So I drove back from the mountains yesterday instead of today (it was a very spontaneous trip so I spontaneously shortened it), but I scheduled today off.. so I’ve got time to try to explain “parts and wholes.”
http://ncsall.net/fileadmin/resources/fob/2008/fob_9a.pdf is the PDF of “Focus on Basics” with a quick article by Dorothea Steinke about teaching adults numeracy. That’s where I first found it. I absolutely, positively knew that the students coming to me from our adult basic ed math class getting help with long division but not understanding the subtraction part and borrowing weren’t really benefiting from crawling through algorithms (and the academic success rate said the same).
http://www.resourceroom.net/mec/index.html has a rough of online version of the intro to the course.
It would be easy to simply assume that these folks “really don’t belong in college, do they?” except… I have learned better from working at The New Community School. Students who “can’t” grasp the most basic abstractions … well, they can. (I was going to stop there but I went to the site — and the students from when I was there are down there in “success stories.”
I won’t go into the research stuff, but it’s there.
Even if it weren’t, working from a “parts and wholes” perspective has all kinds of advantages. The most obvious is that the “same old thing” hasn’t worked through adulthood… why do it again?
Seeing math operations as “you’re either putting things together to find the whole, or taking them apart to find the parts,” it keeps the focus on concepts, not procedures.
But… looking at that rough makes me realize that I *need* to dive in and get working on the current version and my Open Education REsources stuff …