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When I went to school as a child and
learned mathematics, just as now, there were all the same basic
concepts that I had to learn in order to be a functional member of
society and, if nothing else, balance a checkbook.
In Math, as in other subjects, you all
know that there are things that you once learned in school that you
have since forgotten or perhaps slept through when they were taught.
So you dig into the text book and you refresh yourself on some
concepts. You wouldn't, however, think that would be necessary in
1st and 2nd grade math.
My children, as I have mentioned
before, are 5 and 7. My 5 year old is in the middle of grasping the
concepts of addition and subtraction and my 7 year old is just on the
other side of multi-digit addition and subtraction. Well, as my son
worked his way through his 1st grade math, I began to hear
some terms floating around our home that started me to wondering if I
needed to refresh some of my math skills all the way back to 1st
grade math.
One day when attempting to help my son
with some 2nd grade math multi-digit addition problems, I
happened to call the movement of the 1 from the result of the ones
column into the 10s column “carrying”. After a few attempts of
explaining that he must “carry” (which resulted in nothing but a
puzzled look followed by a glazed over stare as I repeated myself), I
took a step back and took another approach.. I explained to him the
concept without the word “carry” and his reply was “oh,
renaming. Mommy told me about that earlier” and off he went to
complete the problem. I chalked one up for me to learning a new name
for an old concept.
A few days later confusion ensued when
suddenly a review sheet my son was working on referred to
“regrouping” and he came to ask me what the instructions were
asking him to do. Just like with “renaming” a few days earlier I
hadn't heard this of term either... fortunately (or unfortunately)
neither had my son. What was this “regrouping”? One of these
“new math” concepts I had heard about? It took my wife to bail
us both out.
Renaming and Regrouping. That was all
new to me. What in the world were those? I came to discover these
are the new terms for the concepts of carrying and borrowing. And
would you think that renaming might be synonymous with carrying and
regrouping synonymous with borrowing? No, it couldn't be that
simple. Renaming and regrouping are actually synonymous with each
other and both are generic terms that encapsulate BOTH the concepts
of carrying and borrowing.
What is the deal here? What was wrong
with good old “carrying” and “borrowing”? I know I am not I
the only one who successfully learned these same concepts under the
names carrying and borrowing? Carrying for addition and borrowing
for subtraction... simple. Who suddenly decided that the names
Carrying and Borrowing weren't good enough? Were those names too
clear? Did it hurt to have a separate name for each concept? Why
lump them under one name? Did it make too much sense and the
children understood it too easily so the names had to be changed? If
they were going to lump both concepts of carrying and borrowing under
one name, couldn't those same people at least have agreed on one name
for the concept?
So, It seems that “renaming” and
“regrouping” are interchangeable terms for the mathematical
operations that we, as children, learned separately as “carrying”
and “borrowing”. Carrying and borrowing weren't bad terms were
they?
Carrying
Okay... logically the term “carrying”
for addition doesn't make a whole lot of sense. What are you
carrying? And where? And why? What “carrying” is involved. To
a 1st grader, “carrying” is “carrying” their
laundry to their room. Perhaps you are lifting (i.e. “carrying”)
the 10 up to the top of the 10s column? Somehow it was drummed into
my head that this concept of moving the 10's value from the ones
column was called “carrying”.
Borrowing
“Borrowing” is a pretty decent
term. I would submit to you that our 1st and 2nd
graders probably already understand the concept of “borrowing”.
After all, you “borrow” a toy... or you “borrow” from one
pile of beans to make that pile smaller and another pile bigger. To
me, it isn't so much of a stretch for them to take “borrowing”
one step further to conceptualize the process of taking from the 10's
column to provide enough to subtract from in the one's column.
One paper that I perused from the
Yale-New Haven Teachers Institute
regarding this topic took the following exception to the term
“borrowing”:
“First
it is important to discuss the terminology of addition and
subtraction which is often confusing and misleading. For many years
the term “borrowing” was used for what is now called “subtraction
with renaming”. The word “borrowing” suggests that something is
being given for a short term use and will later be returned.
Mathematically speaking this is not so in subtraction. Ma mentions
the terms “composing and decomposing of units” used by the
Chinese math teachers to indicate how numbers are constructed and can
be broken down by the processes of addition and subtraction.
Currently in the United States “renaming” is the most popular
term used. It is used in Saxon Math which New Haven uses for its K-4
curriculum. Throughout the paper I will use all three terms. I have
become a fan of the composing and decomposing terms because it seems
to express what is happening to the numbers in addition and
subtraction. “
He evidently wants us to “compose”
in addition and “decompose” in subtraction. That naming schema
is kind of morbid if you ask me... Then again math might be so
horrible for some that they wish they could “decompose” and end
the torture.
Renaming
Renaming
seems a very strange name for
what is being done in addition and subtraction. How are you renaming
anything? Renaming is what your child does fifty times when you get
a new dog or fish, not when you add 18 + 9 or subtract 28 - 9. Are
you re-naming a group of ten units into a group of one units?
"Renaming" is supposedly the most widely accepted term for these
concepts.
To further the objection to the term
“renaming”. I have seen where “renaming” is also the term
used to convert the figure 125,000 to One Hundred Twenty Five
Thousand. Confusing to a child perhaps?
At any rate, I
don't see the logical concept of "renaming" in addition and subtraction for the child to grasp there... but I'm
not the one with a masters degree in teaching either.
Regrouping
I can deal with that term pretty well.
It is actually a pretty good name for what is being done in
subtraction and addition. I can see how we are taking from one
“group” to place more into another “group” (although you are
taking 1 from one group to add 10 to another group and vice versa).
I ask again... what was wrong with good
old “carrying” and “borrowing”?
Hey, as long as we are making up new
names for these concepts, I propose we use “reassign”. It covers
everything. You “reassign” a 10 from the 10's column to the 1's
column. You “reassign” the 10 from the ones column result to the
10's column. That term could be borrowed by and carried (pun
intended) into multiplication where you can “reassign” the 10's
place result of the ones place multiplication to the 10's place.
Hmm... maybe I can get a grant from the
government to write a few whitepapers on changing those concepts to
yet another term.... “reassignment”.
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