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Literacy is to language as numeracy is to mathematics. They both represent a different means of communication which is very important to our civilized life. Both literacy and numeracy are on the decline in the United States of America. There are a lot of differences in form and structure; both in natural language and mathematical language are very powerful tools for representation, description and communication. The use of numeracy is very important for a nation expecting to compete in a global economy. On the other hand the natural language is ambiguous, redundant and concrete and the mathematical language is abstract, precise and concise, precise, and abstract. Full expression of vision and thoughts and visions requires the richness of both mathematical language and the natural. Yin and yang, literacy and numeracy are the example of human communication. Mathematics is a very basic and core subject in child education. All over the world the IQ tests include an assessment based on the system of numeracy and therefore it is very important component of our lives and intelligence. Researchers have found that there is some evidence that humans have an in-born sense of numerology and numbers. According to one study a five month old infants were shown two different dolls, after that they were hidden with a screen. The babies easily identified the different dolls. According to Jean Piaget the concepts of number and quantity in children developed with age. The international study of mathematical achievement has tested many different children from around the world at the stage of fourth-grade the average of which is 11 to 12 years; they also tested the children of eighth-grade the average of which is 15 to 16 years; this included the children in 49 different countries. The criteria for the assessment included algebra and tests for number which are called relationship and patterns at fourth grade. The assessment also included geometry, measurement and data. Another study conducted in 2003 found that children from Singapore had the highest level of performance at both the grade levels. Japan, Taiwan and Hong Kong also had high skills and levels of numeracy. South Africa, Saudi Arabia and Ghana has very low level of numeracy. In most of the countries the difference by gender was negligible, but there were exceptions for instance, the girls performed significantly better in United States, and boys performed better in Singapore. In studies of gender and choice of science careers, age is also found to be related with gender. Therefore it was proved that at different stages the girls performed better with science and mathematics.
A Rising Tide of Numbers
The word numeracy is widely used in England more than anywhere in the world. This tradition of practical purpose has had the effect of equating both literacy and numeracy with the scope of the elementary school curriculum. It is what is meant by “reading, ‘riting, and ‘rithmetic.” Indeed, in countries all over the world, the principal purpose of primary education is to achieve a minimal acceptable level of literacy and numeracy. Yet it is only in the last century that even this goal has become widely accepted. So whatever levels of literacy and numeracy we may have achieved are not standards steeped in ancient tradition. Today’s vision of a literate and numerate society is a rather recent ideal. Expectations for numeracy have risen at least as fast as have the demands for literacy. Daily news is filled with statistics and graphs, with data and percentages. From home finance to sports, from tax policy to state lotteries, and from health insurance to new drug approvals, citizens are bombarded with information expressed in numbers, rates, and percentages.
Historical Perspective
Although arithmetic and geometry arose as instruments of commerce in ancient times, numeracy as a common demand of everyday life is a distinctive product of the scientific age. Just five hundred years ago the merchants of Venice began for the first time to teach addition, subtraction, multiplication, and division as a means of expanding their commercial influence. Three hundred years later, great universities began to require this vulgar arithmetic as a requirement for entrance, alongside Homer and Cicero. Today universities expect students to be ready to learn calculus which itself was just discovered 300 years ago and newspapers expect readers well-versed in compound interest, weighted averages, and statistical margins of error.
Although the definition of numeracy–whatever suffices for the practical necessities of life continually changes, it does not simply expand. Few people any longer need to take square roots by hand, even though such methods were emphasized in school arithmetic for nearly four centuries. Long division, which began its rise in fourteenth-century Venice, has likely passed its prime as hand calculators become as ubiquitous as pencils. By the turn of the century even algebra may be performed more often by machine than by human hand.
Contemporary Evidence
Today’s numeracy should be compared with requirements of today’s society. The Nation’s Report Card, which samples the 70% of 17-year-olds who are still in school, provides a fair measure of what passes for numeracy. Most students in this sample can perform simple one-step arithmetic problems such as comparing six dimes and eleven nickels, or reading a bar graph. However, only half of these students–that is, about 35% of the nation’s 15 year olds can solve moderately more these recent results in the United States confirm evidence gathered a decade earlier by the Cockcroft commission in England. Instead of relying only on written tests (as is typical in the United States), the British commission interviewed hundreds of adults to determine just how they used mathematics on the job and in everyday life. Interviewers in this study discovered a common perception of mathematics as such a “daunting subject” that more than half of those approached simply refused to take part in the study. On the job, the Cockcroft study discovered a surprising pattern. Most workers who needed to use specific job-related mathematics did so by methods and tricks passed on by fellow workers that had little connection (certainly none that they understood) to methods taught in school. Tradesmen frequently dealt in fractions with limited sets of denominators so calculation within this domain could be done by special methods rather than by the general-purpose common denominator strategies taught in school. In another example, a worker who had frequent reason to multiply numbers by 7 did so by multiplying by 3, adding the result to itself, and then adding the original number.
The most important result of school mathematics is the confidence to make effective use of whatever mathematics was learned, whether it be arithmetic or geometry, statistics or calculus. When apprehension, uncertainty, and fear become associated with fractions, percentages, and averages, avoidance is sure to follow. The consequences of innumeracy–an inability to cope with common quantitative tasks are magnified by the very insecurity that it creates.
An Invisible Culture
Mathematics is often called the invisible culture of our age. Although surface features such as numbers and graphs can be seen in every newspaper, deeper insights are frequently hidden from public view. Mathematical and statistical ideas are embedded deeply and subtly in the world around us. The ideas of mathematics of numbers and shapes, of change and chance–influence both the way we live and the way we work. Consideration of numeracy is often submerged in discussions of literacy, exposing only the traditional tip of basic skills for public scrutiny and comparative assessment. Strategies to improve numeracy will never be effective if they fail to recognize that arithmetical skills comprise only a small part of the mathematical power appropriate to today’s world. Approaches to numeracy must reflect the different dimensions in which mathematical and statistical ideas operate.
