DT>  SHEILA KING spoke of Math Facts to DAN TRIPLETT on 12-27-96
DT>  Preface to my rambling.....liked what you have to say here.....think we
DT>  probably agree on most points....if not all....am now trying to define
DT>  our terms...what is "developmentally?"  Question:  Is a child who lacks
DT>  experience/exposure to a certain concept (and therefore doesn't
DT>  understand) different (developmentally speaking) from a child who is too
DT>  young to grasp the concept?
Well, I'm not sure that I 100% by into the "too young to grasp the
concept" idea. I mean, certainly you wouldn't expect 3 year olds to
be able to handle the symbolic abstraction of algebra. So, insofar as that
goes, I do recognize that there are some limits to what a typical person
of a given age can handle. However, given an average child of, say, 5 years
old...you have stated that most children of that age are developmentally
only ready to handle one-to-one correspondence and are not ready to
conceptually handle addition. I'm not certain that well-designed exposure
to certain pre-requisite topics couldn't prepare a given group of average
5-year-olds for addition.
"Developmentally"...I would guess that would mean that the child is
ready to handle the new topic in question. This is probably a function of
the child's age AND their environment, don't you think? So, it would depend
on both, I would guess.
DT>   You would NEVER here me recommend memorization of ANY
DT>  SK>math concepts over understanding the concept behind them. That would
DT>  SK>go VERY MUCH against everything that I do in my high school
DT>  SK>classroom.
DT>  I didn't mean to suggest you would.  What I am saying (I hope) is that
DT>  knowing and memorizing are different things.  (I know you are saying
DT>  this too)  The question I have is...if we are after understanding, and a
DT>  child isn't getting it (let's say many aren't getting it) then where do
DT>  we go from here?  One question that comes to mind is "What kind of
DT>  mathematical foundation has been laid for this kid?  Perhaps kids who
DT>  don't understand some basic math facts need a bit of "foundational" work
DT>  as well?  Does this make sense?
I would think that it's obvious that such a child needs foundation work.
No point in requiring rote memorization of math facts if the child doesn't
understand their significance, first.
DT>  SK>Are these slower kids not developmentally ready? I certainly am no
DT>  SK>childhood educator, but I think that 95% of the kids can handle that
DT>  SK>info by the end of third grade. The reasons why they aren't learning
DT>  SK>the facts is because they are not getting enough help on the
DT>  SK>material, and that includes help in the home from the parents.
DT>  I am inclined to agree with you here.  I really believe that home is
DT>  very important.  I do believe that kids can learn...sometimes just if a
DT>  concept is explained or shown in a certain way...the light comes on for
DT>  a kid.
This is true, too. Which is why it is important to look at a given
concept through several different points of view.
DT>  Another thing is that math, like many other areas of learning, has a
DT>  hierarchy of skills.  You learn a before b and b before c.  If a child
DT>  is old enough to be learning about h, but hasn't yet fully understood f,
DT>  then they need to learn about f.  Some educators say that this child is
DT>  not developmentally ready for h.  His/her development of math concepts,
DT>  even though the chronological age is at h, is still hovering around f.
I think that the above is a different issue. The child hasn't learned the
pre-requisite idea of f, yet. So, go back and teach the missing foundation
material. Then proceed to teach the child h. Kids can have gaps in their
background material without necessarily being "not developmentally ready".
I would think that this type of thing would explain many of the students
in your own classes that you noted had significant improvement within
one school year by applying just a handful of intervention measures.
DT>  Perhaps the term "developmentally ready" is a bit nebulous.....different
DT>  people mean different things.  (agree?)  For me, the term means that
DT>  children at certain ages exhibit certain developmental characteristics
DT>  (physical and cognitive) that are seen consistently in their age group.
DT>  A general level of cognitive development can be expected and we can
DT>  generally predict what concepts a child at a specific age will be able
DT>  to understand.
DT>  But it can also mean that a child, regardless of chronological age, has
DT>  a developmental age....that is s/he has developed cognitively to a
DT>  certain point.
I don't know. The more you try to nail it down, the more confused I
become. While there is certainly value in discussing what, in general, most
five-year-olds can do, I see it as practically useless to apply such
generalizations to an individual child to explain why s/he can or cannot
do certain tasks. Generalizations are useful for planning a curriculum for
a classroom full of students, but not for tutoring an individual.
DT>  SK>For example, my infamous daughter who SHOULD have learned all her
DT>  SK>multiplication by early Dec. actually didn't. We are still working on
DT>  SK>it at home. She didn't bring notices home informing me exactly what
DT>  SK>was going on in the classroom so that I could support her at home
DT>  SK>with extra study time.
DT>  I am comforted knowing that this sort of thing happens elsewhere.  My
DT>  son is 18 and we still have to get after him about homework.  He often
DT>  cannot find his assignment sheets.  Ahhhhh....and he plans to move out
DT>  this summer and go to college next year?
Well, that will be a good learning experience for him, I guess. As one of
seven siblings, my parents had to deal with everything from the model/honors
student to the borderline ADHD kid. Funny thing, of the six of us now
grown to adulthood, we are all making it one way or another.
DT>  SK> I suspect that most of the kids who are not "getting it"
DT>  SK>until fourth grade and later are simply not spending much, if any,
DT>  SK>time outside of the math classroom working on learning these facts.
DT>  SK>This has nothing to do with being developmentally ready.
DT>  Yes....I fully agree here.  Being developmentally ready can be another
DT>  matter all together.
Which is why I objected to your mention that "kids in 3rd grade" or "4th
grade" or "whatever grade" are not "developmentally ready" to have mastered
their multiplication facts. For this particular issue, I think that it's
more a matter of effort expended on the learning. Much like your reference
to what you used to say to your guitar students. You can show the student,
but ultimately the student must do the learning. I think that most of these
kids are simply not doing the learning. The idea that 3rd and 4th graders
are not developmentally ready to handle multiplication is absurd to me! I
think that our students are a LOT more capable than we often give them
credit for.
DT> It appears to be true for your situation and your
DT>  daughter.  If I can read in between the lines here I think you are also
DT>  saying that for kids to be successful learners, the home must be a
DT>  partner in the learning/teaching.   This certainly is my view.
Yes, the home/parents must take an active part in the education. As I
mentioned previously, for those students whose homes cannot or will not
take up this task, we should provide alternative programs to fill that
void. This would go a long way to removing the charge of "minority
discrimation" as a result of certain tests or qualification procedures.
DT>  This has to
DT>  SK>do with learning how to study and memorize (which actually take time
DT>  SK>and effort).
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