Teaching Structur In Algebra

One of mathematics’s part that need to understand deeply in the first time is about algebra. There are strange mistakes have appeared from a lot of students that will cancel some objects in fraction form. They will cancel it and don’t realize that that numbers or expressions are different in a context.For instance, all look equally correct to them. It means that the concept from canceling numbers or expressions in fraction form hasn’t been understood by some students. And now, there is method to teach about algebraic transformations by naming the “glue” in expression, drawing expressions using “trees”, and describing “subexpression addresses” so that students can be helped to solve algebraic problems correctly.

                The first, students has to know which operation is the glue. It is very important, because identifying the gluing operation is essential to being able to construct an expression tree. An algebraic expression containing multiple operations and to name the operation that glues operation together and also in addition operations. For example, x+3y (the addition is the glue) and 2(x+3) (the multiplication is the glue). And recently, in fact the so-called order of operation is far more than a recipe for ensuring that everyone gets the same answer, this hierarchy determines the structure of expressions. But a lot of exercises will be still very useful to help them.

Secondly, teachers has to ensure that their students understand to make diagram of expressions as tree. Naming the gluing is the first step in here. Then identify the pieces that the glue holds together and the pieces themselves are algebraic expressions. If a gluing operation connects component pieces we can say that it has own internal structure.

And the last, students has to know where does a subexpression live. Naming the part of each structure are needed to make it easy to be understood. A factor is piece of a multiplication and a term is piece of an addition. For example, when we have (2+x)(2x+3), the gluing operation is multiplication, so the primary pieces 2+x and 2x+3 are the expression’s factor. And for 2x+3, the gluing operation is addition, 2x and 3 are the term.  Another way to help students when describing the structural location of particular subexpressing is by using the analogy of a street address, start from specific details and expand outward from the street, to city, to sate.

Back to the strange mistakes, it can be hold because students can’t determine there is or no a common factor of both the entire numerator and the entire denominator. So teachers need to same trick to ensure about there is or no a factor in the problem so that can be canceled. Another method to engage students about the structure that can be transformed is by substituting variable with number. It will be more simple because we use number not a variable. Sometime students will be confusing if they have seen variable. So I think it is vary useful to help them.

When we become a teacher, we have to have ability to teach students become genuinely fluent in algebra, so that our teaching can engage students in algebra at its actual level of conceptual sophistication while being accessible to them as beginners.