Dead Comment
Now, pipe down and let the adults speak.
Deleted Comment
Edit 2: Honest question, how can I delete my account on HN? I've come to realize (sadly) how many hours I've wasted on this bullshit. PG, please ban this account.
For example, my rate is between 90 and 110 dollars per hour for long term work. I would like to think I could charge more, but this is what the market will bear where I live. HOWEVER - there's almost always a vendor, and sometimes several vendors, between myself and the company. To the company I work for, my hourly rate looks about 10-40 dollars higher depending on the layers I go through. So for me to make 100/hr, it's likely the client is being charged 130/hr.
I.e. teaching students the steps to solve a math problem is not teaching them how to think about the problem.
I instantly knew 12/13 + 7/8 was ~2 because I visualize two pie charts in my head, both of which are mostly full. This is in contrast to the other way to solve the problem, converting the fractions to a common denominator and then dividing by the denominator. It would take me some time to do the latter, whereas I can instantly do the former.
I don't think the students who got that wrong (nor some who got it right) do any kind of visualization in their heads.
Teachers need to realize that it's the operations in the head that count the most, not rote memorization of steps to solve a problem.
I imagine there are myriad other ways people approach estimation problems like this. In response to the rest of your post, I was never taught how to "think" about math. I was educated in a decent school system, but it was all rote memorization of multiplication tables. I think most people who are interested in learning will come up with their own tricks regardless of curriculum. Of course, imagine how much better I'd be at this stuff if I had math teacher's who were competent :)
its sad to see this type of music dwindle away when it was so rampant during the 60's. its magical feeling the energy from a band that can talk to each other through their music. its the same magic that happens between basketball players when they are in the zone and can pass the ball without looking to their team members.
magical.
What's interesting though is that I love a good solid 20 minute epic trance tune. It's basically the same thing, so I'm not really sure why I prefer electronic "jam" music over more traditional jam bands.