sped 441 learning strategy assignment

SPED 441 Learning Strategy AssignmentBy Chad Bobbit

MathematicsAn important component to

becoming successful in learning mathematics is understanding its Order of Operations.

Operations used in mathematics include: Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction.

Order of OperationsThe correct order in which to perform

these operations is as follows- Parenthesis Exponents Multiplication *notice the

bolded Division letters Addition Subtraction

Strategy = PEMDASThis acronym is a common

memory strategy used to represent the order of operations in mathematics.

The phrase “Please Excuse My Dear Aunt Sally” is used in addition to remember the strategy “PEMDAS.”

RationaleThis strategy is easy to remember, especially

by using “Please Excuse My Dear Aunt Sally to remember PEMDAS.

It is a nationally accepted mathematics strategy.

It directly relates to solving mathematics problems at almost every stage in mathematics.

It gives a pretty clear definition of which operations must be performed first.

Jeon, K. (2012). Reflecting on PEMDAS. Teaching Children Mathematics, 18(6), 370-377

Advantages“PEMDAS” and “Please Excuse

My Dear Aunt Sally” are easy to remember.

Students can write “PEMDAS” on their worksheets/tests when they get them so that they remember to use order of operations while doing their work.

Disadvantages Students may obey the PEMDAS strategy exactly as it reads. This can become an issue because students must remember

that although the “M” for multiplication comes before the “D” for division, multiplication is not automatically done before division. Multiplication and division are done in order from left to right after parenthesis and exponents have been used.

The same goes for addition and subtraction. They are done from left to right after parenthesis, exponents, multiplication, and division have been done.

Possibly write P-E-MD-AS to help students remember. Jeon, K. (2012). Reflecting on PEMDAS. Teaching Children Mathematics,

18(6), 370-377

P-E-MD-AS

Methods - Introduction First the instructor must describe the strategy by introducing

the concept. This should be done by introducing the topic of “Order of

Operations.” The instructor should then list the order in which the

operations must be performed. This includes making note that multiplication/division and

addition/subtraction are equal in that they are done left to right once it comes to be their turn in the order of operations. Multiplication nor addition has priority over division, subtraction respectively. A good way to teach this is reminding the students that subtraction is simply the inverse of addition. Ex: 3-2 is the same as 3+ (-2). The Same goes for division being the inverse of multiplication. Ex: 3/4 is the same as 3 x ¼.


DescriptionNext the instructor should show the order of

operations like so... Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction

The students will recognize the bolded letters, and this is when the instructor should introduce the acronym PEMDAS as a strategy to remember the correct order to perform mathematical operations.

The instructor should closely follow introducing PEMDAS with teaching the students “Please Excuse My Dear Aunt Sally” as a way to remember the strategy PEMDAS.

Modeled PracticeNow that the student know

“PEMDAS,” the instructor should model the strategy by solving multiple problems step-by-step while thinking aloud so that the students can understand how to use the strategy.

The students should watch and listen as the teacher solves these problems aloud, as well as copy down the problems.

Guided PracticeNow the students are ready to

participate in order of operations problem solving.

The instructor should continue to do problems at the front of the class, but instead of doing the problems on their own while thinking aloud, the instructor should take volunteers from the class to answer the next step of the problem. The class should solve several problems in this manner before moving on.

Independent PracticeAfter many examples are done as a class, the students should

be given time to work through problems on their own. A good tool to utilize during this time is giving each student a

calculator that has the order of operations programmed into it. This will allow students to check their answers because there is only one correct answer for each problem and the calculator will help point out order of operations errors.

Another valuable practice technique is using the same numbers and signs in a problem, but moving the parenthesis around in the problem to prove that their placement effects the outcome.


GeneralizationTo promote generalization, students

should be given the opportunity to do story-writing mathematics problems given an equation.

This will help students better understand the meaning of each operation and specific words used affect the outcome


Data CollectionStep 1 - Pretest -Students should take a pretest

with various number problems using all the operations in PEMDAS.

-The pretest should also contain a few word problems to gauge where their understanding is with mathematical story-problems.

Data CollectionStep 2- Introductory through independent

practice phases -The instructor should constantly request

responses from the students to check for understanding. The students should be encourages to think aloud as they work through problems.

-The instructor should also collect in-class independent work to check for individual understanding. These works should be compared to the pretests to check for progress.

Data CollectionStep 3- Posttest -After getting ample opportunities to

perform all types of practice using PEMDAS, and proof from in-class independent practice that students have learned the strategy the students should take a posttest.

-The posttest should consist of the same types of problems as the pretest, including word problems.

ReflectionThis strategy would work well in instruction, and it

has for many years. Young students are receptive to memory tricks, and this strategy is very important to learn and remember because understanding order of operations is crucial to success in mathematics.

With regards to strategy adaptation, there are not many major changes needed. It might, however, be beneficial to spice up the presentation of PEMDAS. Using certain colors or pictures may be more visually pleasing and therefore more memorable. The students could also make up their own phrase to remember PEMDAS instead of using “Please Excuse My Dear Aunt Sally.”

ReflectionInstructors should also keep in mind that

some students may need more guided practice before moving on to independent work.

These students can work in a small group with the instructor while the rest of the class works alone. Students can feel free to come and go from the small group as their skill level rises. It is important to encourage these students to try to do as much as they can independently without prompting while working in the small group.

ReflectionI recommend this strategy to all

mathematics teachers. It is a great way to learn the order of operations, and it will stick with the students for a long time.

I have used this strategy in my middle school practicum setting, and my students were very receptive to it and use it whenever working with operations.

Source CitationJeon, K. (2012). Reflecting on

PEMDAS. Teaching Children Mathematics, 18(6), 370-377

“Reflecting On PEMDAS- Forgo rule-driven instruction. Use these helpful tips to teach the order of operations.”

sped 441 learning strategy assignment

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