weeks in one of my classes and I am seeing signs of change, though.  I hear fewer more questions and students seem to be following my guidelines to find some manner of solution.  Next up, setting up the problems so that individuals develop an understanding of the rules of higher math.  Until now, we were working mostly with old computational skills.  I am adopting my system from Exeter's Harkness math but I am confined to less time and with a broader range of students.  I do know they are more engaged and that students who could care less for a lecture on solving quadratics enjoy they can find different ways to solve a problem.  Watching people use different methods has taught me a great deal about math over the past few years.  Ehh, I just got tired and stuff so I will continue this later...

Some pictures, a story start, and some rambling.

Still going.

   Let's see if I can get to the words on here.  I should be helping at his school or cleaning the house.  Instead, I am going to see which of the mundane sentences I jotted down last night make any sense here.  Writing on the computer is not an organic process for me and it really takes away much of the power of expression.  I relied on the machine form during school and in boring work, that reliance pushed me from the habit of writing as a release and as a place to make the inner discussion real.

 A Story in Progress
     "You jerk."  The lady shouted as she pulled into the elementary school to pick up her kids.  It was hot out, her husband was pretty much useless and the line of cars to get into the school lot was not moving.  She needed to turn left and some asshole and some asshole in a big truck wouldn't stop to let her forward.  To make it worse, he pretended he didn't even notice but he must have for they were just yards apart, sitting in their traveling recliners.  He looked like one of the young men who had come into her office and made work less bearable.  He knew nothing and pretended like he knew everything, that she should be on her knees before him.  At least the old boss wanted her bent over the table so she could get some pleasure from it.
     "You jerk.!"  He heard the woman yell as she passed.
     "Damn lady, I didn't mean to do nothing." He wondered as he could feel the heat sweat out his back and his legs stuck to the seat.  "Does she freak out like that with her kids?"
    He was worried, bothered by the moment.  He was a jerk, that he could admit but not to some stranger and not for being stuck in school traffic.  He wasn't a jerk merely for existing.
    Maybe if these lazy folks wouldn't drive right up to the school. Damn, I hope I get an email from the people soon.  Every time he saw the yellow light next to the E it reminded him that he was broke.  Try as he might, work was not easy to find.
     The messed up thing about it all was work was not the chore.  All these people around searching for a way to make rent and scrambling to pay some old debt or to buy some milk,wasting a few dollars on beer flavored rotten barley to forget, finding someone to blame but really just wanting to work, to feel like they had meaning and to have some cash, they were everywhere.  Begging outside of stores and serving up fries, pushing papers and making traffic stops.  They attacked each other because it was the only thing they could think to do.  Others just watched T.V. on and endless reel.  

     Not that it's a new idea but it's one worth explaining.  What does another person live through?  I was on a selfish version of this thought game, "They just don't know my responsibilities or my concerns, strengths, limitations, motivations, trials, etc.  This self trudgery and fairly useless line of reasoning occurred on yet another walk to the store to get another beer to mollify the worry of the day and give me freedom to dream of something more than the moment.  I was going along the familiar stretch of sidewalk as my son ran about  figuring out how to throw a frisbee.  We found it on the strip of grass that catches all the trash from the evils of the road.  A red VW bug kept passing up and down the street, a couple about my age enjoying driving the loud little car.  Various other people drove by dressed in machine finery or wrapped in torn and patched metal getups.
    All these people going around and meeting demands in their lives were worn down by bearing the challenges of the day or exalted by the events great or small, new love, finding $20, a healthy baby, a kind word.  Here we all were going through time-space in some controlled idea driven by wants and needs.  Consuming on past consumptions.  Actions mandated by habits, choice at moments when the future seemed different or lacked any reality.  Another drink, a new car, a late night fling, doing what one wanted and then the obscure shackles of obligations were locked.  The choices may have  been the best, to not call the woman at the bar back, to not join the Army, but there was and is no way of knowing.
     Scientists are at work proving that time is an illusion.  Perhaps they are right in some sense that it is part of a time-space construct but we know it to be a real law that we live by.  Our mortality is one of the absolute truths, if not the only one.  It is fun to think of time dilating around planets and we may get some useful stuff from it but it ain't the world we live in.  Rain fall, counting a beat, a measure, a rythem as it builds into the puddle, falling over its breaks into a swirl, slipping into a gurgle, falling into the creek and beyond.  All along, we see the present, recall our past, and imagine a future.
     Kindness, sympathy, caring, love: the forces that push for  better moment are how we know that we do understand each others little worlds.  Greed and violence are the actions we take when we only act for ourselves.  I find myself in another conflict and perhaps with a greater understanding of greed.  Seeking, begging, lying, and stealing in order to provide support for my family.  Is it not an honest goal?  But the end provides poor support for the means for it makes me a weaker man  and further scars my being.  Festering sores that I pick at in worry and shame.  Afraid to admit to those I love and further leaving a part of me rotten.

     Seems that I either lost direction or forgot where I was going.  It's the problem with no plan.  Bugs are bit annoying and my stomach is burbling from too much coffee.  Can't seem to shake this filthy nicotine habit.  A car horn goes off in the distance, probably a forgotten alarm.  Maybe a kid found the panic button and now it has stopped.  The bright yellow corvette is going on its laps.  Still....no plan, just gonna revive a habit that never stuck like it should.  Why do the good habits require maintenance of effort while the bad ones just come in to control.

Flowers, children, and shapes.

Sitting in a class with some tunes and folks busy at work making kites.  On my best days, I would think my class was awesome, not so sure about my bad days. It's always a challenge figuring out what the process of useful learning is.  What is worthwhile and what is interesting, what helps build a students understanding and what applies to a real development of knowledge.  I have finally learned that it is okay just to follow the guides and textbooks when
I ain't so sure where to go.  I wish I had swallowed that bid of pride in earlier times but I am not really good at doing that until I keep getting hit in the head with the same board of stubborn imbecility.

Down by the water

One of our favorite places to go for an excursion is down at McKellar Lake. It's a pretty funky place and I imagine it would be a blast to live down there.  The people are always super nice and it's a visual extravaganza. Got some more pictures to come. Would any of these make good cards?

Silver, fruit, and something else I forgot...

The top one is a better picture of a necklace. The middle is one of the earrings before it gets it's findings and finds a home.  The bottom one is the first watermelon I have ever grown.  It's a little one but gives me hope for the future.  I found it when I cut off one of the vines that tried to take over the swing set in the backyard.  I had been looking at all of these others failures of tiny melons and this one just appeared. I think I'll try it tonight. Someday, I'll get some halfway decent gardens and be happy enjoying the fruits of the earth. 

More images for cards...

I will throw these up here for now but soon the tab for Art should have all kinds of useful things. 

I imagine most people would prefer the happier looking ones for cards but I decided to play around a little bit with them.