I feel an important skill -- maybe more so for us -- is to accept multiple solutions.

Look at the problem 73-19. I can traditionally line it up, borrow, and get the answer of 54.  

Or I can take 70-10=60; 3-9=-6; 60-6=54.

Or I can count up 19 to 29 to 39 to 49 to 59 to 69 get 50. Then from 69, 70 ,71 ,72, 73 gives me 4 more for a total of 54.

Sometimes it is too easy for us to see "the right way" as the way we solved the problem.  Manipulatives make the multiple solutions more obvious.

Kathie


-----Original Message-----
From: specialtopics-bounces at nifl.gov on behalf of Myrna Manly
Sent: Wed 9/19/2007 8:32 PM
To: specialtopics at nifl.gov
Subject: [SpecialTopics 700] Re: Different skills
 
Hi all,

I always seem to be a day late in responding to David's questions.  Can I
blame it on the time zone?

He asked about which numeracy skills may have lost their critical nature
over the years and which have gained.  I'm going to start a list that you
can add to (with a little explanation, of course.)

Skills that are less critical:
	- completing accurate arithmetic operations with large numbers.
Since calculators and computers are ubiquitous these days, especially when
one is required to figure an exact result with large numbers (accounting
tasks, scientific calculations, etc), it would be foolish to calculate these
by hand. 

Skills that are more critical:
	- estimating an approximate answer to computations. First, an
estimate is often all that one needs to make a decision or to determine how
much, say, paint that you need to finish a job. Secondly, when you use a
calculator to find an exact answer, you are asking for trouble if you don't
estimate to check if the answer is reasonable.  Large fingers and small
buttons lead to errors.

Comment: Note that this does not eliminate the requirement for knowledge of
"the facts".

 OK, I chose a very common example and left the more interesting ones to
you.  How about data analysis or algebraic reasoning? What kind of geometric
reasoning does a computer animator like Mary's son use?

Myrna 

-----Original Message-----
From: specialtopics-bounces at nifl.gov [mailto:specialtopics-bounces at nifl.gov]
On Behalf Of David J. Rosen
Sent: Wednesday, September 19, 2007 1:13 PM
To: specialtopics at nifl.gov
Subject: [SpecialTopics 697] Components of Numeracy

Colleagues,

For those who have just joined us, all the messages in the discussion  
-- that began on Monday -- are archived at

http://www.nifl.gov/pipermail/specialtopics/2007/date.html

Please send your questions and comments to specialtopics at nifl.gov   
Please do not include attachments in your postings, and -- where  
possible -- quote the section of the message you are replying to.   
Some of the replies also include a string of previous messages that  
makes the posting unnecessarily long.

Here are three more questions for our guests and others:

10. Can you tell us more about efforts to help adult education  
teachers improve their teaching of numeracy? For example the TIAN  
project and others?

11. Can you talk about - and give examples - of family numeracy?

12. Some would argue that math is sequential - shouldn't it be taught  
that way? If not, why not?


David J. Rosen
Special Projects Discussion Moderator
djrosen at comcast.net



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