Practical Numeracy
Many mathematical and statistical skills can be put to immediate use in the routine tasks of daily life. The ability to compare loans, to calculate risks, to estimate unit prices, to understand scale drawings, and to appreciate the effects of various rates of inflation bring immediate real benefit. Regardless of one’s work or standard of living, confident application of practical numeracy provides an edge in many decisions of daily life.
Civic Numeracy
Whereas practical numeracy benefits primarily the individual, the focus of civic numeracy is on benefits to society. Discussions of important health and environment issues (for example, acid rain, greenhouse effect, waste management) are often vapid or deceitful if conducted without appropriate use of mathematical or statistical language. Inferences drawn from data about crime or AIDS, economic and geographic planning based on population projections, and arguments about the Federal budget depend in essential ways on subtle aspects of statistical or econometric analyses. Civic numeracy seeks to ensure that citizens are capable of understanding mathematically-based concepts that arise in major public policy issues.
Professional Numeracy
Many jobs require mathematical skills. Today’s jobs, on average, require more mathematical skills than yesterday’s jobs. Leaders of business and industry repeatedly emphasize the role of mathematics education in providing the analytical skills necessary for employment. One measure of the seriousness that business attaches to mathematics is that American industry spends nearly as much each year on the mathematical education of its employees as is spent on mathematics education in public schools.
Numeracy for Leisure
No observer of American culture can fail to notice the immense amount of time, energy, and money devoted to various types of leisure activity. Paradoxically, a very large number of adults seem to enjoy mathematical and logical challenges as part of their leisure activities. The popularity of puzzles, games of strategy, lotteries, and sport wagers reveals a deep vein of amateur mathematics lying just beneath the public’s surface indifference.
Games and puzzles, ranging from solitaire to chess and from board games to bridge, reveal a different vein of public empathy with mathematical thinking. Many people in widely different professions harbor nostalgic dreams, often well-hidden, of the “Aha experience” they once enjoyed in school mathematics. The feeling of success that comes with the solution of a challenging problem is part of mathematical experience, a part that many persons miss in their regular lives. The popularity of magazine columns on mathematical and computer recreations attests to the broad appeal of recreational mathematics.
Cultural Numeracy
Like language, religion, and music, mathematics is a universal part of human culture. For many, albeit not for the majority, it is a subject appreciated as much for its beauty as for its power. The enduring qualities of abstract ideas such as symmetry and proof can be understood best as part of the legacy of human culture which is passed on from generation to generation.
Although it may sound to some like an oxymoron, mathematics appreciation has always been an important part of cultural literacy. To understand why so many of the greatest thinkers from Plato to Pascal, from Archimedes to Einstein rooted their work in principles of mathematics; to comprehend the nature of mathematical knowledge; to witness the surprising effectiveness of mathematics in the natural sciences; to explore the role of mathematical models in the great new scientific quest to understand the mind; to understand how order begets chaos, and chance produces regularity these and countless other facets of mathematical activity reveal their power and significance only on the level of philosophy, history, and epistemology.
Educational Implications
Traditional school mathematics curricula do not deal uniformly with all aspects of numeracy. A pragmatic public supports two facets virtually to the exclusion of the others. But even within the two areas that are emphasized, the classroom treatment is often inappropriate to the objectives. Indeed, school mathematics is simultaneously society’s main provider of numeracy and its principle source of innumeracy.
Civic, leisure, and cultural features are rarely developed in school mathematics, except perhaps in occasional enrichment topics that are never tested and hence never learned well. These aspects of numeracy are slighted because neither teachers nor administrators embrace a broad vision of numeracy. All too often schools teach mathematics primarily as a set of skills needed to earn a living, not as a general approach to understanding patterns and solving problems. The disconnection of mathematical study from other school subjects–from history and sports, from language, and even from science is one of the major impediments to numeracy in today’s schools.
Diversity
Diversity in kind is matched indeed, probably overwhelmed by diversity in accomplishment. For example, pre and post tests of eighth grade students show that each of the four major tracks remedial, regular, enriched, algebra ends the year less well-prepared than the next highest class had begun the year. Enormous variation exists, even at that level, among students who study mathematics. In eighth grade alone, the four-year spread in entering skills was increased, as a consequence of one year of educational effort, to nearly seven years.
Mathematical learning progresses in proportion to what one already knows. Hence the range of student learning grows exponentially. The further one moves up the educational ladder, the farther apart students become. It is not uncommon for the mathematical performance of students entering large universities to be spread across the entire educational spectrum, from third or fourth grade to college junior or senior. In no other discipline is the range of achievement as large as it is in mathematics.
One measure of the spread is provided by the mathematical performance of U.S. students as they enter adulthood. We know that on average they do poorly. The weakest leave school, usually as drop-outs, with the numeracy level of an average third grader. The strongest compete successfully in an international mathematical Olympiad, solving problems that would stump most college teachers of mathematics. The gap between these extremes is immense, and filled with students.
Equity and Excellence
Increased variance leads to inequity. In jobs based on mathematics, inequity translates into severe under-representation of women and minorities. Concern about this issue has traditionally been based on issues of equity that all Americans deserve equal opportunity for access to mathematically-based careers. Demographic reality now shows that inadequate mathematical preparation of major parts of our work force will produce an America unprepared to function effectively in the twenty-first century. Equity has joined economic reality as a compelling factor in mathematics education.
