Still Failing the Kids
Examining Florida’s Math
Standards
by Katherine Livermore
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NCTM - National Council of Teachers of Math FCF-EP - Florida Curriculum Frameworks - Elementary Program GLE - Grade Level Expectations - Sunshine State Standards SCANS- Secretary’s Commission on Achieving Necessary Skills |
One of life’s inevitable truths is that if children are still failing to learn, new standards, tests, and school grading systems, no matter how highly touted, are not doing their jobs effectively. Many of Florida’s parents find their children in this situation today. For too many of Florida’s students, not one thing has improved through recent education policy changes, despite all the publicity stating otherwise. Along with the reports of alleged improvement, the papers are full of the protests of educrats and teachers who dislike being held accountable for the job they are doing. They say they are being forced to teach to the test and decry having to put so much pressure on the students to pass assessments that do not evaluate the “more important”, socializing aspects of education today. They also lament that the A+ Plan does not adequately take into account the social factors that make teaching such a difficult task, such as poverty and single-parent families.
The problems that I have encountered, however, are of another sort. I am meeting 1st and 2nd graders who have no idea how to add or subtract. These students do not know that in order to add, one starts with the higher number and then counts up. The notion that there are two quick ways to figure the answer to a subtraction problem is completely mystifying. (The kids can’t count backwards in any event.) They are clueless when it comes to recognizing such basic concepts as: If 6 + 6 = 12, then 12 - 6 = 6. Most to the point, they have not been taught that math involves doing something to come up with the answers; having not been taught the procedures necessary for computation, they are left to rely on the rote memory that most teachers pretend to despise. The best analogy for this is the Whole Language approach to reading, where children are expected to memorize words by sight. The math student is quite capable of remembering that 4 + 3 = 7, but for the average child, this does not transfer to remembering, by sight, that 9 + 8 = 17, let alone to 125 + 324 = 449. Faced with these problems, they will shift and fidget and lift their eyes to the ceiling as they wait for the answer to appear from their memory bank or simply state that they don’t know the answer. Older students will ask for a calculator. Even double digit adding and subtracting, with the added complexity of borrowing & carrying (called other names now), are out of the question.
The 3rd, 4th & 5th graders have the misery of trying to remember the multiplication tables to add to their addition and subtraction woes. Parents are usually wonderful about ignoring the teachers’ remonstrating against using memorization for mastering this body of knowledge. Out they will go to the local store, and home they will come with the flashcards. Night after night, it’s drill, drill, drill. However, they rarely know to provide the pencil and paper exercises integral to enabling the children’s advancement to applying this knowledge to ever more complex multiplication problems, and they do not know that this area of skills and knowledge must be periodically reviewed and practiced in order to be retained. Many parents do try to show their children how to do long multiplication and division; this is often how they discover the problems with addition and subtraction.
The 5th, 6th & 7th graders need help with fractions. It is no exaggeration to state that many of these students can visually identify 3 or c on a pie chart (only the “most commonly used” fractions) … period. Once shown how, sans manipulatives, adding and subtracting fractions with common denominators do not present much of a problem, if the numbers involved are simple, single digit, but easily finding the common denominator for two different fractions takes a strong familiarity with the multiplication tables. Reducing a fraction to simplest terms takes division – you see the dilemma. Piled on top of all the skill deficits, and particularly regarding this age group should effective instruction have been withheld until the children have reached this level, the obstacle of poor attitude will often present itself. Because the students have been conditioned to believe that the answers to mathematics problems are supposed to just “come” to them from out of the blue, or perhaps from group brain-storming, the multi-step procedures of working complex problems strike many students as incredibly prodigious amounts of work. The parent or tutor explaining what must be done in order to multiply two mixed numbers - and don’t forget to reduce - may be met with obstinate resistance. Students who started out loving Math come to believe it’s an impossibly difficult mish-mash.
