Saturday, January 24, 2015

A Short History of Math Instruction in the United States



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...






No comments:

Post a Comment