Math Mastery — Posts

Are there any additional or long term benefits of math tutoring?

The short answer to this question is “yes”.  I would say that there are at least four additional benefits that come with tutoring and mastering math, that may not be on everyone’s radar when they sign up for tutoring.   These are the skills of being systematic and methodical, being able to think logically, being able to think critically, and being able to look at something from more than one point of view.

Most parent’s primary goal in providing math tutoring for their child is to improve their grades, or perhaps to provide support for them in an accelerated math program.   And of course everyone looks forward to the improved self confidence and the positive attitude towards learning that comes with improved scores on homeworks and tests.   In addition, every one is aware that math skills can be useful in a variety of real life situations, from the most basic tasks like balancing a checkbook, to those undertakings requiring very advanced mathematical abilities such as theoretical physics, or designing the next rover for Mars.

So improved grades, enhanced self confidence, and real world math skills are often the items that are at the top of the list when someone signs up for tutoring.  Besides these benefits, with a good tutor, and with time, the skills of logical and critical thinking, the habit of considering multiple perspectives, and being methodical, are all skill sets that can be developed as a result of math tutoring.

Perhaps the first of these is simply learning to be systematic and methodical.  As one gets into Algebra, and as math problems start to get more complex – often requiring multiple lines of calculations – it becomes necessary to work them in a systematic and orderly fashion.   Skipping steps, or doing too much of the work in one’s head will often result in incorrect answers, especially for the beginner.   So becoming really good at math means learning the discipline of being rigorously systematic and methodical while working a problem.

Then of course math and logical thinking go together.  The student learns that if one thing is true, then mathematically, another truth always follows from that.   While this kind of reasoning is somewhat implied in Algebra,  it is the heart and soul of the proofs that one does in Geometry.   Getting good at math means getting good at following a logical train of thought.

The next two skills go hand in hand and are more easily, or at least more quickly, developed with the help of a tutor.  These are the skills of critical thinking, and the ability to look at something from more than one angle.

Critical thinking is not quite the same as logical thinking.  With logical thinking, you understand when one thing implies another, and so that being at point ‘a’ means that you will end up at point ‘b’.   With critical thinking you are stopping to ask “Does this make sense?”, “Is this true?”. This is a very useful question to ask as you are doing math.  It can save you from grievous simple arithmetic errors, as well as other more complex mistakes.

For example, if you multiple and calculate that 35 x 47 = 783, and you ask yourself  “Does this make sense?”, you will realize that your answer should probably be between 1200 (30 x 40), and 2000 (40 x 50).  If you work the problem again, and get the correct answer of 1645, you will know that you have an answer that makes sense.   Since students who are struggling just to get their homework done usually don’t take the time for this kind of thinking, having a tutor who does ask these kinds of questions will really help teach the discipline of looking at an a problem critically.

The same thing is true of learning to use multiple approaches in order to check one’s work.  As problems get more complex, one of the best ways to check ones work is to look at it from another angle.  If you created the  graph of a line by plugging in points for x and y, what happens if you put the equation in y intercept form?  Does the slope look right?  Is the line going through the y axis at the right point?  Having a tutor come along and ask these kinds of questions helps the student to understand what they are learning from more than one perspective, and it helps ingrain the habit of checking one’s work by looking at it from another angle.

So in the short run, the goal of math tutoring is going to tend to be about test scores and grades.  In the longer run, math tutoring can help instill habits and skill sets that will be invaluable, and that will last a lifetime — far outliving the achievements that were the impetus for tutoring to begin with!

Why does math seem so difficult?

One of the reasons math seems hard is because it requires a certain amount of repetition and dedication. Math takes time. The frustration comes when you are putting in the time and not getting the desired results because there are gaps in your understanding.

Even a very skilled classroom teacher is not going to be able to tailor every lesson and explanation so that all of the pieces fit together every time for every student. With math, sometimes just a tiny missing piece is the difference between all of your answers being right and all of your answers being wrong.

That is the beauty of having a private math tutor — the missing pieces can be identified, and the needed explanations given so that one’s time and effort yield success and mastery rather than frustration and confusion.

Also, for many students, math seems difficult in part because they are not used to having to consistently apply themselves to a subject in order to do well in it. Bright students may have gotten through middle school math just fine without ever really worrying about completing their homework. Somewhere in high school this lackadaisical attitude often tends to create less-than-desirable results. A tutor can emphasis the importance of keeping up on one’s homework, and create a certain amount of accountability.

Math does require diligence. And all the diligence in the world is of limited use without sufficient understanding. Lack of either hard work or lack of understanding will tend to create problems for the student, thus giving the subject the reputation for being “hard”. But the flip side is also true. With both hard work and understanding, math can yield the delight of success in an arena where mastery once seemed utterly impossible.

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