Reclaiming Real "Basic Skills" in Mathematics Education

Reclaiming Real "Basic Skills" in Mathematics Education

by Nakonia (Niki) Hayes

Raise your hand if you know what "basic skills" mean in today's world of math education. What's the basis for your answer? Is it from personal experience as a student, comments made by a teacher or administrator, or media reports on the "math wars" between traditional and progressive educators?

It's a safe bet that most folks will say "basic skills" mean "knowing how to add, subtract, multiply, and divide correctly." It's an equally sure bet that many teachers trained in the progressive, whole-math approach will shudder at the thought of having to use what they consider traditional methods to teach basic skills—those boring, rote, repetitious activities they label "drill and kill" (called "drill and skill" by traditionalists).

Basic skills have been scorned and systematically dismissed as a valuable part of learning in mathematics by progressives for almost 40 years. That negativity escalated to a new level when the National Council of Teachers of Mathematics published their Curriculum and Standards in 1989. "Math wars" have been waged between traditionalists and progressives ever since.

Now a demand for a "return to the basics" among some parents, educators, and businesses is gaining momentum. Consistently low math scores on standardized tests in public schools and college placement tests are prompting that call for action. Before turning back the clock, however, it will be important to clarify what "basic skills" mean today.

Are there places where basic skills are still taught successfully, according to students and teachers? As a matter of fact, basic skills are the foundation for the growing business of adult education. A staggering number of adults, who have been part of public education opportunities but who did not learn the principles, rules, or "mechanics" of core subjects, for whatever reason, are now spending money and personal time to learn those skills.

A review of these programs shows a changed perspective is needed about when and where to learn basic skills and what they are today. These skills aren't just for young learners—and evidently never have been. "Basics" exist in every new subject or environment, whether in work or personal settings. In essence, each domain in life has its own set of "basics" and principles to be learned that impact mastery and success within that domain.

Kimberly S. Lightle writes for the Eisenhower National Clearinghouse website, designed for math and science teachers at http://www.enc.org, and explains what students need to learn in order to be successful in the workforce. In "Today's New Basic Skills: What Students Really Need to Know," she says, "The basic skills of reading, writing, and arithmetic have morphed into the 'hard skills' of basic mathematics, problem solving, and reading at higher levels and the 'soft skills' of working effectively in groups, making effective oral and written presentations, and using computers well." Ms. Lightle also quotes from Teaching the Basic Skills: Principles for Educating Children to Thrive in a Changing Economy, a 1996 book that lists the following skills needed to get a good job:

read at ninth grade level or higher;

do math at ninth grade level or higher;

solve semi-structured problems where hypotheses must be formed and tested;

work in groups with persons of various backgrounds;

communicate effectively, both orally and in writing; and

use personal computers to carry out simple tasks.

She concluded that workers nine years later, in 2005, require even greater skills and "very few will require less." (The subsequent question could be, "What are ninth grade reading and math skills and who decides?")

A strong example of adult education is offered by the University of Nevada, Las Vegas (UNLV). They operate the Center for Workforce Development and Research with 12 modules that teach workplace basic skills. The use of specific strategies, tactics and/or principles is designed to teach workers organization (linear thinking) and evaluated plans of action (critical thinking). These modules include the following:

1) Business Planning—an overview of strategic planning; practice the steps of creating a business plan and budget.
2) Communication—fundamental strategies with basic guidelines and rules for business writing, basic proofreading, and completing paperwork.
3) Critical Thinking—steps of critical thinking for logical/effective problem solving and how to put these strategies into action.
4) Decision-Making—a skill-based procedure.
5) Integrity—strategies for professional improvement and avoidance of negative thinking.
6) Leadership—useful leadership principles in the workplace.
7) Math—basic math skills for analyzing and solving word problems; refresh and sharpen skills in addition, subtraction, multiplication, division, fractions, and decimals.
8) Negotiation—techniques to manage conflict effectively; tactics to create winning outcomes.
9) Responsibility—cultivation and exhibition of job responsibility.
10) Self-Management—goal-setting techniques; put proactive and positive mental attitude tactics into action.
11) Time Management—specific steps to maximize productivity and effectiveness; more organization, less stress! [their exclamation]
12) Working with People—smart strategies for respecting others and understanding different cultural backgrounds.