In my opinion, these deficiencies are generated by the Sunshine Standards themselves. The errors inherent in the Standards have naturally led to the selection of atrocious textbooks and to serious flaws in the FCAT. From there it is a short step to the misleading, highly inflated school grading rubric. It is too simplistic to posit that the Standards are too easy or too hard. Instead, the Standards are often either inadequate or inappropriate to grade level, filled with obscure Edu-code, and cluttered with useless, confusing, non-sequential content which leaves uncovered the skills considered absolutely essential for a person to thrive in today’s society. All of this is wrapped up with recommendations of methodologies and strategies that have been proven to fail in producing academic achievement for students. Fixing defects such as these will take more than a little tinkering; it will take scrapping and starting over. Fortunately, there are models of excellence right here in the United States, and in some schools in Florida, to use in re-reforming the latest reforms. This paper examines how the errors in the Sunshine State Standards have negatively impacted the teaching and learning of Mathematics. Since I believe that what occurs during the elementary years is the cause of the shenanigans passing for a high school math curriculum, the focus will remain on grades K-8.
Origins and References
The problems begin at the beginning. On page 5 of the Florida Curriculum Framework- Elementary Program, the SCANS Report is cited as the major instigator of the standards movement that has taken place in states across the nation beginning in 1989. Florida joined this same movement by beginning work on writing standards in 1993. The SCANS Report trumpets the notion that the schools’ main task should be to prepare students for their future jobs. There is much high-faluting language throughout the report with many references to the needs of our “high-tech” society. Parents and other like-minded community members felt a surge of hope that this meant a return to the effective teaching of reading, writing and math. Unfortunately, another definition of the word “technology”, which is not often widely advertised, is “social engineering”. Since the states (most of them, identically) began reforming their schools to align with this “philosophy”, the SCANS report has been credited with the dumbing down associated with School-to-Work/Career programs. Sadly, “The SCANS competencies provide the basis for Florida’s Education Goal 3 Standards.”(FCF–EP, pg. 6)
The U.S. Department of Education, reacting to the SCANS Report, came up with the goals outlined in America 2000/Goals 2000. States across America did their usual half-hearted job of pretending that their new goals originated within the states when, in fact, they were almost exact copies of the Goals 2000 the Fed.’s handed down to them (with plenty of funding, of course). Goals 2000 is indelibly linked to the dumbing down that comes to the local school house in the form of OBE. Florida called her new “state” goals Blueprint 2000.
Committees were formed, at the national level, to tackle the more detailed writing of standards guidelines for each of the various subjects. The guiding document used in the framing of the Florida Math Standards originated with, you guessed it, the heartily derided National Council of Teachers of Mathematics (FCF, pg. 6). The NCTM is largely held responsible for the dumbing down of (pick one) a. New, New Math; b. Fuzzy Math; c. Whole Math; d. Rain Forest Math; or e. All of the Above.
Way back on pg. 442 (FCF–EP), in the extremely spooky “Chapter 4: Teaching and Learning”, we find Howard Gardner, the multiple intelligences shaman (root word: sham). His unproven theories have been adopted by school systems throughout the country because they appear to justify all the kooky teaching strategies that come in under the “diversity” and “learning styles” headings. The writers must have thrown in education historian, Diane Ravitch, in order to lend these standards documents a little legitimacy. Nothing doing. Ravitch is quoted (FCF-EP, pg. 29) from her book National Standards in American Education: A Citizen’s Guide, saying that Americans want and have standards that are strict, explicit and stringent when it comes to construction, telecommunications, water, food and air. That’s it! The implication is that since the public wants and needs standards in order to maintain our quality of life, that the succeeding written standards must therefore be good. It’s simply untrue. Ravitch stands solidly against progressive idiocy in all of her written works.
With the use, and in one case – abuse, of guiding lights such as these, the continued decline in achievement in mathematics of our Florida students was assured.
Point of View & Code Words
One of the ways in which the true meaning of educational jargon can be decoded is to take stock of the results and then work back to the language used by educrats and teachers to describe what is done to cause these results.
