Number sense: counting vs. scaling?

[Maria Droujkova]

One of the suggestions last week was to have more discussions. SandyG writes: "I would much rather have held our own discussion board discussions rather than reading ones other people had. I think there are some really fascinating people in our class, and the discusssions could have been interesting and educational. We have heard about classmates that are actively doing things with math and who have experiences that I could have learned from, but I haven't had the opportunity to interact with them as I had hoped.  Perhaps there would have been more retention if we had hosted our own discussions. Many of my classes require online discussion posts with a set number of required comments and responses, and honestly, most people always go way over the required number of posts simply because the discussions are captivating and meaningful and the discussions become conversations. I wonder if something like that would work here."  http://p2pu.org/en/groups/ed218-developing-mathematics-the-early-years/content/meta-bonus-class-participation/?pagination_page_number=1#13258

This week's topic - number sense and measurement - was the theme of choice for many people, and a part of it lends itself well to discussions. The first task is here:  http://p2pu.org/en/groups/ed218-developing-mathematics-the-early-years/content/week-10-number-sense-and-scale-sense-march-19-25/ 

I quote from the task. Please discuss by replying to this email and then comments by others: 

"Curricula of some countries (such as US or China) emphasize counting tasks more, and curricula of other countries (such as Eastern Europe or Singapore) emphasize scaling tasks more. This is not new: for example, Ancient Egyptians were more into counting and Ancient Greeks more into scaling. Needless to say, there are Math Wars about these choices in the current math ed circles. What is your take on the two approaches to the number sense?"

I hope the discussion will help to add depth to the task!

Cheers,
Maria Droujkova
919-388-1721

Make math your own, to make your own math

 

[Garrett, Sandra]

For me, counting seems to be more precise, and I like things to be very black or white.  Scaling, I think, leaves room for opinion.  One article I read explained scaling as using the focus button of a camera to zoom in and out to exam how the different parts make up the whole picture. What I'm wondering from all this is if right-brain vs. left-brain dominance plays a part in the preferece at all?   Have you ever heard of any correlation between learning preferences and whether a person prefers scaling vs. counting? 

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[Maria Droujkova]

On Tue, Mar 20, 2012 at 7:32 PM, Garrett, Sandra <sgar...@arcadia.edu> wrote:

For me, counting seems to be more precise, and I like things to be very black or white.  Scaling, I think, leaves room for opinion.  One article I read explained scaling as using the focus button of a camera to zoom in and out to exam how the different parts make up the whole picture. What I'm wondering from all this is if right-brain vs. left-brain dominance plays a part in the preferece at all?   Have you ever heard of any correlation between learning preferences and whether a person prefers scaling vs. counting? 

Precision is a mathematical value - interesting connection!

One precise math domain that is based on scaling and splitting is origami. I knew origami required, and supported, mathematical precision just from helping kids learn it. But then I found the whole world of origami mathematics - for example, Huzita-Hatori axioms! http://en.wikipedia.org/wiki/Huzita%E2%80%93Hatori_axioms Origami geometric constructions are more powerful than Euclid's construction. For example, you can trisect angles under origami axioms, but not with Euclid's straightedge and compass rules.

http://www.youtube.com/watch?v=tE4lqYzS2m0

Cheers,

MariaD