Question: Will the Common Core Standards Fix This?
It’s a rare thing anymore for me to
meet a student who knows how to subtract correctly. Many of them subtract upside down, at least
for part of the problem. I am not
talking about little 1st graders who are just beginning to learn; most recently I am talking about having met a
2nd grader closing in on third grade, a 6th grader, and an
8th grader all doing the same thing.
Faced with a problem such as 92 – 18, too many of today’s students will
place a 6 in the ones column and an 8 in the tens. The 8th grader started reaching
for his calculator when I told him he was wrong. He’s been using a calculator for 3 - 4 years
now and knows how to do absolutely nothing without it. That young man opted for an after school
tutoring program when he saw I wouldn’t allow him to use his calculator - nor
count on his fingers. (I’m hoping
they’ll finally teach him how to do something besides push buttons.) The 2nd grader will be fine, and
the 6th grader is learning the multiplication table with mini
lessons on adding & subtracting using the age-old, efficient procedures
everyone grew up with before the Educators started foisting New Math on us.
It isn’t hard to figure out how
this has been happening – the standards used by Florida, and many other states,
have the teachers trying to cram so much material into the kids that there is
no time for them to actually learn anything.
The curriculum has everyone flying from one disconnected area to
another, often spending no more than a week on any one topic, no matter how
complicated, and no matter what the students’ skill set. One week it’s the four operations with
fractions, the next it’s converting decimals to percents – this with kids who
hardly know what a fraction is and who have the same problems as above with the
four basic operations even with whole numbers.
Compounding the problem is a lack
of emphasis on teaching the standard algorithms for arithmetic operations. By “standard algorithms” I mean the step by
step procedures we older folks all learned as kids. For instance, with a 2-digit subtraction
problem, the student will subtract the ones column first, borrowing if the
bottom number is bigger than the top, then subtract the tens column. (The Experts make a big deal out of calling
borrowing and carrying “regrouping” or “exchanging” as if this clarifies
matters. I don’t care if they call it
seizing and hauling as long as the kids learn how to solve the problems.)
Instead, we have parents as well as
students struggling with the results of nonsense such as Florida’s 2nd
grade standard MA.2.A.2.2 which states:
“Add and subtract multi-digit whole numbers through three digits with fluency
by using a variety of strategies, including invented and standard algorithms
and explanations of those procedures.” The key
phrases are “variety of strategies” and “invented” algorithms. This translates to the classroom as an
enormous number of methods that must be learned for even the simplest tasks,
and they really do mean to have the kids try to invent their own strategies for
solving math problems. This reminds me
of how they expected kids to “invent” spelling or “construct” the meaning of
text during the dark days of Whole Language.
I am not kidding. Below is just
one quote that can be found by Googling math algorithms.
“Invented strategies are flexible
methods of computing that vary with the
numbers and the situation.
Successful use of the strategies requires that
they be understood by the one who
is using them—hence, the term invented.
Strategies may be invented by a
peer or the class as a whole; they may even
be suggested by the teacher.
However, they must be constructed by the
student.”
The Experts must have gotten tired
of waiting for the 7 year olds to come up with algorithms that took a series of
geniuses a few centuries to figure out, so they decided to be creative and innovative
and invent some themselves. Under the seductive
guise of helping children understand the concepts
of math, it’s as if they were trying to make math as hard and horrifying as
possible. Below is one of the more counterproductive
“invented algorithms” I’ve seen so far:
To solve 35 – 9, the student is
supposed to cross out one of the tens and fill in the bottom block of ten ones
with ten little boxes. Then the student
is to cross out the top 5 boxes in the top block of ones plus 4 in the bottom
block. This leaves 2 tens with 6 ones in
the bottom block.
The next problem, which is
recreated on the back of an envelope, is set up to solve 63 – 28. The students are to cross out 3 tens, filling
the bottom block of ones with ten little boxes (I used slashes). Then the student is to cross out the 3 ones
in the top block plus 5 ones in the bottom block which leaves 3 tens and 5 ones
as the answer.
The above were taken from a
second-grader’s worksheet with the appropriate standard (above) written in the
upper right corner. (Publisher: Houghton Mifflin Harcourt)
The expanded form is popular for
far too long in a student’s career. This
looks like:
15 + 39
10 + 5 + 30 + 9
10 + 30 + 5 + 9
40 + 10 + 4
50 + 4
This can go even further and look
like this at a higher grade level:
34 + 27 = (3 x 10 + 4) + (2 x 10 + 7) expanded form
= (3 x 10 + 2 x 10) + (4 + 7) associative and
commutative properties
= (3 x 10 + 2 x 10) + 11
= (3 + 2 + 1) x 10 + 1 distributive property
= 6 x 10 + 1 = 61 simplified form
And there are these (for 3rd Grade):
I found the paragraph under this example pretty interesting. The kids are instructed to work in pairs or groups, hence the "shared" algorithms. And the remark about how adults use the method that starts with the 1"s - silly grown-ups!
And there are these:
If you would like to explore the
wonderful world of invented math, all you have to do is Google something like:
“Standard algorithm for addition”. Give
yourselves plenty of time, there’re just tons of these examples out there. I clicked on a couple dozen – they would
start off with showing the requested standard procedure and then go off on
their flights of fancy. Many of the
sites that exhibit alternative algorithms for basic math have university
addresses and are put up by folks who no doubt consider themselves the “Experts”
in their fields. This is not a reason to
believe that their opinions deserve any special kind of respect, especially
since all their theorizing is proving to be such a dismal failure for so many
children. Should you feel yourself being
swept up in their seemingly high-minded, intellectual sounding, jargonistic
gobbledy-gook, just remember, it’s people just like these who brought our
children travesties like Whole Language and invented spelling – indeed the
entire dumbing-down era of OBE and Blueprint 2000.
The public schools are confusing
the introductory modeling of math concepts with the methods for performing the
functions, and the resulting mish-mash isn’t working. In fact it’s proving to be detrimental to the
academic progress of American students.
This is why we keep having to import so many foreign born, and educated,
students to fill up the higher education seats in American Universities – we’re
not even teaching our kids how to add and subtract correctly. And the jobs – the high end, math dependent
jobs.
And guess what? Singapore schools teach their students the
standard algorithms! Duh!
So – are the Common Core Standards
going to fix this? Maybe not. We’ll be taking a close look.
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