Understanding basic mathematics expressions and the concept of equations is very important for the success in algebra. People who are successful in algebra were very strong in the mathematics basis of addition, subtraction, multiplication, and division. The students' mastery of the basics would make them more oriented to understanding algebra.
This article is about giving the teacher an idea of how to create the syllabus of the initial course in algebra. Since basic arithmetic is required before the student takes the first algebra class the teacher should not rely on that the student did that before. The first chapter should be about whole numbers. The students should have a good understanding of whole numbers. This should include counting, ordering, and arithmetic operations done on whole numbers.
The teacher should create a laboratory experiment using calculators to teach the students the concepts behind whole numbers.
As an example laboratory experiment the teacher should ask the students to use the numbers 1, 2, 3, 4 and the operations add, subtract, and multiply to form two expressions for each of the even values from two to ten. Then the students can repeat this to produce two expressions for each of the odd numbers from one to nine. The students can verify their answers by using calculators. The students can examine different expressions that give the same answer and compare their algebraic properties.
The students should then multiply three numbers of 1, 2, 3 and 4 to produce a number divisible by two. They should repeat this step to get a number divisible by three and they should repeat this step once more to get a number divisible by both two and three. Then they should be asked how we can get the greatest possible value by multiplying two of the four numbers. Finally the students should repeat the experiment using the numbers 0, 1, 2, 4, and 7.
The second topic that should be taught is the equation. The emphasis should be made on the underlying mathematics principles and not the formulas. The basic concept of the equation is the equal sign. The student should understand that this marks that the equation is balanced or in other words the expression on the right is equal to the expression on the left. The teacher should give a laboratory experiment using calculators to verify this concept. He should, for example, give the students a set of numbers say 1, 2, 3, 4, and 5 and ask them to create two equal expressions using the operations of add, subtract, and multiply. Each expression should contain at least three of the five numbers. The student should repeat this experiment several times and each time he should write an expression to the right and an expression to the left and he should put the equals sign between them. He should check that they are indeed equal by the calculator.
At this stage the student is ready to learn the algebraic expression. The student can start to learn that the mathematics expression is a series of one or more terms separated by a plus or a minus sign. The expression is composed of a variable and a coefficient and a constant. The single term of an expression is either composed of a variable which is a symbol or it may be composed of a number multiplied to a symbol. This number is called the coefficient. Lastly the term by be composed of a number only and in this case it is called a constant. The variable, which is the symbol, could be raised to a power. Exponents appear in super script above and to the right of the variable.
There should be laboratory experiments in order for the students to understand the concepts of algebraic equations. The students should be asked to evaluate simple algebraic equation with out exponents. They should evaluate them at different input points. They should use the calculators to verify the results. Next the students should be given equations with exponents and asked to evaluate them and verify results with calculators. The students should examine the effect of exponents on results. They should understand why we are using a symbol for the variable and they should understand which is the dependent variable and why.