My post wasn't directed to PEMDAS specifically, but the underlying
issues related to the need to utilize strategies that may allow the
student to get the answer right without knowing the math underlying
it. My point is, by the time students get to PEMDAS they are so far
behind in their math understanding that many are using tricks to get
them to the right answer (for those students that can blindly follow
the rules), but they still will lack the understanding. As we all
know, a weak foundation causes a house to crumble. We have a whole
population of crumbling math students because their foundation has not
been presented in a meaningful way for them, while it may be a
perfectly meaningful way for a student who learns either by any method
or by the method presented. We don't have math specialist that have
lots of strategies and various methods teaching our elementary
students, we have well meaning elementary teachers (many of who don't
understand math) teaching our students math without the proper
training to make sure that the students have the basic building block
math skills in order to learn math. This isn't meant to be a bash,
but it is reality.

On 6/22/09, Terrence wrote:
> I could see using manipulatives for exponents. In fact, when I teach
> exponents, one thing I do is we fold a piece of paper. We first fold
> it in half and I ask how many rectangles did it make? We folded it
> once and it made 2 rectangles. 2^1=2. Then we fold it in half again
> 2^2=4, then in half again, 2^3= 8, and so on. At the end, I ask, what
> if we hadn't of folded it it at all? How many rectangles would we
> have if we never folded it in half? 2^0=1.
> How would you use manipulatives for PEMDAS? When I tech P E MD AS, I
> let them know that P stands for Parentheses and all grouping symbols:
> vinculum, absolute value symbols, parentheses, brackets,
> etc.
> Over the course of the class, we encounter several types of grouping
> symbols.
>
> Once P's and E's are simplified, I tell them"if we are walking along
> the problem from left to right, will we pass division first or
> multiplication first?" Same with addition/subtraction.
> Maybe I'm going about it all wrong, but that's how I do it until I
> find a better way.
>
> On 6/22/09, Jo wrote:
>> You could go a step further and ask how many teachers used
>> really different methods of teaching exponents or other math
>> concepts. Did they try manipulatives along with writing the
>> information in various ways? What were the visuals like - just
>> numbers written on the board 3 x 3 x 3 = 3^3? Some kids really
>> need math to be hands on and visual, but there are few truly
>> hands on math programs used in classrooms. And if they are, it
>> is rarely by all teachers for different groups of students.
>>
>> So, I guess my point is, you CAN say it is the student if you
>> expect that all should be able to learn by various explanations
>> not different methods, but the reality is that not all students
>> learn math that way and few teachers use manipulatives or good
>> visuals after the first few years (if at all depending on the
>> school). So, I would be more pressed to say it is the TEACHING
>> (not saying bad, uncaring teacher - just not enough training in
>> a system not designed to teach all students) not the student in
>> many cases. But what is seen by the time the kids reach middle
>> to upper grades is that they are woefully confused and many have
>> given up trying to understand because it is futile and they are
>> blamed for their failure (not trying hard enough).
>>
>> On 6/22/09, algie2 wrote:
>>> Going out on a limb here, but I think we as teachers place far
>>> too much blame on teaching methods when trying to figure out
>>> why true learning hasn't taken place.
>>>
>>> I had a couple of really low high school classes this year.
>>> They were all taught Order of Ops with P E MD AS. They all had
>>> trouble with it. We spent tons of time on not just the what
>>> but the how and why of P E MD AS. They were bored beyond
>>> belief. We've been doing this since middle school! When do we
>>> get to Algebra! But they still had trouble. As a class they
>>> couldn't consistently evaluate an arithmetic expression
>>> accurately. Some were very defensive about it -- but I did it
>>> this way...(hmm, what is it about "order" that you don't get).
>>> There were a few in this group that simply could *not* get the
>>> hang of exponents no matter how many times (and ways)it was
>>> explained and broken down for them.
>>>
>>> When we did get to algebra, they had mountains of trouble
>>> "undoing" Order of Ops. No, you can't isolate 3x by subtracting
>>> 3 -- let's relook at P E MD AS. (What, again? But we've been
>>> doing this since middle school...)
>>>
>>> While at the beginning of the year I may have thought their
>>> prior teachers did a poor job of teaching Ord of Ops, by the
>>> end of the year I realized that it didn't much matter -- these
>>> kids just were not going to master it. Meanwhile, other
>>> students (college prep or honors level) were taught the acronym
>>> the very same way by the very same prior teachers and fully
>>> mastered Order of Ops. The variable is the students.
>>>
>>>

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