Interestingly, the basic skills taught in adult education are the same ones that public schools—and even the NCTM Standards—say they are addressing. The wording may be different but the ideas are the same. So why the declared antipathy of NCTM Standards toward teaching basic skills in K-12 classes?

A summary of the math wars at this point may be helpful. With the 1989 publication of its Curriculum Standards by NCTM, the "soft skills" listed above were codified, promoted, and widely adopted by college teacher-training programs and professional development personnel in school districts. Basic skills were regarded as lower-level thinking and activities, especially with the assumption that calculators would eliminate the need to know basic operations of adding, subtracting, multiplying, and dividing.

The how of learning was to be facilitated and the what (product) did not have to be correct answers to problems. Subjective assessments, in turn, created an environment of soft grading. But math, which is by its very nature based on precision and "right" and "wrong" answers, did not fit cleanly into the literary model of creative expression and subjective opinions. Nonetheless, "whole math" went forward as a replicate of the misused and abused "whole-language-osmosis-approach" to learning basic principles of a discipline. Process became product in mathematics education.

This approach, with its discovery learning and big-picture understanding of concepts, which was to lead to an "intuitive understanding of principles and algorithms" among students, set into motion open warfare between progressives and traditionalists. Many traditionalists maintained that much could and should be learned from teacher-directed instruction and that repetition was not a dirty word. In fact, many believed that repetition is the "mother of pedagogy." Enriched repetition and remediation were expected to be part of any good instructional program with appropriate and transcendent activities that engaged students—not just tickled their thinking processes.

In addition, some traditionalists believed that good teaching is composed of three parts: 1) instruction (what to do); 2) facilitation (how to do it); and 3) transcendence (why do it; i.e., its meaning/relevance). A singular emphasis on facilitation ignores the need for initial explanations, principles and properties. Such basics give historical purpose and rules for problem solving, which can then be used as a baseline from which to build abstract reasoning and creative solutions. The accusation that traditionalists focus only on instruction, with little or no facilitation during class work, has been a continuous criticism in NCTM publications.

Transcendence has always been the weakest link in K-12 teaching, according to Professor Reuven Feuerstein, director of the International Center for the Enhancement of Learning Potential in Jerusalem. Transcendence is more than transference. The first means "to exceed, rise above, and go beyond the limits." The second means to "convey or remove from one place to another." Transference means lateral, not vertical, movement. The NCTM attempt to introduce meaning and relevance, or transference, centered on the use of "integrated activities" and a multitude of manipulatives. They assumed the act of doing math would provide meaningful relationships to learners. The fact is that it takes deliberate teacher-guided direction to "discover" transcendence.

Adult education programs, however, do seem to show evidence of transcendence. The lessons require concrete learning of basic skills and content knowledge, perhaps even using formulaic methods, on which applied learning and creativity can then be based. Admittedly, these are willing learners who have realized the necessity of education. Yet, the conclusion is that direct instruction and application of skills, in a restricted time, and which most likely require learners to pass a test in order to earn a certificate or license to work legally in their fields, is the format accepted by adult learners.

Meantime, an economic boom developed over the past 17 years for publishers and authors as "integrated math" textbooks have flooded the classrooms and training programs. Those texts, now under fire because their curriculum has been described as episodic in scope, are criticized for being a mile wide and an inch deep. This is creating a shallow understanding of fundamental math skills, algebra, geometry, and trigonometry among most high school students, according to colleges and universities. Consequently, students' math deficiencies must be met with remedial coursework (basic skills) at the college level, with no credit being earned toward graduation.

