SPED 441 Learning Strategy Assignment

1. SPED 441 Learning Strategy Assignment By Chad Bobbit

2. Mathematics • An 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.

3. Order of Operations • The correct order in which to perform these operations is as follows- • Parenthesis • Exponents • Multiplication *notice the bolded • Division letters • Addition • Subtraction

4. Strategy = PEMDAS • This 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.”

5. Rationale • This 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

6. 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.

7. 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

8. P-E-MD-AS

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

10. Description • Next 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.

11. Modeled Practice • Now 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.

12. Guided Practice • Now 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.

13. Independent Practice • After 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. Jeon, K. (2012). Reflecting on PEMDAS. Teaching Children Mathematics, 18(6), 370-377

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

15. Data Collection • Step 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.

16. Data Collection • Step 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.

17. Data Collection • Step 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.

18. Reflection • This 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.”

19. Reflection • Instructors 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.

20. Reflection • I 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.

21. Source Citation • Jeon, 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.”