Zequals

[Algot Runeman]

This technique sounds like a good element to include in the developing
language of math.
It seems to me that this is similar to the "back of the textbook"
location of graphing in algebra.
I have stated before, I think that if I had seen the estimation
potential of graphs and the physical representation of formula result as
lines and curves, I might have understood algebra sooner.

Making math approachable by emphasis of seeing the big picture before
focus on the details has a strong benefit, as I see it.

http://www.fastcodesign.com/1672473/can-a-new-symbol-make-you-better-at-math

--Algot

--
-------------------------
Algot Runeman

algot....@verizon.net
Web Site: http://www.runeman.org
Twitter: http://twitter.com/algotruneman/
sip:algot....@ekiga.net
Open Source Blog: http://mosssig.wordpress.com
MOSS SIG Mailing List: http://groups.google.com/group/mosssig2

[Joshua Zucker]

On Tue, May 7, 2013 at 3:33 PM, Algot Runeman <algot....@verizon.net> wrote:

Making math approachable by emphasis of seeing the big picture before focus on the details has a strong benefit, as I see it.

I think so too, but a lot of people seem to think that dealing with details first and then backing away to see the big picture is better.  Is there any research about these two types of approaches, and in particular about whether long-term retention is better with one over the other?

Also, as for the zequals, I don't think it's a very useful notation, since the more interesting question is when it's OK to do a very rough estimate (like 248 * 84 as 200 * 80) and when you need to be cleverer (like the almost-as-easy 250 * 80) to get an estimate that's accurate enough.

--Joshua

[Bradford Hansen-Smith]

Joshua, I don't think there is much research about starting with big pictures or details. We don't start anything from the largest or biggest picture. What exactly is the big picture, for that matter to know how small a detail is best to start with?  My experience tells me the biggest most comprehensive place is better to start since you can never know it all anyway. By starting with the most inclusive whole, unity, everything will always be interrelated and in the context of all that is presently and yet to be realized potential. Inherently every detail carries the Whole but if you do not start with the whole you do not know that. Starting with the largest picture reveals endless details to discover as opposed to starting with details to then discover connections between parts making larger parts with more detail. Endless parts and details will never complete unity of the whole. The big picture, unless philosophically comprehensive, will always be just one more detail of a larger part. Many students say math details in themselves without context have little meaning.

Brad

--
You received this message because you are subscribed to the Google Groups "MathFuture" group.
To unsubscribe from this group and stop receiving emails from it, send an email to mathfuture+...@googlegroups.com.
To post to this group, send email to mathf...@googlegroups.com.
Visit this group at http://groups.google.com/group/mathfuture?hl=en.
For more options, visit https://groups.google.com/groups/opt_out.
 
 

--
Bradford Hansen-Smith
www.wholemovement.com

[John Mason]

Try searching "Deep" and "Surface" learning.  Research in the 1960s and 1970s:

Gordon Pask & Brian Lewis worked on the distinction between "holists" and "serialists"

Then Marton & Saljo developed the "surface" and "deep" distinction.

This in turn developed into "strategic" learning and teaching (don't know what is used to refer to 'non-strategic'!!

see for example

Marton, F. & Säljö, R. (1976). On Qualitative Differences in Learning — 1: Outcome and Process. Brit. J. Educ. Psych. 46, 4-11.

Marton, F. & Säljö, R. (1976). On Qualitative Differences in Learning — 2: Outcome as a function of the learner's conception of the task. Brit. J. Educ. Psych. 46, 115-27.

Marton, F. & Saljö, R. (1997) (2^nd edition). ‘Approaches to Learning’. In F. Marton, D. Hounsell, & N. Entwistle (Eds.) The Experience of Learning. Edinburgh: Scottish Academic Press.

Ausubel, D. (1960). The use of advance organizers in the learning and retention of meaningful verbal material. Journal of Educational Psychology, 51, 267-272.

JohnM