Learning Mathematics Requires Different Skills

Practice over and over, but make certain the answers are right.  Practicing over and over a wrong technique is counterproductive, for it leads to engraining the error in memory.  And, when practicing, always think!  Understanding is the way to confidence.

Believe you will succeed and you will, or will you?  Belief in success is the first step.  But it does not just happen.  It must be a real belief, based in fact.  Just thinking I can do this is not to last long after repeated failure.  The underlying principle is to first learn well, then believe.  And, that learning come from having the mathematics explained, then reinforcement with much practice.  Getting practice problems right should be the stepping stone to actual, success based, confidence.

There is a dilemma here, expense.  In this area one can choose from public education, private education, or homeschooling.  There is a saying. “You get what you pay for.”  When parents are not invested, too many students have no or little support from their parents after school, and the concept of no child left behind has come to mean entire classes are left to proceed at a slow pace as long as one student languishes, perhaps deliberately.  Perhaps it is not even the child’s fault, it often lies with the disengaged parents.  

Private education is better, since the parents are invested.  They write the checks and will more often do what they can to see that their dollars are not wasted.  So, they might be more apt to sit at night and help a child with homework.  And when more students are prepared, and the expectation that education move at a proper pace, the classes are more likely to actually learn.

Homeschool is a way a parent can get directly involved and assure proper success.  But, this is not without expense.  One parent might have to forego a salary to stay at home, and there are materials that cost.

In mathematics it is critical the material be completely covered, since mathematics builds on itself.  How can a person do division if subtraction is not already mastered?  So, if subtraction is poorly done one year will not division in the next year be difficult on both the teacher and the student?

I teach mathematics in a college, and I often get the mathematics courses that are aimed at the education majors.  How some of these students ever graduated from high school is a mystery.  I had them adding and subtracting fractions in a way that would cause them to actually understand what is happening, and they struggled with the task.  There was a repeated clamoring for calculators.  The problem is they plan to use calculators in teaching the early grades, mimicking too often their own teachers.  That will not prepare a student to divide in algebra when variables appear.  There is a belief that if I can do the problem it is fine, and being bothered with understanding is not desire.  So, they really do not understand arithmetic.  They cannot then explain arithmetic. 

Even worse, I once tutored a high school student who could not solve any problem without a calculator.  She had been taught incorrect calculator technique.  She told me the high school had a problem with about a dozen students, all from her former elementary school.  They were dividing by two numbers without first inserting parentheses, getting wrong answers. 

So, what is being taught is not always right, and it comes from the problems too many teachers had in learning mathematics, which has now been inserted into their teaching methods.

We must realize that studying mathematics has a twofold objective.  Yes, we must understand the problems well enough to get the correct answer, as we could with a calculator.  But we must also develop a thought process, or problems will present themselves later.

This is the first step to success.  Find a book that goes into depth on the difference in studying mathematics and studying other subjects.  Mathematics follows the rules of logic.  It means mentally planning a logical series of steps to a solution. 

A good start is to encourage playing chess.  The thought process chess will develop will carry over while not have the student even be aware that it is developing a study skill.  It is a fun way to develop a skill for a subject.

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Overcoming Math Anxiety

Recognize the difference in study methods for mathematics compared to other subjects.  One cause of anxiety with mathematics is the failure to succeed after what seems to be more than adequate study time and effort.  The amount of time and effort is secondary to properly utilizing that time and appropriately studying.  The subject is different, and evoking a different thought process is the real solution.  After that, practice is essential.  Learning one idea must then be incorporated with other, already mastered, ideas.  That is why success with a few problems is not enough.  Different material that you should have mastered is imbedded in the problems, and you must see ideas working in concert with each other.

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The introduction image is because it is my book.  Actually, in this case I authored the book shown.