MATH RULES THAT WILL EXPIRE 1
PEMDAS is a rulethat has gained momentum in the elementary mathematics teaching inthe US. This rule is used to teach students methods of solvingnumerical expressions that contain various operations (Karp,Bush, & Dougherty, 2015). The rule helps students to solveexpressions that would otherwise be complicated and provide wrongresults if not solve correctly and chronologically. Central toelementary mathematics, this rule helps in deciding which operationshould be carried out first to enhance the outcome of any expression(Beckmann, 2014). However, one ofthe shortcomings of this rule is its generalizations by the student.It is imperative to note that the rule has helped various studentsthough there is a need for the teachers to continue delineating thegeneralization that constitute its shortcomings. For instance, theorder of the rule could be broken to allow for minimization of itsshortcoming.
Although the ruleshould expire by K-6, there is a need for the rule to be reserved inK-8. Allowing the rule to be used in K-8 will allow students who donot understand another order of operations to use the rule, whichbecomes easier for them. For instance, in an expression such as 30 –6(1+4) + 10 * 5, it would be hard for students who doesn’tunderstand math easily to note that one doesn’t have to follow theorder in this sum. The sum may be done by distributing 6 among 1 and4 and later subtracting the answer from 30, later continue withmultiplication and add the resultant answers.
Getting Rid of Fractions
Getting rid offractions is also another rule that has been taught to elementarystudent. One of the strengths of getting rid of fractions rule isthat it makes operation of an expression easier to a low gradestudent and to those who take time learning math operations. The ruleis also simple in terms of usage as elementary student are likely tobe able to get the value of the least common divider. However, therule has a shortcoming in that the elementary grade students becomemisguided that the rule is applicable in all cases. As equationsbecome complicated, it becomes hard to compute an expression bysimply getting rid of fractions. Although the rule has been helpful,there is a need for teachers to create new methods of teachingstudents on how to tackle expressions containing fractions. AsAharoni (2015) notes, there is a need for math teachers to possessalternate techniques that will enhance their teaching models.
If this rule hasto proceed to K-8, teachers need to help their students in ways ofconverting simple fractions into decimals to enhance operation speed(Streefland, 2013). Forinstance, teachers should be able to teach their students offractions that can simply be changed into decimal. Such fractionsinclude ½ which can be translated into 0.5.
Therefore, in an equation such as:
½ x = 10, the student can solve as 0.5x= 10
By dividing both sides by 0.5, the value of x is derived as 20.
Moreover,considering that some rules such as that of getting rid of fractionsusing a common denominator cannot be applied in all cases, there is aneed for teachers to prevent them from proceeding to K-8 unless thestudents are unable to uses the methods being taught in class(Sterling, 2013).
“Solve” versus “Simplify”
The two termshave been used interchangeably but it is important to note that thereis a significant difference in their meaning and mathematicalimplication. “Solve” should be used to find the set of values forthe unknown factors in an equation, which refers to the solution tobe derived (Stapel, 2017). On the other hand, “simplify” refersto the process of reducing the complexity of an expression to a formthat is easier to understand and operate with. Ideally, thedifference between the two terms extends from that of equations andexpressions (Tussy & Gustafson, 2012). Notably, solve involvesthe determination of an equation’s solution while simplify entailsthe reduction of an expression’s complexity. However, it isimportant to note that simplification can involve both expressionsand equations considering that the complexity of an equation can alsobe reduced. On the contrary, solving strictly involves equationswhere two or more values are considered equivalent (Bracken &Miller, 2013). The difference between the two terms is illustrated inthe following examples.
Solve: 6x – 4 =20
In this exercise,the equation has a variable that is unknown (x), whose value shouldbe determined. Notably, there is an equal sign separating two sidesof the problem. The first step is to rearrange the equation to makeit easier to work with.
6x = 20 + 4
6x = 24
Dividing bothsides by six to determine the value of x, we have
x = 4
Simplify 4y + 9 –2 – 3y
It is importantto note that there is no equal sign, which makes it an expression. Byplacing similar terms together, the variable (y) and numerals, theequation will be simpler to understand.
4y – 3y + 9 –2, which becomes
y + 7
Aharoni, R. (2015). Arithmetic for parents. Toh TuckLink: World Publishing.
Beckmann, S. (2014). Mathematics for elementary teachers withactivity manual (4th ed.). Boston, MA: Pearson.
Bracken, L. & Miller, E. (2013). IntermediateAlgebra. Boston, Massachusetts: CengageLearning.
Karp, K., Bush, S., & Dougherty, B. (2015). 12 Math RulesThat Expire in the Middle Grades. Nctm.org. Retrieved16 March 2017, fromhttp://www.nctm.org/Publications/Mathematics-Teaching-in-Middle-School/2015/Vol21/Issue4/12-Math-Rules-That-Expire-in-the-Middle-Grades/
Stapel, E. (2017). Simplifyingversus Solving. Purplemath.com.Retrieved 16 March 2017, fromhttp://www.purplemath.com/modules/simparen3.htm
Sterling, M. (2013). Algebra II for dummies. Hoboken,N.J.: John Wiley & Sons.
Streefland, L. (2013). Fractions in realistic mathematicseducation. New York: Springer.
Tussy, A. & Gustafson, D. (2012). IntermediateAlgebra (5th ed.). Boston,Massachusetts: Cengage Learning.