If it depends on knowing how to do other skills, has dependencies, as you say, then it is pretty much impossible from the outset. I can't run before
I learn to walk, and if walking is dependent on my knowing how to run, then I'm going to be SoL.
Now, there is a time and place for learning alternative strategies and approaches, but the alternatives that depend on you knowing the basics are not
the place to start.
Honestly, I don't know. Maybe it's something that can't be done. We all only learn this stuff once and half of us probably don't even remember
learning it so it's not like any of us can look at a bunch of methods and say definitely which works best. I remember when I was taught addition we
used a number line made of masking tape and put on our desk then we would count spaces forwards and backwards on the number line.
The real question is, if we teach this after a more traditional method... where do we take time out of teaching in the future to teach the alternative
methods? As a population we have very poor math skills, in what has become a bit of a routine for me I was once again today watching college students
having to use their fingers to figure out 19-6.
I don't know what common core is about, but learning to simplify mathematics and take what seems to be complex, break it down into simple parts, is
definitely not a step in the wrong direction.
I taught myself this because I was bored in advanced mathematics classes. I had 100 average and was 99th percentile on standardized tests year after
No, I'm not joking. Not sure what you're not getting here.
Are you going to watch that video and honestly tell me that this isn't a step in the right direction? This is how I learned concepts intuitively. I
visualized what the problem meant. I did this often times before learning it in the classroom. There were real world problems, and I figured out how
to go about solving them on my own. Then when I went to learn these terms, I knew how to do it already.
It's the best way to learn, not merely how without any real understanding, but WHY, to get the concept mastered. I would often visualize the solution,
then work my way backwards towards the starting position. Then I'd write out my reasoning short-handed, which the advanced math teachers could
decipher, and knew I never cheated, so would give me full credit. I learned more efficiently because of the basics being taught my own style. It's
good to see teachers are finally describing what some of the gifted kids self taught.
edit on 17-9-2014 by pl3bscheese because: (no reason
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