• U.S. education system gets failing math grade
    By ALEXANDER S. BELENKY | June 08,2008
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    Public education is likely to remain among the key issues in U.S. presidential campaigns. Every election season, society widely discusses challenges that American workers will face in their careers in the 21st century.

    The new global economic environment demands the retraining of many Americans. New technologies open opportunities for workers who can meet the requirements for high-tech jobs. The competitiveness of American tech workers depends on their ability to quickly acquire new skills as the country's needs change.

    A worker's ability to adapt to technological innovations is in large part based on the analytical skills and particular knowledge he or she has developed as a student.

    Five components of contemporary education are critical for a person to succeed in life. Mathematics develops intuition and logical thinking. Physics also develops intuition, and it's critical to developing the ability to understand the physical world. Arts develop imagination, creativity and the ability to look at phenomena from a new perspective. The study of languages enhances communication skills. Athletic activities create the healthful foundation for success in any field.

    A student proficient in these five areas can develop the necessary skills to work in any field. It's long been recognized that students who are successful in mathematics are almost inevitably successful in physics, chemistry, biology, computers and other sciences, though mathematics and physics develop, generally, different types of thinking in students.

    Success in mathematics predisposes a student to succeed in other school subjects because this discipline in particular helps students develop analytical thinking, the most critical ingredient of proficiency in other subjects.

    Yet, American public schools mostly prepare students for passing math tests. This approach to mathematical learning, however, doesn't necessarily develop analytical thinking and may even suppress it.

    A student who successfully passes the tests often cannot solve a problem that doesn't formally resemble those he has solved in the past. This is the case even when solving the problem doesn't require techniques beyond those already known to the student. This student, who is prepared only to perform rote mathematical tasks, is usually unsuccessful in other school subjects.

    This phenomenon has an explanation. The existing teaching model for mathematics encourages students to memorize problem solving techniques, but it doesn't teach the logical fundamentals of these techniques. Consequently, the system doesn't help students understand the logic of finding solutions.

    Memorizing solution techniques is often sufficient to pass the tests, especially those with multiple-choice answers, even if this isn't accompanied by understanding the techniques. Though memorizing facts without comprehending the logic behind them is tedious, boring and time-consuming, it's a habit many students employ in the study of all subjects.

    Such students may eventually score well on the SAT and other national tests. But they cannot compete in colleges and universities with students, especially with European school graduates, whose analytical thinking was gradually developed over the years. After receiving bachelor's or master's degrees, European students have a distinct advantage over their American counterparts in university studies and in finding well-paid jobs in the United States.

    Teaching the logical fundamentals of mathematical techniques requires memorizing only a few basic concepts and facts. Most of the techniques that students study at school are relatively simple logical corollaries from the basic facts and concepts. Logical reasoning establishes connections between new problems and these facts and concepts.

    Yet, teaching basic mathematical concepts and facts is practically absent in the existing system of teaching mathematics in American schools, and so is training for establishing connections between these basic facts and problems under study. Their absence diminishes the chances that a student will ever develop analytical thinking, since the knowledge of the basic facts and the ability to establish such connections underlies analytical thinking, allowing a student to successfully approach problems that haven't been studied before.

    Mathematics teachers should first explain basic mathematical concepts and facts. Only after students comprehend the basics should they study particular solving techniques. Finally, the students should develop the ability to establish logical links between the studied basic facts and every problem that they are trained to solve.

    Under this approach, not only do scores for tests improve dramatically, the ability to think logically rapidly develops. Upon noticing progress in their mathematical studies, the students start trusting themselves. They realize that what once seemed to be achievable only to others is now achievable to them as well. This is how hope and self-confidence come even to those who could have been a loss to society otherwise.

    Also, developing analytical thinking in students forces all school teachers to better prepare for classes in subjects other than mathematics. The students possessing elements of analytical thinking are likely to notice inconsistencies and ask about more details in classes on any subject.

    Memorizing facts instead of comprehending their logic isn't a productive way of learning for everyone though it remains the major one for many. Moreover, not all school students (and not even all adults) possess the ability to memorize any reasoning without comprehending its logic. This is similar to what happens in teaching left-handed children to write with the right hand. These children simply aren't comfortable or even capable of doing it. But this doesn't mean that they can't learn to write.

    Different children are predisposed to different styles of thinking. What is good for many may not work for other students. For instance, surprisingly, a more formal and abstract approach to teaching mathematics is often more productive for many "hard" or even "hopeless" students, who usually experience difficulties in studying mathematics in the traditional manner.

    Teaching the logical fundamentals of mathematical techniques accompanied by one to two hours of everyday properly designed mathematical exercises can gradually develop analytical thinking practically in every student. Yet, under the existing priorities in public education, the test scores are what matter. Even if school teachers want to develop analytical skills in children, they do not have time.

    Children whose families can afford an experienced math tutor and children whose parents can help them develop analytical skills have an advantage at school. But is there a solution for the other students?

    Specially designed after-school programs may be one solution. Training already working teachers and preparing new ones to run such programs could start rather quickly. Methodological materials that are based on proven, world-recognized educational systems are widely available. Scientists actively working in the field of mathematics and its applications are the most experienced potential instructors, since they use analytical thinking in their everyday lives. These instructors are the best for both training mathematics teachers and working with students in the framework of after-school programs. Also, contemporary information technologies can contribute to enhancing after-school programs in the new format.

    Particular schools could become national models for developing and conducting after-school programs in the new format. Once both mathematics teachers and the students from the designated schools in a state start feeling the power of analytical thinking, they will share their experience with the other schools in the state, contributing to the transition to better teaching of school mathematics.

    The battle for the country's future starts at school. Developing analytical thinking in American children is critical for their competitiveness in colleges and universities and at high-tech jobs in the 21st century. The 2008 election is an excellent opportunity for addressing one of the core issues in public education – adequate mathematics programs – by offering viable proposals for bettering the status quo.

    Alexander S. Belenky, has a doctorate in systems analysis and applied mathematics and visiting scholar at MIT's Center for Engineering Systems Fundamentals. He is the author of several books on mathematical methods.

    in systems studies.
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