Doing a Different Equation

12 NOV 2009

This morning a cable news show reported that the number of deaths in the US due to H1N1 flu was 4000 rather than 1000 as had been reported earlier.  The reporter went on to explain that the 1000 figure was the result of counting laboratory confirmed cases of H1N1 which resulted in death whereas the number 4000 is reached when all cases of H1N1 as identified by health professionals are counted.

At that point the anchor took over and felt compelled to clarify and summarize the story with the following statement.

There aren’t more H1N1 deaths than before, it’s just that we are doing a different equation.

The anchor’s statement is illustrative of broadly held misunderstandings and general ignorance of mathematics.

1.  Counting is mathematics – mathematics is counting.

The anchor immediately thought of mathematics (equations, variables, and all that stuff) as soon as the subject of counting came up.  Why on earth should the subject of counting conjure up visions of equations?  Only ignorance of mathematics can be responsible.  It is not explicit in his statement, but thirty years of experience prompts me to guess that he also thinks mathematics is about numbers only.

2.  We do mathematics.

Listen to the words when students, teachers, parents, and the general public speak about mathematics.  Compare those words and that language to the words and language used when other subjects are discussed.

Students study history, social studies, language arts, etc.  They read literature, history or other subjects.  They neither study nor read mathematics, but rather they do mathematics.

Teachers encourage their students to do their math every day to avoid falling behind.  Parents check to insure their children have studied their spelling, read their literature, studied their history, and done their math.

Students and ultimately all of our society learn from this language and come to view mathematics as something we do. We think of mathematics more in terms of a motor skill rather than an intellectual activity.  In fact, the impression that mathematics is a motor skill is so prevalent, that most people and indeed many teachers believe one learns mathematics by working hundreds of insipid problems listed in textbooks.

3.  Everything mathematical is an equation.

A common response when shown any mathematical expression is to attempt to “solve it”. It is a commonly held belief that mathematics consists entirely of equations.  Such simplistic and completely wrong impressions of mathematics overlook the more important aspects of mathematics such as:

  1. Mathematics as an intellectual activity,
  2. Mathematics as an application of deductive reasoning,
  3. Mathematics as a study of structures,
  4. Mathematics as a precise, descriptive, detached language.

4.  Equations always elicit the same response – do it.

It is a commonly held belief that mathematics consists of equations and it is believed that what one does with an equation is “find x”.

Ask this question of a College Algebra class.  “What is the degree of the polynomial in the equation 3x3 + 2x2 – 7x = 0?” Sixty to seventy percent of the students will attempt to solve the equation because the visual stimulus is in the form of an equation.

There is little appreciation that the variable x may represent any number in an equation such as 3x + 2 = 8, but that some of those numbers make the statement true and some make the statement false.

In mathematics classes there is no knowledge nor interest in the relation between an equation such as 3x + 2 = 8 and its twin siblings 3x + 2 < 8 and 3x + 2 > 8 whose existence is guaranteed by the Law of Trichotomy and whose solution sets are related and delineated by that same Law of Trichotomy.  For the majority of students and hence the majority of society they are three unrelated problems.  I suspect that is because they are usually presented in totally unrelated and widely separated chapters in most algebra books.

Similar comments can be made with respect to virtually every topic in mathematics.

The fault does not lie with students, the fault lies with teachers and what is promoted as mathematics education.

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