On Aug 22, 2013, at 6:13 PM, Richard Strausz <Richard.Strausz@farmington.k12.mi.us> wrote:
> Here is another. Do you like the textbook problem as given or do you prefer any of the suggested improvements? > > http://blog.mrmeyer.com/?p=17810 > > Richard
I found Dan's reply funny...
"Personally I?d get rid of this ?draw some circles? nonsense. It feels like busy work and makes the task feel arbitrary. Straws and paper cups. Or pringles cans and boxes. Or any tactile thing that we don?t spend setup time on and which we might ever want to put inside other things."
Replace busy work with...busy work.
It amazes me how pedagogically inept most of the posters (including Dan) are on this site. They don't appear to have any plan or design in mind to get from A to B in one year of mathematics. Endless repeats of the same basic activity. No structure. No layering. No chain of reasoning from one topic to the next.
Mathematics is probably the most structured subject there is to teach and the easiest subject in which to find the structure. Yet Dan and most of his followers avoid structure at all costs. I used to think this was just deliberate, but I have come to realize that they avoid the structure because they are unaware that it exists or just don't understand it. To them, mathematics is nothing more than a disconnected series of vignettes. Unfortunately, teachers like this get tasked with teaching students who struggle the most and they (the teachers) miss out on the experience of seeing this structure play out successfully with better students. Thus, the teacher never learns.