Comments and answers for "What do you think about mnemonics like "PEMDAS" or "FOIL"?"
https://naturalmath.com/community/questions/278/what-do-you-think-about-mnemonics-like-pemdas-or-f.html
The latest comments and answers for the question "What do you think about mnemonics like "PEMDAS" or "FOIL"?"Answer by Jen
https://naturalmath.com/community/answers/2479/view.html
<p>I don't care for mnemonics as a stand alone learning technique. I have seen children and experienced myself get a mental block about how to creatively approach situations/problems because of a "this is how it's solved" mentality. </p>Mon, 07 Apr 2014 11:51:19 GMTJenAnswer by Sblair
https://naturalmath.com/community/answers/2467/view.html
<p>I really find it useful. I am currently teaching my daughter how it works now.</p>Mon, 07 Apr 2014 11:33:42 GMTSblairAnswer by jkshuler
https://naturalmath.com/community/answers/2460/view.html
<p>One thing I specifically don't like about PEMDAS is that kids think that the order of operations start with parenthesis, the "P", and that's not true. If I use the mnemonic (which I will use for some students), I change it to GEMDAS, and the G refers to grouping symbols (which there are many beyond parenthesis). If you're going to use the mnemonic, please let expose students to the term "grouping symbols" (things like brackets, parenthesis, absolute value, fraction bar).</p>Mon, 07 Apr 2014 09:29:18 GMTjkshulerComment by sherylmorris on sherylmorris's answer
https://naturalmath.com/community/comments/2353/view.html
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I totally get this, however, when you are afflicted with "math anxiety," when you've already been forced to <span style="line-height: 1.45em;">memorize math ideas quickly (not at the speed of your understanding) crutches can help you breath.</span>
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<span style="line-height: 1.45em;"></span>
</p>Wed, 12 Mar 2014 23:03:42 GMTsherylmorrisAnswer by sherylmorris
https://naturalmath.com/community/answers/2352/view.html
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Sillyness, I know, but this is what my mind retrieved.
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A Rat In Tom's House Might Eat Tom's Ice Cream.
</p>Wed, 12 Mar 2014 22:56:33 GMTsherylmorrisComment by sherylmorris on sherylmorris's answer
https://naturalmath.com/community/comments/2351/view.html
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Thank you. I wasn't understanding.
</p>Wed, 12 Mar 2014 22:51:31 GMTsherylmorrisAnswer by lfahlberg
https://naturalmath.com/community/answers/2250/view.html
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If ever I saw a reason not to like PEMDAS it was this quiz question in a forum on linkedin: What is 8-3+2? So many people using PEMDAS literally (doing addition before subtraction) answered 3. It was heartbreaking. Just today a university student answered 3, but many were also teachers. What was worse was we could not think of a way within the public school system to fix this problem. (This thread was the longest I have ever seen with over 140 comments and has been active more than 6 months.) This isindeed a real problem.
</p>Mon, 17 Feb 2014 18:26:02 GMTlfahlbergComment by hdongen on hdongen's answer
https://naturalmath.com/community/comments/883/view.html
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I also didn't know about FOIL and PEMDAS, not in English nor in Dutch. I don't need those. I can perfectly well figure this out by myself, even if it takes a little longer.
</p>Sun, 08 Sep 2013 12:13:12 GMThdongenComment by hdongen on hdongen's answer
https://naturalmath.com/community/comments/881/view.html
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I really agree with you. I have done the How to Learn Math course during the summer and took a different approach to math teaching with my son since then. Although I am good at approaching a problem from different angles, I found that sometimes I had the urge to just follow the rule... but then I realized that no sense is coming from that approach, so I let my son figure it out all by himself. We are now learning about basis arithmetic with fractions, and he has used what he already know, visualized things and found out why some things do not work. Sometimes I have to slap myself on the hand, but it is worth it.
</p>Sun, 08 Sep 2013 12:09:27 GMThdongenAnswer by Susie
https://naturalmath.com/community/answers/782/view.html
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I am so glad to read this. I thought I might be obstinate by opposing using PEMDAS (made better by Please Excuse My Dear Aunt Sally???) instead of the reasoning - my thinking is the "tightness" of the bond of multiplication vs. addition and parentheses superseding the others. I am distressed at how often I see FOIL and SOH CAH TOA. I have had students I was tutoring or substituting object to me encouraging them to think without these. Thanks for the support!