In a "Position Paper on Basic Mathematical Skills" published by the National Council of Supervisors of Mathematics [emphasis added], a rationale was given for expanding the definition of "basic skills." It may surprise some people to learn this paper was written in January, 1977.

"There are many reasons why basic skills must include more than computation. The present technological society requires daily use of such skills as estimating, problem solving, interpreting data, organizing data, measuring, predicting, and applying mathematics to everyday situations.

"The changing needs of society, the explosion of the amount of quantitative data, and the availability of computers and calculators demand a redefining of the priorities for basic mathematics skills."

The math supervisors said "basic skills" fall under 10 areas that are interrelated and may overlap, and the order of their listing is not by priority or importance. For the sake of brevity, the 10 areas have been summarized:

Problem-solving—the principal reason for studying mathematics: posing questions, analyzing, translating and illustrating results, drawing diagrams, using trial and error, applying rules of logic, recognizing relevant facts, subjecting conclusions to scrutiny.
Applying Math to Everyday Situations—interrelated with all computation activities: use everyday situations, translate them into math expressions, solve, interpret results in light of initial situation.
Alertness to Reasonableness of Results—calculating devices in society make this skill essential.
Estimation and Approximation—techniques for estimating quantity, length, distance, weight, etc.; know when result is precise enough for purpose at hand.
Appropriate Computational Skills—addition, subtraction, multiplication, division with whole numbers and decimals and simple fractions; complicated computations will usually be done with a calculator; knowledge of single digit number facts and mental arithmetic; use of percents should be developed and maintained.
Geometry—concepts of point, line, plane, parallel, perpendicular, basic properties of simple geometric figures with emphasis on measurement and problem solving; recognize similarities and differences among objects.
Measurement—minimally: measure distance, weight, time, capacity, temperature, angles; calculate simple areas, volumes; use both metric and customary systems with appropriate tools.
Reading, Interpreting, and Constructing Tables, Charts, and Graphs—condense numerical information into manageable/meaningful terms and use conclusions with simple tables, maps, charts, graphs.
Using Mathematics to Predict—elementary notions of probability to determine likelihood of future events; identify immediate past experience that does not affect the likelihood of future events; use math to help make predictions.
Computer Literacy—understand what computers can/cannot do.

The math supervisors also explained that Minimal Skills are primarily limited to computation (unemployment likely); Basic Skills include the 10 topics described in their Position Paper (employment likely; doors to further education open); and Expanded Skills include the basics and a success at gaining more knowledge (potential leaders; educational opportunities increase as math skills grow).

They stressed that learning basic mathematical skills is "…a continuing process which extends through all the years a student is in school…any effective program of basic mathematical skills must be directed not back, but forward to the essential needs of adults in the present and the future, said the supervisors. [italics added]

How is it these recommendations have been around for almost 30 years, yet it was the 1989 NCTM Standards that gained attention and momentum? The NCTM use of psychologically-oriented pedagogy was eagerly accepted by teacher training programs. Math education was radically redirected. How did they manage this victory in a field (education) notoriously slow to change?

Perhaps a more stunning question can be posed based on both adult education programs and the math supervisors' 1977 paper. It appears, if taken as a whole, the 1989 NCTM publication is a creative extension of the 10 areas listed by NCSM, but with an emphasis on the "soft" basic skills required in adult education. The discovery teaching methods insisted upon by NCTM, and its clear disparagement of content instruction and "basic skills" throughout their materials, has evidently obscured this reality.

The 2000 edition of Curriculum and Standards supposedly took a more careful approach toward basic skills, according to a The New York Times article on April 13, 2000. They said the new Standards had done an about-face regarding basic skills, by recommending that "…teachers emphasize fundamentals of computation rather than focus on concepts and reasoning." Yet this was followed by a contradiction in the NCTM "Commonsense Facts to Clear the Air." They wrote, "More than ever, mathematics must include the mastery of concepts instead of mere memorization and the following of procedures…(and) use technology…to arrive meaningfully at solutions to problems instead of endless attention to increasingly outdated computational tedium."

