Math Education: The Process and Skills
The Two Types of Math Education
First, let's discuss two types of math education. For our purposes, we'll name these math computation and math application.
Math Computation
Math computation is mastery of the basic operations of mathematical calculation. These are the math skills of addition, subtraction, multiplication, division, powers, roots, fractions, factoring, etc. These are predominantly a left-brained analytical activity.
The left hemisphere of the brain performs linear thinking, like math procedures, very well. It likes to take things apart, examine and practice the detail and individual skills involved.
Math Application
Math application is predominantly a right-brained holistic activity. The right hemisphere of the brain prefers to put all the pieces together and see the big picture.
This brain activity encompasses conceptualization, thoroughly understanding the process, knowing how to set up a problem, and what series of calculations are necessary to solve it. Word problems are a good example of math applications, these translate a verbal expression into a mathematical expression.
These problem solving skills are often called "Higher Order Thinking Skills", or "HOTS", because they can be more complex than the operational skill involved.
Both types of math education are absolutely essential to the thinking process. In general, neither is more important than the other. In specific situations, one type may be more appropriate than the other.
The Importance of Mastering Both Types of Math Education
Since higher order thinking skills are one of the end goals of the education process, the current methodology of modern math instruction in the United States is to emphasize HOTS as "more important" than basic skills and to over-emphasize conceptual math and word problems. The result has been to marginalize, even demonize, the teaching of basic math skills. The results have been disastrous! Our graduate math and science programs, as well as high paying math and science professions, are now predominantly filled with men and women educated in other countries because they still train in both higher order thinking and basic math skills.
The Pyramid of The Learning Process
Higher order thinking skills are not "more" important than basic skills, neither are they "less" important. They are just another level in what we call "the pyramid of the learning process". HOTS can be a much higher level of complexity, it's true, but no more important than the foundation, where basic math skills are mastered. The broader and stronger the foundation, the higher the pyramid that can be built upon it.
Good problem-solving skills come naturally to those who have good basic computation skills. Since they have mastered the basic set of skills, more of their mental capacity is freed up to concentrate on the other. Their confidence in their own ability and the rapidity with which they can solve calculations involved give them a pronounced advantage.
The most important step in the learning process should always be whatever step the learner is on right now. Basic skills are a pre-requisite for higher order thinking skills. An over-reliance on conceptualization to the point of marginalizing basic skills is like trying to build a pyramid from the top down and will only result in a student who has neither basic skills nor higher order thinking skills.
Our Math Curriculum Trains For Mastery in Both Skills
Jones Geniuses Math programs are designed to fill the need for mastery of both computation and application skills. For the most part, it's better if the student masters basic skills before diving into higher order thinking skills. If attempting to engage in HOTS too early, this only takes time away from mastery of the basic skills needed to build a firm learning foundation.
Many math education curricula now proscribe that kindergarten students begin learning algebraic concepts, probability and statistics. What kind of probability can you teach to a student who can't count to ten? You can flip a coin and demonstrate that it comes up heads half the time and tails half the time, assuming the child understands heads, tails, and half. Of course, this would not be so bad except that these concepts are being put into the curriculum at the expense of basic skills like counting and addition, which have been increasingly marginalized. Higher order thinking skills can and should be taught at every level of math education but will not be successful unless basic skills are mastered first.
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