Mathematics is an invention of man—totally—and as such exactly mirrors man’s brain. It is man’s nature to count; and all mathematics is based on counting, even the most sophisticated calculus. The foundation is counting; and the pillars of the system are addition and multiplication. Taught properly, mathematics is easy to learn.
Our mathematics system can best be appreciated if a firm foundation is laid for the student. A student who tackles algebra without a sound knowledge of and an ability to quickly solve problems in arithmetic will be frustrated; not by algebra but by the distraction of solving the associated arithmetic. The basic operations of addition, multiplication, subtraction and division must become automatic, requiring little thought.
A parallel may be made with driving a car. To drive effectively, one must practice until the motions required are automatic; the same is true in mathematics.
The human mind stores in long-term memory what keeps coming back day after day. Many math curriculums are designed in units which are studied and forgotten. Basics+ never forgets a topic because there is constant review. Continuous practice in addition and multiplication tables, long addition, etc. is integrated into the study of fractions and other areas to assure mastery. Constant review is essential to a good learning program.
The books are self instructive and require little teacher instruction. When students start with this program in kindergarten and spend at least 45 minutes a day working on it, it is not unrealistic to have most students in algebra by fifth grade or before. This seems impossible to some, but consider this. If a student learns a topic the first time and constantly reviews it, then reintroducing the topic year after year is unnecessary and eliminated. The time saved is dramatic.
This speed should not be interpreted as pushing children. The author has found that if children are in a well-structured program which they understand and can perform in, the children do the pushing. Young children are learning machines. They want to know all they can. One of the biggest errors in today’s education is the underestimating of our youth’s potential and eagerness to learn. Many schools bore our children with a slow, disorganized curriculum.
Many in the mathematics teaching profession have declared that computation is out and calculators are in, that it is no longer necessary to know how to do the basic operations of math because a calculator will always be nearby to solve the problems. Calculators are false gods which can bring down the mightiest—by disappearing at an inopportune moment or by being used incorrectly. The operator must know more than the calculator in order to use it effectively.
The writers of this program love calculators and computers and use them daily. The reason for this love is an understanding of these tools and the knowledge that we command the tools.
In the mathematics education hierarchy, there is an aversion to memorizing and drilling. The belief is that only theory is needed and electronics will do the rest. It is these groups with this same theory that brought us the “new mathematics” in the 1960s which was a certified disaster. This author taught the “new math” and found that students did not care about theory and really couldn’t understand it until they could do the operations. They wanted to know how not why.
One must be proficient in the calculations to master mathematics. Many topics which are considered hard are, in reality, easy, if they are set on a firm foundation. Concentration on fractions or algebra is lost when a student must count on his fingers or use a calculator to do simple arithmetic. Seeing a student dependent upon a calculator with dead batteries is a pitiful sight.
The Basics+Mathematics program is designed so that students work problems which are easy and progress in small steps to the more complex. There is considerable drill in learning the addition and multiplication tables which are essential to the mastery of fractions, powers, roots, ratios, decimals, and signed numbers.
12 Algebra |
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11 Signed numbers |
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10 Powers & Roots |
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9 Ratios & Percents |
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8 Basic Algebra |
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7 Decimals |
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6 Fractions |
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3 Subtraction |
5 Division |
2 |
4 |
1 Counting |
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It has been the author’s experience that, at present, most students know their multiplication tables better than the addition tables. This may be because they can figure out addition on their fingers while multiplication is not as simple and requires memorization. Students should know both these tables so well that there is no hesitation in their answers. Students who have to figure out each time the sum of 8 and 7 and who use time which should be devoted to whatever topic they are studying stand a fair chance of coming up with the wrong answer; and they have broken concentration on the topic being studied. It is much more accurate and efficient to memorize the correct answer through working problems.
Basics+ has been tested in classrooms, homeschools, and used in tutoring situations, resulting in revisions that make the program more effective. It is anticipated that this field testing and review will continue. If the weakest student can understand and master the material so will the best student, but quicker. Weaker students may need to go through a book again to master the material. Better students may want to skip books or material, but this should not be allowed because of the practice required to assure the material is in their bones (or their long-term memory).