tag:blogger.com,1999:blog-1244374124386026741.post4234016773628747351..comments2016-12-28T19:10:18.762-08:00Comments on Leaf and STEM Learning: Why I will never use PEMDAS to teach order of operationsLD Helferhttp://www.blogger.com/profile/15362613994636151867noreply@blogger.comBlogger12125tag:blogger.com,1999:blog-1244374124386026741.post-88095775640461378792016-12-04T19:40:02.579-08:002016-12-04T19:40:02.579-08:00I don't use any type of mnemonics at all. I t...I don't use any type of mnemonics at all. I teach my students that we simply perform the operations in order of power unless we are explicitly told otherwise (parenthesis/brackets). This means we have to actively have conversations about what types of operations are more powerful. Addition and subtraction are equally powerful as they are the inverse of each other. Multiplication and division are repeated addition and subtraction, so are more powerful. They are also equally powerful, as they are the inverse of each other. Exponentiation is repeated multiplication, so this must be more powerful that simple multiplication, and so on. This forces students to think about what is actually going on with each operation, and make a decision based on 'power ranking'. Jim Potterhttp://www.blogger.com/profile/10231833468923470176noreply@blogger.comtag:blogger.com,1999:blog-1244374124386026741.post-48113783679421863172016-08-10T05:11:31.237-07:002016-08-10T05:11:31.237-07:00I don't use PEMDAS either - thought I was the ...I don't use PEMDAS either - thought I was the only one! Students make too many mistakes forgetting the left to right aspect...they have already been taught PEMDAS in 5th grade so I have to undo the previous teachers' work : (Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1244374124386026741.post-51972142134888687162016-07-29T09:30:53.654-07:002016-07-29T09:30:53.654-07:00Wow what a super great idea!! I will give GEMA a t...Wow what a super great idea!! I will give GEMA a try this year. Thank you for sharing!Mrs. Matahttp://www.blogger.com/profile/14474807935270525342noreply@blogger.comtag:blogger.com,1999:blog-1244374124386026741.post-7929658652207833692016-04-18T06:41:12.397-07:002016-04-18T06:41:12.397-07:00Thank you for your comments. With order of operat...Thank you for your comments. With order of operations, I found in years where I taught no mnemonic at all, the students tended to come up with their own. For example, one year where I did not use a mnemonic, my students came up themselves with PGI--which they called "piggy." To them it stood for parentheses, groups, individuals. That was a younger group of students, so we were not studying exponents. You can see the obvious flaws with "piggy" for when the students reached higher levels of math. This led me to the decision to introduce a mnemonic myself that could move into higher level math with my students. I would only have them one year, the next I knew that they would move to classroom where the teacher probably used PEMDAS. If I gave them GEMA and a strong foundation of the reasoning for order of operations, I could have some assurance that it wouldn't get undone by a future teacher with lots of tricks.LD Helferhttp://www.blogger.com/profile/15362613994636151867noreply@blogger.comtag:blogger.com,1999:blog-1244374124386026741.post-14213030339752417562016-04-17T15:40:15.202-07:002016-04-17T15:40:15.202-07:00I gave up on mnemonics long ago. PEDMAS (and all o...I gave up on mnemonics long ago. PEDMAS (and all of its variations) and FOIL skirt the actual concepts our students need to learn, they are limited in their scope and they always need scaffolding to fine tune those ambiguities.<br /><br />I teach the structure of the expression to teach the order of operations: grouped operations, within-term operations (exponential operations and multiplicative operations) and between-term operations (additive operations). It turns out to be the same as GEMA, but it informs my students why the operations are ordered the way they are.<br /><br />Reasoning and informing always trump remembering yet another disconnected and meaningless mnemonic.Shawn Urban (@Stefras)http://bit.ly/stefdigsubnoreply@blogger.comtag:blogger.com,1999:blog-1244374124386026741.post-27914275225144974072016-01-10T13:23:02.967-08:002016-01-10T13:23:02.967-08:00And the use of "E" as "exponential ...And the use of "E" as "exponential operations" will help them when it's time to integrate roots. Roots are the inverse of exponents, so fall in that same position in the order.Bon Crowder @MathFourhttp://mathfour.comnoreply@blogger.comtag:blogger.com,1999:blog-1244374124386026741.post-43392619850747740402015-10-11T19:50:47.550-07:002015-10-11T19:50:47.550-07:00BOMDAS with a line drawn under the MD and under th...BOMDAS with a line drawn under the MD and under the AS to show that these are to be done in the order that they appear worked for me. Beware Of My Dear Aunt Sally.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1244374124386026741.post-86952409548364464542015-09-13T17:13:31.117-07:002015-09-13T17:13:31.117-07:00Very interesting to hear about teaching techniques...Very interesting to hear about teaching techniques from around the world! Thank you!LD Helferhttp://www.blogger.com/profile/15362613994636151867noreply@blogger.comtag:blogger.com,1999:blog-1244374124386026741.post-31067581207358216722015-09-13T14:28:47.815-07:002015-09-13T14:28:47.815-07:00Here in South Africa we learn BODMAS....works like...Here in South Africa we learn BODMAS....works like magic....brackets of division,multiplication,addition ,subtraction.....no problemsashie hariparsadhttp://www.blogger.com/profile/11477938499820572723noreply@blogger.comtag:blogger.com,1999:blog-1244374124386026741.post-49559536212351767882015-09-08T09:01:57.694-07:002015-09-08T09:01:57.694-07:00Aunt Sally, if I remember, Loves Raspberries (Left...Aunt Sally, if I remember, Loves Raspberries (Left to Right), which kept it straight for me. But, I like the "multiplicative operations" which would emphasize that division is the multiplication of an inverse.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1244374124386026741.post-88294106726748999622015-08-23T22:11:57.950-07:002015-08-23T22:11:57.950-07:00This post was featured on the August issue of Math...This post was featured on the August issue of Math Teachers at Play! I hope it sends some blog traffic your way :) You can check it out at <br /><a href="http://mrseteachesmath.blogspot.com/2015/08/math-teachers-at-play-89.html" rel="nofollow">Math Teachers at Play #89</a>Mrs. E Teaches Mathhttp://www.blogger.com/profile/14333418485408024108noreply@blogger.comtag:blogger.com,1999:blog-1244374124386026741.post-66913734734626243722015-07-22T15:10:42.318-07:002015-07-22T15:10:42.318-07:00I totally agree! My students had so much trouble w...I totally agree! My students had so much trouble with this. I love how you mentioned some solutions to the problem as well. Great post!<br />-Kelsey from www.wifeteachermommy.comKelsey Sorensonhttp://www.blogger.com/profile/17262007958586105119noreply@blogger.com