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The Status of Mathematics Education in the United States

Most students will fail to achieve the mathematical skills necessary to pursue a technical career unless a heavy emphasis is placed on the fundamental principles of mathematics.  Some algebra classrooms place much emphasis on higher order thinking skills at the cost of lower emphasis on drill and practice.  While we agree that higher order thinking skills are necessary for effective application of mathematics to problems, we retain the belief that effective higher order mathematical thinking requires firm understanding of fundamental mathematical principles.  Mentor believes that most students do not achieve an adequate grasp of these fundamental principles without liberal application of old fashion drill and practice.

Without a complete understanding of these fundamental skills, a student's learning path may lead to failure or to an excessive amount of memorization.  With an understanding of the fundamental principles of algebra, the algebra user can construct formulae as needed and not have to depend upon a long list of procedures, each procedure applying to a particular problem or problem type.

Algebraic problems are solved by rigorous application of logic and the laws of algebra and their consequences.  All problems are not subject to mathematical analysis.  It used to be that teachers would discuss well formed problem.   Such a problem had a definite answer that the student could find by algebraic means.  A student either gets the right answer or does not get the right answer.  Mentor believes that problems in which any student's answer can be judged to be as good as any other student's answer do not belong in the mathematics classroom.  This may be wonderful for the student's self esteem but it is bad for the student's education.

The National Council of Teachers of Mathematics is dedicated to reforming mathematics education.  The NTCM develops new curriculum to teach mathematics.  The argument is made that great benefit would result if all of the new curriculum could just be implemented.  However, international testing suggests that additional emphasis on mathematical fundamentals in general and algebra fundamentals in specific is needed.

The axioms of algebra are the basic rules of this subject.  These rules (axioms), and other rules (theorems) that can be derived from them, give us certain knowledge of things that can done with algebraic expressions and relations.  Without these axioms and theorems, the student must rely on memory for procedures to deal with each type of problem encountered.  The Laws of Algebra are easily learned and the most important theorems can be presented during the course of an algebra class  See What is Algebra for more discussion about why these laws are important.

Fortunately, individual teachers are very dedicated to their profession and to their students.  Mentor would like to see less of the education budget go to administration and more go to the classroom.  Academic competitions, such as MATHCOUNTS should receive the level of attention and funding as athletic competitions.  Mentor would like to see teachers have less reporting requirements and more time for fundamental academics.  Although it is too early to tell how it will actually work, Mentor has hope that the recently passed educational reform act, Leave No Child Behind, will have the effect of curbing social promotions, which burden teachers with students who are often not prepared for a particular class.

Mathematics Education is too Important to be left to Schools Alone

This is not an indictment of teachers.  Rather, it is a plea for parents and students themselves to be engaged in the education process.  If teachers could, they would willing give their students a pill containing necessary knowledged.

It is an unfortunate outcome of modern society that most of those who teach mathematics have never used mathematics outside of the academic environment.  This is not unreasonable for K-12 teachers, but it would seem reasonable for teachers at the university level to have some involvement with the use of their art in real life.  Instead, the application of mathematics (applied mathematics) has become linked with the notion of less rigorous course work.  The use of mathematics, such as that by physicists, engineers, computer specialists, accountants, and statisticians, should be a significant part of the mathemataics curriculum.

Mentor Products, Inc. offers a computer program that will help algebra students work algebra homework problems.  The Mentor Mathematics Advisor will allow algebra students to enter lines of algebra into the Advisor as they would write with pencil and paper.  The student will be advised on the correctness of each step.  Parents can use the Mentor Mathematics Advisor to verify that answers are correct.  The Mentor Mathematics Advisor cannot assist on those modern problems in which any answer is OK.  But then, students don't need help on a problem for which any answer will suffice.  The Mentor Mathematics Advisor does not assist with word problems; see What is Algebra.   It will advise the student on each step leading to the solution of a word problem once the problem is formulated into an algebraic problem.

Some Educational Indicators

Test scores that compare United States algebra students to students in other industrialized countries have shown in the past and continue to show that there is room for improvement in our educational system.

An interesting web site that points out many problems in our society was been put together by Michael Hodges.  Click on the Hodges Education Report to go directly to his education pages.  The reports by Hodges highlight, in a very readable and understandable form, some results from Trends in Mathematics and Science Study (TIMSS).  The Lynch School of Education at Boston College is to be commended for putting the detailed TIMSS information on the net.

Other Sites of Interest

While Mentor believes that it is important for you to do your own work, at times it is helpful to see an answer that you cannot find yourself.  QuickMath is an interesting site that provides support for this.  Mentor cautions you not to overuse this service but wants you to know of the tools that are available to you.

The REDUCE symbolic mathematical language is a powerful tool for the manipulation of mathematical expressions, the solution of equations, and many other advanced mathematical operations. Indeed, the The Mentor Mathematics Advisor uses REDUCE as an artificial intelligence engine. Mentor strongly recommends the REDUCE software for mathematics students who have achieved mastery of algebra.

Another site that addresses algebra problems is Algebra.Com.  At this site, you are given opportunities to work problems interactively.

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