The dominant syntax of both the Florida Curriculum Frameworks and the more detailed Grade Level Expectations lays all the responsibility for performance on the heads of the students. Every single benchmark and expectation is headed by, “The student”, and then goes on to list all the accomplishments expected of the students under each goal. It’s “The student understands…”, “The student uses concrete materials…”, “The student explains…”. “The student will analyze”… this, that and everything else. Perhaps this would not be so unnerving if it didn’t so accurately express the thoroughly discredited progressive position on how learning occurs (i.e.: learning occurs naturally when the student is provided with a sufficiently motivating stimulus, which is always depicted in opposition to direct, effective instruction). As it is, this point of view upholds the instructionally passive, “facilitator” role of teachers and serves the schools as a “philosophical justification” for depriving students of the skills and knowledge they need. It also provides the structure necessary for the system to by-pass its own accountability for learning failure by neither defining nor addressing its role as a teaching facility. The disappearance of teaching is further signaled in schools where students are to be “active and/or independent learners” who “will develop an understanding” through the use of “creative and innovative ways” which will help the students “construct, devise, and discover their own knowledge”. Instead of imparting knowledge, the teachers are exhorted to set up the classroom environments which will optimize “opportunities” for student learning. This keeps the teachers extraordinarily busy decorating their classrooms, creatively deflecting parental complaints (now called “concerns”) and planning how to keep the students occupied for the hours that must be filled now that instruction and skill reinforcement are gone. The teachers’ main task, however, has descended to recording each student’s individual progress and labeling the multitude of failings in the most funding-rich way possible. Essentially, the Standards are a listing of what will be assessed, not what will be taught.
Understanding the extent of the instructional vacuum created by handing off all responsibility for student learning to the students, beginning when they are five years old, helps illuminate the intent behind the repeated insistence that families must become “full partners” in their children’s education. I’ve had parents tell me, with baffled disbelief, that they’ve come to think that they are the ones expected to do all the teaching. What good learners they are! But many parents do not know how to teach, nor what to teach and when. The consequences of progressive revivals are especially harsh for the children of parents who themselves were subjected to this same type of dysfunctional schooling. It is no secret that the poorly educated congregate in the lower socio- economic levels of our society. When schools refuse to teach, illiterate parents will not be able to fill this tremendous gap, and are least able to afford independent help. Hence the system’s poverty excuse perpetuates itself down through the succeeding generations of so many trapped families.
It is the withholding of direct, explicit, sequential instruction that makes the SCANS goals possible to achieve, and it is the NCTM’s widely imitated use of unfamiliar terminology that lulled the public, at least temporarily, into a dangerous complacency. When educrats proclaim themselves as experts, they must be referring to their skill at implying a highly intellectual handling of knowledge and concepts, while bringing our children down to breath-taking levels of ignorance.
Both the NCTM and the Floridian Frameworks writers break the Math standards into separate categories or strands. The NCTM divides content into Number; Operations and Computation; Geometry and Measurement; Probability and Statistics; Patterns and Relationships; and Problem Solving. Their priorities are indicated by calling for increases and decreases in attention to specific skills and practices. Florida’s Math strands are subdivided into Number Sense, Concepts and Operations; Measurement; Geometry and Spatial Sense; Algebraic Thinking; and Data Analysis and Probability. As previously noted, specifics are then given in lists of what students will know and do. Comparing further, however, it becomes evident that these slight differences matter not at all when it comes to the content covered and methods implemented.
In their 1989 “Summary of Changes in Content and Emphasis in K-4 Mathematics”, under the Number category, the NCTM calls for an increase in attention to: “Number sense; Place-value sense; Meaning of fractions and decimals; and Estimation of quantities.” (pg. 20) This can sound pretty rigorous to those of us who do not remember being taught anything about fractions and decimals until we reached higher grade levels. Juxtaposed to this, however, they recommend a decrease in: “Early attention to reading, writing and ordering numbers symbolically.” (pg. 21) These appear contradictory; what else could “number and place-value sense” be except the reading, writing and ordering of numbers? The confusion is cleared up when we read, in the helpful FCF-EP, “ Number sense is often described as an intuition about numbers and their relationships. This includes having a feeling for comparisons among numbers, a knowledge of the effects of various operations on numbers, the ability to make reasonable estimates, the ability to represent numbers in several ways, and the skills to interpret and use numbers from real-world situations.”(pg.75) (emphasis is mine).
