Help with Math: Tutoring, Or Homeschooling Math Approach

Before beginning to help with math you must know where the problem lies.  And, when you ask the person to be helped you need accurate information.  So, ask.  But do not accept the answer of everything to what do you not understand.  Most people know more than they realize.  If this happens and even if it does not, probe by asking the person to show you how to solve a certain problem.  Start out with an easy problem.  This lets you know where the barrier is.

The reason for this is it is better to fix the problem rather than start a new approach.  A new approach is likely to be half learned, as was the first one, and the student will get the two methods confused.

Try to explain the step that is the barrier as a first step.  It may be rote learning is not the person’s style, so be ready with an explanation.  Never just give steps and say do it like that.  The why is important, and once why is understood the problem often is understandable.

There are several ways people learn math.  One way is the traditional technique where the problem is studied, and the method is understood.  But, not everyone works well at that level of abstraction. 

The other two methods of learning, hands-on and visual, are similar. Working a problem hands-on requires use of manipulatives.  Math manipulatives exist for arithmetic through algebra, and can be algebra tiles, base ten tiles, sticks and blocks, and aids in working with fractions, decimals, and percents.  In fact, some packages of different manipulatives designed for a given level are available.  The student can work with these and actually solve math problems.  Visual learners can learn from watching you use the manipulatives, or by watching or viewing problems solved on paper or on a video. 

So, before expending energy and causing frustration, first determine if the student will benefit from a hands-on or visual learning environment.  Work for success.

Find three towers, one for fractions, one for decimals, and one for percents.  If these use the same size pieces, and match colors they can be used together to show the decimal, percent, and fraction equivalences.  

A complex problem may have many steps, but most of them may be familiar to the student.  Take solving quadratic equations by factoring as an example.  The student should first have learned factoring, and also have learned to solve a linear equation.  Now, there is just one step to insert.  Dropping a lengthy problem on a student all at once is daunting, but if it is explained that there is just one new step, and everything else is known, confidence can result.  And confidence is a major step in having the student be able to solve math problems.

Start with simple problems that are easily solved.  Once the student learns to solve these go to a slightly more complex problem.  Again stay at that level until the student has mastered the problems at the level.  Eventually, you will get to the most complex problems. 

As an example of what I mean here I will use the linear equation.  Start with just one step to the solution, such as a division or an addition.  Then add a step, and explain why the steps are done in order.  Eventually work up to problems with parentheses, and finally get to problems where the variable appears in multiple places.  After the idea is firmly entrenched, introduce the special case problems such as those with an infinite number of solutions, and those with no solution.

Dumping a variety of complex problems on the student initially might well destroy the confidence that is so important for success.  Build the confidence and the complex problems may very well also be mastered.

While it is best to explain the one step the student does not understand, there are times when the lack of understanding is more severe.  It is for these times that I recommend, if the teacher allows different approaches, to abandon the technique and try something else.  Some people get one approach, but not another.  Change approaches as a last resort, but have another method available if needed.

In some cases the problem in understanding math may just be a matter of confidence.  But you cannot just command a student to have confidence.  Learn how to help build confidence by reading a good book on overcoming the fear of math.  If the student is old enough, invite the student to read the book as well.

Math is learned by practice.  But, working numerous problems wrong is counter-productive, as it entrenches the wrong technique.  Either find problems where solutions are given, or solve the problems yourself.  Then, check, or allow the student to check, one problem at a time, and only allow the student to go on if the problem is mastered or an error is explained by you.  Help when errors occur, then give another similar problem. 

Be reasonable.  I would think about three or four problems successfully solved would allow for progression to the next level of complexity.  Overdoing practice where the student is fine with understanding is exhausting on both you and the student, and may cause resentment to working on.  

Calculators are powerful tools, and some like the TI-83 and TI-84 can be used to solve equations.  Others can even handle much of calculus.  But, the calculator does not develop the logic the problems were designed to develop.  Part of learning math is to develop a thought process.  The problem may be incidental to what the deeper purpose is, so calculators may not be allowed in school. 

But, calculators do have a role.   They can be used for checking purposes.  Their accuracy is reliable, so allow use of a calculator in checking answers.  Here, if the level is arithmetic, an inexpensive calculator, or even a phone, may do.

The TI-30 will do nicely for arithmetic, the TI-84 can solve equations, and the I-89 can express answers with radical symbols and even factor.  Use these for checking work, not to solve problems.

I will share two disasters where helping with math went wrong, so you can see what might happen.

In the first case I was teaching at a university, and part of the math faculty duties was to assist with the math tutoring lab one hour a week.  The university had students to do most of the tutoring, while one or two of us was there to help with courses that the student tutors could not, like calculus and statistics.  One student who often worked the same hours I did had just passed algebra, and gotten an A.  So, he helped with algebra.  But it was soon apparent he was doing severe damage.  Hos approach, and often with objection from the students he helped, was to just toss everything the student had learned and insist on learning the method he understood.  Faculty often have the skill to solve the problem by many methods.  I would hear students pleading, saying that is not how we do it in class.  But, he would not yield, possibly because he could not understand another method. 

The other case was a high school student I was helping with physics.  She seemed to know the material quite well.  But her grades were in the failure range.  One day, she had to divide one number by two others, like 90/(2X5).  She typed the problem into her calculator and got the wrong answer.  There was no use of the parentheses in her calculation, so she actually multiplied by the five instead of dividing by it.  I explained the subtle difficulty and she started getting high grades.  Then she told me that there were about ten others from her former elementary school, and all were having problems.  Here, a teacher at the elementary school apparently taught the students to be calculator dependent, and failed to teach them the proper way of using that calculator.  So, it was probably a teacher who caused damage by doing things wrong.

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