Problem solving, thinking, and some effort..

4leaf(1)
Finding patters.

This is an older post from my other blog.

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…
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