SHEILA KING spoke of Math Facts to DAN TRIPLETT on 12-27-96
Preface to my rambling.....liked what you have to say here.....think we 
probably agree on most points....if not all....am now trying to define 
our terms...what is "developmentally?"  Question:  Is a child who lacks 
experience/exposure to a certain concept (and therefore doesn't 
understand) different (developmentally speaking) from a child who is too 
young to grasp the concept?  
SK>-> Many educators in primary education would argue that these
SK>-> children don't know these facts because they are not
SK>-> developmentally ready for such concepts.  If what they say is
SK>-> true, then no amount of tutoring will bring about mastery.  Should
SK>-> a child in third grade know that 9x9=81 and understand numerically
SK>-> what that means (i.e. that 9x9 is the same as
SK>-> the 9+9+9+9+9+9+9+9+9=81?  I would think that understanding
SK>-> the concepts behind the facts is equally important.
SK>Of course understanding behind the concepts is equally, if not MORE,
SK>important. I don't think I ever said otherwise.
No you didn't.  I was just thinking out loud.  It's a serious question 
though.  I know that many kids memorize facts...but can they apply them?  
When I was in elementary school, math was fun and I did understand the 
stuff.  But I see many kids, even 5th graders, still struggling with 
some basic math concepts.  I am left to wonder why?  
 You would NEVER here me recommend memorization of ANY
SK>math concepts over understanding the concept behind them. That would
SK>go VERY MUCH against everything that I do in my high school
SK>classroom.
I didn't mean to suggest you would.  What I am saying (I hope) is that 
knowing and memorizing are different things.  (I know you are saying 
this too)  The question I have is...if we are after understanding, and a 
child isn't getting it (let's say many aren't getting it) then where do 
we go from here?  One question that comes to mind is "What kind of 
mathematical foundation has been laid for this kid?  Perhaps kids who 
don't understand some basic math facts need a bit of "foundational" work 
as well?  Does this make sense?  
SK>Are these slower kids not developmentally ready? I certainly am no
SK>childhood educator, but I think that 95% of the kids can handle that
SK>info by the end of third grade. The reasons why they aren't learning
SK>the facts is because they are not getting enough help on the
SK>material, and that includes help in the home from the parents.
I am inclined to agree with you here.  I really believe that home is 
very important.  I do believe that kids can learn...sometimes just if a 
concept is explained or shown in a certain way...the light comes on for 
a kid.  
Another thing is that math, like many other areas of learning, has a 
hierarchy of skills.  You learn a before b and b before c.  If a child 
is old enough to be learning about h, but hasn't yet fully understood f, 
then they need to learn about f.  Some educators say that this child is 
not developmentally ready for h.  His/her development of math concepts, 
even though the chronological age is at h, is still hovering around f.  
Perhaps the term "developmentally ready" is a bit nebulous.....different 
people mean different things.  (agree?)  For me, the term means that 
children at certain ages exhibit certain developmental characteristics 
(physical and cognitive) that are seen consistently in their age group.  
A general level of cognitive development can be expected and we can 
generally predict what concepts a child at a specific age will be able 
to understand.  
But it can also mean that a child, regardless of chronological age, has 
a developmental age....that is s/he has developed cognitively to a 
certain point.  
SK>For example, my infamous daughter who SHOULD have learned all her
SK>multiplication by early Dec. actually didn't. We are still working on
SK>it at home. She didn't bring notices home informing me exactly what
SK>was going on in the classroom so that I could support her at home
SK>with extra study time. 
I am comforted knowing that this sort of thing happens elsewhere.  My 
son is 18 and we still have to get after him about homework.  He often 
cannot find his assignment sheets.  Ahhhhh....and he plans to move out 
this summer and go to college next year? 
I have since talked to the teacher and let her
SK>know that I was not very happy with the fact that she never contacted
SK>me about it until AFTER the multiplication unit was finished! But, my
SK>kid could've learned the multiplication as well as any other kid IF
SK>(that's a very big IF) she had worked on it at home at all (which she
SK>did not). I suspect that most of the kids who are not "getting it"
SK>until fourth grade and later are simply not spending much, if any,
SK>time outside of the math classroom working on learning these facts.
SK>This has nothing to do with being developmentally ready. 
Yes....I fully agree here.  Being developmentally ready can be another 
matter all together.  It appears to be true for your situation and your 
daughter.  If I can read in between the lines here I think you are also 
saying that for kids to be successful learners, the home must be a 
partner in the learning/teaching.   This certainly is my view.  
This has to
SK>do with learning how to study and memorize (which actually take time
SK>and effort).
And all too often this important item is left out.  Do you think that 
too much responsibility (for teaching all things) is left up to the 
schools?  I believe that many kids exit the learning mode once the 
dismissal bell rings. 
Dan
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