There are many people—educators, parents, and business leaders—who have been working in the trenches for years to bring balance to math education. These folks are the ones who should give a new succinct definition for "basic skills." With a focus on its powerful role and responsibility in math education, supporters of basic skills can take the high ground—and simply stop defending its importance.

It would be interesting to learn how NCTM pulled off this coup. Better yet, how can a coup be reversed without a bloody battle? Believe it or not, The Art of War is a little book that can offer some insight. This explanation of leadership skills is based on Sun Tzu, a Chinese warrior who lived around 2,500 ago. Widely studied today in schools for business, education, and military leaders, Sun Tzu offers wisdom for avoiding war yet gaining territory, particularly by outwitting opponents through honest assessments of one's own abilities and those of the opponent. In addition, he says it's preferable to win while allowing opponents to "save face."

Clearly, a major target for changing attitudes about "basic skills" must be teacher-training programs. Those will be key, and difficult, territories to reclaim. This could be moved along more quickly with the formation of a national coalition for those who support a balance of content-based and conceptual instruction and who can offer a clearly communicated view to activate the public—which can impact school and education directions. Two active groups at this time are Mathematically Correct (http://mathematicallycorrect.com) and NYC HOLD (Honest Open Logical Decisions on Mathematics Education Reform) at http://www.nychold.com. Among the many activists is William G. Quirk, an experienced teacher holding a doctorate in mathematics and an entrepreneur who developed and presented courses dealing with interactive systems design (http://www.wgquirk.com). Another is Diane Ravitch, Research Professor of Education at New York University and a recognized leader in rational approaches to teaching and learning (http://www.dianeravitch.com). When and how can all these leaders be brought together so their messages will become a united voice heard by the public—and then the policy makers, including those in schools of education?

Meantime, isolated individuals at site-based levels know that real time for real teaching is as limited as money—and both are being wasted. Many teachers work in school districts that insist the NCTM Standards be followed. There is little room to maneuver if a teacher wants to deliver a traditional curriculum that includes both basic skills and concepts. Much individual time and energy can be spent explaining the need for a more balanced math program within a classroom and/or working surreptitiously to provide traditional lessons. More often than not, teachers lose the argument, eventually give in, or leave.

But! Every new day provides a new starting point for new planning. For example, a school's math department can discuss this article and its explanation of today's "basic skills." Evidence can show the Standards are themselves an embroidered form of basic skills. Other resources, named throughout this article, can also be discussed. (That's called process.)

Such departmental meetings must activate plans to bring clarity to site-based issues before agreement can be expected. Each side must work to help the other side "save face." They must implement, sooner rather than later, a site model with strategies to address potential problems and successes (such as sharing the results). And they must be willing to take the time required to plan and implement these changes, as opposed to being given time to do it.

In summary, continuing to waste the time available for student productivity, while adults process arguments, must stop. It's more than being unproductive. It's unintelligent behavior—and a bad model for both mathematics education and children.

About the author

Niki Hayes served as Principal at North Beach Elementary School in Seattle. While there, she led reform efforts which resulted in huge gains in the Washington Assessment of Student Learning. Due to health requirements, Niki started teaching half time as a math teacher at Ballard High School. Next year, she will return to full time math teaching. She formerly worked as an education specialist for Region 12 Education Service Center in Waco, Texas where she served as 504 coordinator for its 79 school districts and as a teacher trainer for the SPED programs. She has also been a principal for a P-12 public school on the Spokane Indian Reservation. Nakonia (Niki) Hayes can be reached at n.c.hayes@worldnet.att.net

©September 2005 New Horizons for Learning
http://www.newhorizons.org
info@newhorizons.org
For permission to redistribute, please go to:
New Horizons for Learning Copyright and Permission Information