A Paradox in Mathematics

HANDS-ON:

A PARADOX:

SUGGESTIONS:

TEACHING:

To math, science owes a great deal of its success. In fields like physics, engineering, genetics, computer programming, chemistry and astronomy, great discoveries would be difficult or impossible without the help of complex math formulas and theories. It is often said that "math is the language of science."

As a result, we put great emphasis in our schools on teaching math. We all need to know basic math no matter what our occupation, but our math programs stress the importance of higher math like calculus, algebra and trigonometry because we know that many students will one day face the need for such problem-solving skills in domains such as biology, physics, chemistry, economics, engineering and teaching.

These demands will not be limited to the aforementioned fields since our world is rapidly becoming so complex that its problems in all fields are no longer easily solved. Today, we have numerous math teaching programs, tests and the curriculum drawn up by the National Council of Teachers of Mathematics, most of which mention problem solving as an objective, yet teach only textbook-type problem solving skills.

SO WHAT YOU HAVE IS THIS PARADOX:

	We go to great lengths to teach higher math because we realize its importance in all of the domains mentioned earlier.
	Higher math skills are used in almost every field to solve problems and serve as the base for quantitative analysis BUT…
	We do not teach the Complete Method of Creative Problem Solving, also called The Scientific Method, the Method of Inquiry and the Method of discovery as well as many other names.

AS A RESULT…

Students frequently resent learning higher math subjects, viewing them as irrelevant and failing to see the everyday as well as future career applications of skills taught.

WE MUST SHOW THEM MATH'S RELATIONSHIP AND USE IN THE COMPLETE METHOD OF CREATIVE PROBLEM SOLVING, also called THE SCIENTIFIC METHOD.

An inadequate transfer of learning exists where students do not learn how to apply their math skills to complex problems until a subsequent college course or job training.

While math is largely concerned with deductive reasoning, everyday practical thought involves induction and imaginative thinking. Pupils need to be taught creative / imaginative applications of math because today's problems are not always textbook type.

STUDENTS WILL BE MORE INTERESTED IN MATH IF THEY ARE SHOWN ITS PRACTICAL USE IN PROBLEM SOLVING THROUGH THE SCIENTIFIC METHOD:

We must consider teaching math in terms of its use of The Scientific Method in solving complex problems. Experienced mathematicians, scientists, engineers, etc. all stress that if a problem can be solved using mathematics, then the solution will be more reliable knowledge than if solved without math.

However, because of the exclusion of The Scientific Method from National Science Education Standards as well as from national mathematics reform programs and other teaching standards across the country, future mathematicians, scientists and members of the aforementioned fields are forced to solve complex problems without the aid of any method beyond the specific formulas found in their textbooks.

Raymond Nickerson explained in The Teaching of Thinking (1985) that,

"…one needs to have not only the domain-specific knowledge that is essential to skilled performance, but the knowledge of when and how to apply that knowledge in specific contexts" (p. 102).

Without The Scientific Method, education lacks transfer of learning where the students learn to apply knowledge and skills to all problem solving. And unfortunately, today's problems are far more difficult than textbook-type as we are presented with new challenges and information with each passing day.

The Scientific Method readily serves as an opportunity to take "real world" problems into the classroom for dissection and analysis so that students may grasp and appreciate difficult higher math skills they so desperately need to learn.

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