What do you think about mnemonics like "PEMDAS" or "FOIL"?

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.

I really find it useful. I am currently teaching my daughter how it works now.

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).

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.jpg

Sillyness, I know, but this is what my mind retrieved.

A Rat In Tom's House Might Eat Tom's Ice Cream.

Please Excuse My Dear Aunt Sally = PEMDAS = parentheses, exponents, multiplication, division, addition, subtraction = the order of operations. FOIL = first, outer, inner, last = order for factoring

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!

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.

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.

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?

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.

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.

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 LOL