By Stephen Portz
I
remember growing through my public school days during the 60’s and 70’s and
having the usual struggles with homework.
My father worked in the aerospace industry at Kennedy Space Center and was a
whiz in math. I would go to him for help
with my math homework and he would check my arithmetic and would make things
look so easy. He actually thought stuff
like that was fun! I considered him a
math god for his ability to do word problems and calculations so quickly in his
head. But as my program of study moved
into the high school years and the math got less concrete and more
abstract, dad was not able to help me anymore.
He would look over what I was supposed to do and then look at the sample
problems and try to make reason of the assignment. Invariably, he would shake his head and tell
me that he couldn’t make sense of this “new math.” I remember thinking, “What
the heck is this new math and how is it different than the old math? I couldn’t do what my dad could do with
numbers - he was pretty impressive and after all he was the proverbial rocket
scientist, and if he couldn’t do it how could I ever expect to master it?”
“What
the heck is this new math and how is it different from the old math?"
All of
these concerns have stayed with me. As a
secondary school engineering technology teacher and as a parent that has tried
to help my own children navigate through math classes, my curiosity about the
impact that the changes in the math curriculum has had in our country persists. More recent international tests (PISA) have
revealed that whatever has been done of late to try to improve math education
has been appalling ineffective as United States students scored 29th
of the 65 countries tested. Another
troubling statistic is that the US has fewer high performing youth, just 2% of
test takers as compared with about one third of all students in Singapore scoring
as high performing.
While conducting this study in the evolution of math education, the thing that strikes me most is how often the educational “experts” have tinkered with educational philosophies, methods, and content down through the years. There is a feeling of a constant state of flux and instability like some haphazard research experiment gone wild. Who can calculate the effects that this experimentation has had on our country’s computational and competitive ability? Educational Professor William Bagley from the University of Illinois, similarly lamented,
“In no other country are the
professional students of education so influential. In no other country is
school practice so quickly responsive to the suggestions emanating from this
group. We may stigmatize our schools as "static,"
"reactionary," "slow to change,"-- reluctant to adopt what
we, in our wisdom, prescribe. But compared to other countries, ours is the “educational
expert's” paradise."
Quoted
in Diane Ravitch, Left Back, p. 193.
The
subject of math education in America has been so often debated, reformed, and
repackaged in the educational community that all efforts to right the ship have
commonly been referred to as the “math wars.” It may be supposed that math
instruction, like many subjects, have proponents for certain methods as well as
detractors for others, since its very inception.
Even
the celebrated physics icon Richard Feynman at one time waded into the fray, "If
we would like to, we can and do say, 'The answer is a whole number less than 9
and bigger than 6,' but we do not have to say, 'The answer is a member of the
set which is the intersection of the set of those numbers which is larger than
6 and the set of numbers which are smaller than 9' ... In the 'new'
mathematics, then, first there must be freedom of thought; second, we do not
want to teach just words; and third, subjects should not be introduced without
explaining the purpose or reason, or without giving any way in which the material
could be really used to discover something interesting. I don't think it is
worth while teaching such material."
Richard
Feynman 1965 essay "New
Textbooks for the 'New Mathematics"
Although
the new math movement was highly criticized and eventually discarded, it is
interesting to note that it was the only time in our educational history that mathematicians,
and not educators, actually wrote the curricular materials:
“Mathematicians have agreed for years that emphasizing
sets and number bases in math programs designed for the lower grades was a
horrendous mistake. Notwithstanding these errors, however, the difference
between the current slew of textbooks and those from the new-math days of the
1960s is definitely worth noting: Accomplished mathematicians wrote many of the
texts used in that earlier era, and the math—though misguided and inappropriate
for the lower grades and too formal for the high school grades—were at least
mathematically correct. Some of the high school texts were absolutely
first-rate, and new-math–era textbooks like Mary Dolciani’s “Structure and Method”
series for algebra and geometry continue to be used by math teachers who
understand mathematics and how it is to be taught. (They usually used them on
the sly, since most teachers are required to use the books that the schools
have adopted.)”
Some historical perspective is warranted
here. Prior to our country’s Sputnik
moment, teacher’s education programs were mostly institutions that taught
pedagogy, not subject area content. The
philosophy here being, that if you know how to teach students and you have a
content textbook, then any material should be able to be taught by any
certified teacher. With regard to math
instruction, this time period was distinctive in that leading math professors
in the country were very vocal about the impropriety of teaching advanced math
topics to the masses. Prior to WWII less
than 50% of students graduated from high school. Students going on to college were in the low single
digits and so the effort to teach everyone geometry, algebra and trigonometry
was seen as foolishness because most students would never use the skills.
"With regard to math
instruction, this time period was distinctive in that leading
math professors
in the country were very vocal about the impropriety of teaching
advanced math
topics to the masses."
During
WWII, the academic competencies of the American GI were called into question by
Admiral Nimitz. At a time of great
national security urgency, military recruits had to be trained in math to
understand gunnery and logistics computations because their public school
education was so poor.
http://www.math.cornell.edu/~henderson/courses/EdMath-F04/MathWars.pdf
After
Sputnik was launched, Americans felt the schools were in crisis. Nikita Khrushchev
famously banged his shoe on the desk at the United Nations and shouted “We will
bury you!” This of course prompted the ensuing
rush to educate our students in the hard sciences. The National Science Foundation (NSF),
created in 1950 to promote basic scientific research, was expanded in 1957 and
began to examine and promote change in secondary school education in math,
biology, chemistry, and social sciences. The changes in the curricula and texts
had a filter-down effect on the primary schools as well.