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Regarding 7*8, 6*7,and 6*8, do these really need a mnemonic? Given tiles, can't students group them into rectangles that can be broken apart? There are so many ways to see them and those ways promote algebraic thinking and understanding the distributive property (FOIL (!) later on). For example, 7*8= (5+2)*8=(5*8)+(2*8) or 7*(2*4)=(7*2)*4 or 7*2*2*2. And 6*7 = 2(3*7) or (6*5)+(6*2) or (5*7)+7. I saw an example of a teacher "quizzing" her students by asking them to write down how many ways they could show what 6*8 equals, instead of using a timed test. My experience is that kids love seeing facts this way once they see that they can, and they enjoy explaining how they see.
</p>Thu, 29 Aug 2013 23:20:37 GMTSusieAnswer by kwilburn
https://naturalmath.com/community/answers/765/view.html
Please Excuse My Dear Aunt Sally = PEMDAS = parentheses, exponents, multiplication, division, addition, subtraction = the order of operations.
FOIL = first, outer, inner, last = order for factoringFri, 23 Aug 2013 17:40:47 GMTkwilburnAnswer by daniela
https://naturalmath.com/community/answers/596/view.html
Sorry for the stupid comment, it looks like I am the only one who does not know, but I don't. Can someone tell me what they mean?Thu, 18 Jul 2013 10:07:03 GMTdanielaAnswer by MobySnoodles
https://naturalmath.com/community/answers/285/view.html
I want to caution against mnemonics, too. When you memorize math ideas slowly enough (at the speed of your understanding) you internalize each idea's structure. Your brain indexes names of individual objects or actions, together with their connections. Every time you retrieve those rich memories, you reinforce the whole structure!
When you use a mnemonic, you reinforce the mnemonic, nothing else. So, instead of contemplating relations between multiplication and powers in the order of operations, your brain contemplates how silly the word PEMDAS is, and what it may mean in Chinese - in other words, random the mental clutter and noise! That clutter can even stick in the brain forever, clogging up your logic and reasoning.
![alt text][1]
For example, it's a bad idea to use mnemonics for multiplication facts. The exception are the three facts that are hard to remember because of two good reasons. First, they are not covered by easy patterns (like the nine patterns). Second, they are beyond the subitizing range. Dehaene's book "The Number Sense" explains these reasons why 7*8, 6*7 and 6*8 are hard. I am okay with mnemonics for those three facts!
[1]: /storage/temp/31-thenumbersensedehaene.jpgTue, 04 Jun 2013 22:32:16 GMTMobySnoodlesAnswer by Denise Gaskins
https://naturalmath.com/community/answers/283/view.html
I dislike them for the same reason I dislike it when adults push young children to memorize math facts. Once we memorize something like that, we think that we "know" it, and therefore we stop wondering about it. But it is only through repeatedly thinking our way through a lot of similar calculations that we begin to understand the deeper structure of the mathematics, what the numbers or variables are actually doing, and why it works that way.Thu, 30 May 2013 14:55:39 GMTDenise GaskinsAnswer by mpaul
https://naturalmath.com/community/answers/281/view.html
A focus on mnemonics indicates a shallow procedural level of thinking. I completely agree with the previous post that a mnemonic can be helpful in certain situations, but unfortunately a preoccupation with such things has replaced deep concept formation in a lot of our math education. Instead of making kids memorize mnemonics in order to be able to follow the steps of a procedure, we should instead be asking them to explain their reasoning. A huge problem with mnemonics divorced from reasoning is that it's possible to mix up the mnemonic. Once after a trig test I noticed that a student had written 'SAH COH TAO' at the top of their paper. Sadly, they had followed that rule consistently.Thu, 30 May 2013 13:36:31 GMTmpaulAnswer by abrador
https://naturalmath.com/community/answers/279/view.html
I don't have any problem with mnemonics per se -- they are, well, just that -- a great way to recall information. Only that selecting to use mnemonics as a means of recalling information indicates that the person may have no deeper structure that would be sufficient to recall so as to regenerate the information. For example, I might remind myself to buy: oats, milk, banana, apples, strawberries, walnuts, cinnamon, and honey by finding some acronym, uhhm, BOSCH MAY, and perhaps humor myself all the way to Monterey Market by thinking about having viewed a piece by Hieronymus last month (May). But then again, I might chunk up of of these items by saying "Neomi's breakfast." That would be all I need in order to regenerate the entire list of ingredients for my 6:45am culinary bravado. My point is that if you need a mnemonic then this implies that you do not have any other way to chunk the information. In the case of "FOIL" (I don't even know what PEMDAS is and do not care ever to find out), it is quite sad if you really have never figured out the rule underlying this sequence. Worse, teachers who offer mnemonics might assume they need never explain the logic underlying this sequence. These teachers, for example, might mark as incorrect a solution that followed, uhhm, OILF, even though it is perfectly acceptable. OK GTG BRB LOLThu, 30 May 2013 00:22:03 GMTabrador