Having students confidently capable of reading, writing and ordering numbers symbolically through sequentially higher numbers would take an explicit imparting of factual knowledge, while the words “intuition” and “feeling” are antithetical to the word “knowledge”. Even the children’s “reasonable” estimation of quantities are to be based on their uninformed instincts, rather than based on the children’s “knowing” something. It’s true that when left to discover or construct the quantitative logic of our number system, children develop only a vague understanding of place value; I’ve seen a great deal of hesitancy in this area in children as late as 4th grade. Certainly many children lack the ability to consistently apply this “understanding” to related problems. They cannot, for instance, figure out the ordering of 3 or 4 digits into the greatest or least numbers. As for the early introduction of the meaning of fractions and decimals, Webster’s New World Compact School and Office Dictionary (no pun intended) defines the meaning of “fraction” as: “2. Math. a) a quantity less than a whole, expressed as a decimal b) any quantity expressed in terms of a numerator and denominator” (pg. 172). The meaning of “decimal” is given as: “a fraction with a denominator of 10 or some power of ten, shown by a point (decimal point) before the numerator (Ex. .5 = 5/10).”
The FCF-EP’s reference to the students’ “knowing” the effects of operations takes us back to the attentions of the NCTM. Under Operations and Computation, the NCTM calls for increased attention to: “Meaning of operations; Operation sense; Mental computation; Estimation and the reasonableness of answers; Selection of an appropriate computational method; Use of calculators for complex computation; and Thinking strategies for basic facts”. (Summary… pg.20) Receiving decreased attention under the same category are: “Complex paper-and-pencil computations; Isolated treatment of paper-and-pencil com- putations; Addition and subtraction without renaming (Ed.– this is the borrowing and carrying of my school days); Isolated treatment of division facts; Long division; Long division without remainders; Paper-and-pencil fraction computation; and Use of rounding to estimate”. (Summary …pg. 21)
The students can be expected to discover that (+) means add, (-) means subtract, (x) means multiply, etc. Through “exploration” with their calculators, the children can also be relied upon to figure out that adding and multiplying result in higher numbers while subtracting and dividing result in lower numbers, hence the effects of these operations are expressed as something the students will know. Since the operational procedures themselves probably will not be figured out, especially as the kids venture into higher numbers, precision had to lose importance to the estimation … of answers. Happily, not any higher or lower number will do since the estimates are to be reasonable. Learning to make these reasonable estimates, also referred to as “predictions” in Florida’s Grade Level Expectations, must take gobs of carefully nurtured intuition. A great deal of time is spent on this estimation training. Perhaps it’s because answers that are too wildly off the mark risk being labeled as “guessing” by the concerned public. Here again, however, estimates are to be based on intuition since the use of rounding is to be virtually omitted. The students I’ve met have all heard of rounding, but cannot explain at what point one rounds up or down. Yet they receive pages and pages of estimation practice, at the expense of practicing the actual algorithms.
Beyond the facts they know by sight (mental computation), the students’ ability to perform these basic operations remains limited to sense (intuition and feeling), because at the point where sight memorization begins to fail them (complex computation), the students are to select an appropriate computational method. The appropriate method is decidedly not to include pencil and paper computation. Thinking strategies include all manner of bells and whistles designed to help children “sight compute”, much as reading strategies have been introduced in lieu of phonics, and are just as effective – not.
Children left to their own devices will try all manner of creative ways to figure out how to add and subtract numbers that need renaming, only to be completely baffled when they check their convoluted answers against those of a calculator. By focusing more on problems that do take this level of computational ability, the educrats skip a crucial step in the skill-building sequence and further push students’ early reliance on calculators. This tactic is echoed in the peculiar treatment of division. As suspected, division is quite gone. The children are not to be taught the division facts nor the procedure of long division, but they are to be presented primarily with long division problems that call for the added complexity of renaming! By eliminating paper-and-pencil fraction computation, the NCTM effectually forbids the teaching of the fractional operations, but considering the steadily mounting mathematical deficits, this could have been simply their way of preventing higher grade level teachers from attempting the impossible.
The folks responsible for Florida’s standards place themselves squarely in league with the calculator-pushing NCTM when they state, “…mathematics curriculum should be designed to prepare students to use their knowledge of number in flexible and creative ways, not just in routine, predictable calculations. In this respect, the emergence of calculators and computers as powerful tools for representing and manipulating quantitative information has presented a formidable challenge to more traditional forms of instruction.” (FCF-EP, pg. 75) These “tools” have presented a formidable challenge to academic achievement, too. So, that’s what they mean by “challenging”!
(Next: More on Florida’s Math Standards)
