For students of all ages, math continues to be one of the toughest subjects to learn and master. Just the thought of the subject plants negative thoughts into many students’ minds. Fortunately, the anxiety that students have towards learning math can be eliminated.
To build self-esteem when learning math, there is a hierarchy of learning that a student must follow in order for him/her to feel confident about learning the subject. For instance, a student should not try to learn fractions when he or she has yet to master adding and multiplying simple numbers. That will cause a student to lose confidence and perhaps fail in math.
Obtaining the services of a great math tutor will help a student build confidence in the subject, because the tutor will be able to help him/her build the mechanics that is vital to achieving better grades with math. Believe me, it is not an overnight fix by any means; but with learning the basics of each math subject along with practicing math problems will ultimately see positive results.
I will discuss the 4 levels of hierarchy students will need to learn in order to gain confidence with math and build high self-esteem:
ARITHMETIC
One of the first lessons a student will learn in math is to count from 1 to 10. He/she will learn that each of these numbers have a value and how they relate to each other.
In mathematics, there are different types of numbers. The types of numbers that a student will learn during his/her grade school education are called real numbers. Real numbers can be broken down into several parts. The first set of real numbers that a student will learn are called natural (or counting) numbers: 1, 2, 3, 4, 5, etc.; all the way to infinity!
Once a student gets a good feel of how these numbers operate, he/she is taught arithmetic operations: addition, subtraction, multiplication and division. A student should first master adding and subtracting single digit numbers, then proceed with learning how to add and subtract multi-digit numbers. Once the student masters addition and subtraction, then he/she should create a single-digit multiplication chart and memorize it. Once the student memorizes the chart, he/she should be able to tell you what “3x6” or “8x9” is without hesitation. Dividing these numbers will come easy once the multiplication chart is memorized. Afterwards, a student should learn to master multiplying and dividing multi-digit numbers.
PRE-ALGEBRA
The arithmetic portion of math is pretty straightforward. Now that a student has mastered the arithmetic, he/she will begin to learn about the other types of real numbers and number types as illustrated below:
a. Whole numbers: these are natural numbers, which also includes the number zero
b. Integers: contains the number 0, the natural numbers and their negative counterparts (ex. -2, -1, 0, 1, 2)
c. Fractions and decimals: these are numbers that are not whole numbers or integers. An example of a fraction is a number like“1/2”, where the 1 is the numerator and the 2 is the denominator. An example of a decimal is a number like “5.125”. Fractions can be converted to decimals and vice versa.
d. Rational numbers: these types of numbers consist of whole numbers and integers. They also consist of fractions, along with decimals that can be converted into a fraction.
e. Irrational numbers: these numbers are decimals that cannot be converted to a fraction, because the decimal values go to infinity and there is no set pattern.
f. Exponentiation (powers) and square roots: Exponentiation is simply a number multiplied by itself which is normally expressed “x squared” or “x to the second power”, where x represents a real number. A square root is simply an inverse of the power. For instance, the square root of 49 is 7, because 7 to the second power is equal to 49.
Once the student learns about these types of numbers listed above, he/she will need to learn how to add, subtract, multiply and divide these numbers. This is an area many students struggle with.
In addition to learning about the different types of numbers and performing arithmetic operations on these numbers, a student will also learn about inequalities. For example, the expression, 8 > 3, in which the “>” signifies “greater than”. A student will see more of these expressions when he/she takes Algebra. A student will also get a taste of geometry, where he/she will learn about shapes, an area of a shape, etc.
ALGEBRA
Once a student learns how to add, subtract, multiply and divide all types of numbers; whether they are whole, integer or rational numbers, now it’s time to generalize the process. That’s where Algebra comes into play. There are rules regarding how to calculate different types of numbers. With Algebra, they are expressed in the form of variables: letters that represent a number or value. A student will discover that Algebra will be used in many future math and science courses.
OTHER MATH AND SCIENCE SUBJECTS
Once a student learns Algebra, it opens the gates to learning many subjects, such as Geometry, Trigonometry, Calculus, Statistics and even Physics. Each of these subjects use some form of Algebra.
Building confidence and self-esteem with learning math does take baby steps. It is not something that be obtained overnight, but the time and effort in learning and practicing math problems will ultimately show with improved grades. Help is available outside the classroom if a student needs additional help with certain mechanics. In closing, knowledge plus perseverance plus practice will equal straight A’s on the report card.