But
the effort to have a large federal entity producing curriculum for the state
educational systems and local school districts met with resistance. Especially after the highly controversial
MACOS curriculum was created and disseminated by the NSF in 1970. This curriculum fell into disfavor because of
the way it challenged students to think about belief systems and the way it
questioned absolutes of morality. The
MACOS incident raised considerable suspicion about a strong central agency of
the government using tax dollars for what some perceived as an indoctrination
scheme.
Mathematics presented a different situation. Mathematicians criticized the new
programs because the content was too abstract and neglected significant
applications; teachers criticized the programs because they were too difficult
to teach; and, parents criticized the new math because they worried that their
children would not develop fundamental computational skills. The movement had a
far reaching effect, in the academic year 1976/77 almost 60% of school
districts were using one or more of the federally funded programs in grades 7
through 12; and 30% of school districts reported using at least one program in
elementary schools.
After
a period of time the political clamor had died down and another crisis in
education emerged with the 1980s report, “A
Nation at Risk.” Once again federal
agencies were empowered to study and make recommendations for how to improve
our nation’s schools.
So the
history of federal funding of curriculum has been a long on again
off again
study of agencies finding and then walking a fine line between
rising to meet
the security demands of our nation without prescribing content
and methods
which take away from the freedoms and powers of its citizenry.
In 1989, the National Council of
Teachers of Mathematics (NCTM) published its Curriculum and Evaluation
Standards for School Mathematics—an extensive set of mathematics standards for
grades K–12 which de-emphasized memorization of number facts, the learning of
proofs, and algebraic skills, but encouraged the use of calculators and
“discovery learning.” Two years later,
the NSF promoted the standard and awarded millions of dollars in grants to
textbook writers who aligned with it, as well as the districts who adopted the new
NCTM Standard.
This
spiked an additional wave of controversy in math education which emerged in the
1990s prompting what President G W Bush would refer to as the teaching of
“fuzzy math.” Several of the methods
that came out of NSF grant funding involved a de-emphasis of arithmetic
computational skills by students, an increased use of calculators even in
primary grades, and a notion that the teaching of efficient algorithms should
take a back seat to students developing their own creative ways to solve
problems in what is termed “discovery learning.” A telling quote from the book
publisher states:
“The authors of Everyday Math do not believe it is
worth the time and effort
to develop highly efficient paper-and-pencil
algorithms for all possible whole number,
fractions and decimal division
problems....It is simply counterproductive to invest
hours of precious class
time on such algorithms. The math payoff is not worth the
cost, particularly
because quotients can be found quickly
and accurately with a calculator.”
Below
is a flow chart of funding for the development of math education curriculum
during the 1990s:
Pay particular attention to 1999 and beyond to understand the repercussions and fallout of these math policies...
To
understand the public backlash against the NCTM math programs of the 1990s, one
needs to understand some of the mathematical shortcomings of these programs.
The mathematics books and curricula that parents of school children resisted
shared some general features. Those programs typically failed to develop
fundamental arithmetic and algebra reasoning skills. Elementary school programs
encouraged students to invent their own arithmetic algorithms, while
discouraging the use of the superior standard algorithms for addition,
subtraction, multiplication, and division. Calculator use was encouraged to
excess, and in some cases calculators were even incorporated into kindergarten
lesson plans.
More recently, Senator Tom Coburn
of Oklahoma introduced legislation to curtail NSF research that was viewed as wasteful use of
taxpayer dollars. This action specifically targeted research that can be construed as have political
implications/motivations such as studies on voter patterns as well as other social science research, but it has had
the effect of causing the agency to consider more carefully all the research that
it funded and the way the public perceives the influence of the NSF.
The effect of this scrutiny has
been to guard against what may be construed as undue influence. As a result, the party line at the agency is
that the NSF does not prescribe or dictate curriculum to the states. But without question it definitely funds
research in curriculum development to its surrogates such as the NCTM. It is likewise disingenuous to portray these
activities as non-influential to state and district educational bodies and textbook
publishers as well.
Fast forward to Common Core Math Standards and much of the hullabaloo begins to have some context, like the road most traveled.
Some questions to consider going forward:
As we have seen through the years what certain "educational experts" have wrought and the result, what assurances does anyone have that this math makeover will be effective or at least less damaging than past efforts?
What standards and curriculum are used by high performing international programs? Do the common core math standards use any elements of these successful models from around the world?
Are high performing countries recognizing that the US has new math standards and are migrating to that as well because they are so good? For example, the NCTM Math Standards from the 1970's were originally adopted by Israel but they abandoned them for the Singapore Standards.
As is frequently said, ad nauseum: "the standards are not the curriculum" which is kind of like saying to a product designer the design specifications do not effect the design limits and constraints.
Of course they do, unless perhaps you are applying a new math standard...
Of course they do, unless perhaps you are applying a new math standard...
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