Exponents

[metrologist]

Why would they [primary teachers] need to know?  Whilst I vaguely remember learning some algebra in primary school, I'm not sure it was required.  Why pick on primary school teachers?  They have an ever growing work load and constant changes to curriculum from a government who wants "all UK children to be above average"  (Direct quote from Michael Gove there).

The particular school and several others around here run K through 8, and I consider them primary; although, I believe the classic definition of primary education is k through 5. I would expect primary mathematics program teachers to have earned certain credentials to be in that position, which would certainly exceed the educational requirements of the level they are instructing.

The 6th grade class here appears to be in chapter 11 or 12, and should finish the program by mid June I believe. This is not the actual program but the topics are the same: http://mathonweb.com/help_ebook/index.htm

I did provide some context and description of the specific issue I had.

[rstofer]

I have noticed a lot of threads that deal with education or the basics of engineering/mathematics have this air of "in my day things were better" from the older generation.  Of course people are going to think that, because otherwise it implies that their education - and by extension, themselves - is/was substandard or outdated.

I have noticed a lot of people trying to explain away simple and widely acknowledged facts by insinuating that they exist only in imaginations of fragile egos.

Things were NOT better.  My grandson and I were working through one of his physics problems the other night and it involved a rather ugly polynomial.  We took one look and decided to just set it up in MATLAB.  Turns out one of his other classes is MATLAB - a forward thinking university that requires a MATLAB course.  We kind of laughed when he asked how I would have solved it back in the early '70s.  I moved my hands around in a familiar 'slide rule' fashion and mimicked writing intermediate results.

I could imagine being able to learn the various material with much more depth and understanding if I wasn't bogged down doing arithmetic.  Just compare solving a 5x5 matrix by hand versus dropping it into MATLAB.  Statics was a fun class but it will be more fun with MATLAB.  He can spend more time understanding WHY elements are in tension or compression and not wondering if he dropped a sign.

Things were NOT better!  The tools, the online tutorials, even the textbooks are far superior to what the 'old folks' had.  I wish I were back in college!  I would eat that stuff up.

[tggzzz]

   7 - 7 - 7 = 7
   and
   7 - 7 - 7 - 7 = 0

We had APL on the IBM 1130 back in '70 but I never got around to playing with it.  I didn't realize it evaluated from right to left.

Interesting!

When at university (mid 70s) I went to an APL talk by someone from IBM Hursley. It was interesting, albeit at 90degrees to everything else in the world! That's where I squirrelled that fragment away in my mind, to be excavated when "helpful".

I wonder what, if anything, buried code will think of it 

[tggzzz]

I'm still unsure why this thread has so many replies (I'm aware I'm adding to this!).  Precedence is indeed important and despite what nominal animal suggested, I'm pretty sure almost all "mathematicians" could state the order, perhaps with the acronyms BODMAS or PEDMAS.  Especially as it is so fundamental to even basic algebra. 

Whilst the average Joe who was taught this in basic mathematics has probably forgotten because most simply do not need to use this, I am willing to bet Engineers will be more likely to know this.

Engineers ought to. I wouldn't bet on UK primary school teachers knowing though

Why would they need to know?  Whilst I vaguely remember learning some algebra in primary school, I'm not sure it was required. 

It isn't algebra, it is arithmetic. When a maths teacher lectures me about the evils of calculators, I expect them to know what 1+2*3 is. It can be fun to watch their faces when I show them a calculator which says "7" when they expect "9".

Why pick on primary school teachers?  They have an ever growing work load and constant changes to curriculum from a government who wants "all UK children to be above average"  (Direct quote from Michael Gove there).

Michael Gove will say whatever he thinks his audience wants him to say; usually he gets that right

Besides, most children can be above average. Given these examples scores, 90% are above average: 5 5 5 5 5 5 5 5 5 4.

[CatalinaWOW]

From the Web, with all the assurance provided by that source.

History Lesson
So where did this order of operations come from? Whose fault is it? =^)

1646 - In Van Schooten's 1646 edition of Vieta, B in D quad. + B in D is used to represent B(D^2 + BD).
1800s - The term "order of operations" was starting to get used in textbooks. It was used more by textbooks than mathematicians. The mathematicians mostly just agreed without feeling the need to state anything official.
1920s - In this time period, the mathematicians were debating about whether or not multiplication should take precedence over division. Although they'd still argue over who won this argument, today it's become most common (and taught predominantly) that multiplication and division are equal, read from left to right. The reasoning is to keep it simple and to let the parentheses do it's thing!
1960s - As mathematicians began writing books about algebraic notation, they basically agreed on the idea that multiplication would take precedence over addition. It's a natural hierarchy that lends itself well to writing polynomials with as few parentheses as possible. So at a time when the authors of these books on mathematics had to begin their book with a list of conventions... it wasn't needed on the basic order of operations... they all seemed to have agreed.
You'll still find textbooks that don't fully agree with each other, but the basics are commonly set now, and the world is full of order and peace, thanks to the Order of Operations!


This actually agrees fairly well with what I understood.  These conventions have simmered for quite a while, but the definitions have only stabilized in the last century.  The importance grew dramatically around the 1950-1960 time frame when computers came along and multiplied the consequences of mistakes.  Until machines got in the act a misunderstanding didn't propagate very far before it became obvious and could be corrected. 

I think Brumby said it best.  There is still enough confusion in this (clearly demonstrated by the number of internet polls on the result of some sequence of operations and by Excel and APLs choice of going another direction) that if you care about the answer being determined correctly use parenthesis as required.  Even if there is one true way to do precedence the odds are high that someone out there will not understand them or use the same rules.  We use checksums and error correcting codes to ensure correct communications.  Parenthesis serve the same purpose.  Extras symbols, but correct transmission.

[Buriedcode]

Why would they [primary teachers] need to know?  Whilst I vaguely remember learning some algebra in primary school, I'm not sure it was required.  Why pick on primary school teachers?  They have an ever growing work load and constant changes to curriculum from a government who wants "all UK children to be above average"  (Direct quote from Michael Gove there).

The particular school and several others around here run K through 8, and I consider them primary; although, I believe the classic definition of primary education is k through 5. I would expect primary mathematics program teachers to have earned certain credentials to be in that position, which would certainly exceed the educational requirements of the level they are instructing.

The 6th grade class here appears to be in chapter 11 or 12, and should finish the program by mid June I believe. This is not the actual program but the topics are the same: http://mathonweb.com/help_ebook/index.htm

I did provide some context and description of the specific issue I had.

I can't say I've seen the evidence for primary school teachers not knowing about precedence in mathematics, I only know two, and both seem pretty well educated to me, but it seems to be quite a specific thing to claim.  And I still don't know what this really has to do with the thread.  Again - why pick on primary school teachers? (I'm assuming this is specific to the UK, since the term "primary school" is generally a UK thing).

It seems I've hit a few nerves in this thread.  I apologise, it wasn't my intention to insult or anger anyone. I amazed (and impressed) by how passionate some get over such matters.  I now see that excel, as well as other software do things differently to convention, but these can be mitigated through use of parentheses.  What else is there to the thread?

[ebastler]

I now see that excel, as well as other software do things differently to convention, but these can be mitigated through use of parentheses.  What else is there to the thread?

Nothing, really. Except that, whenever the thread seems to have reached that consensus, someone new pops in and states the opposite.

Lets give it another day. My guess is that someone will come along, wondering what all this debate is about, given the obvious fact that -3⁴ = 81. 

[tggzzz]

I can't say I've seen the evidence for primary school teachers not knowing about precedence in mathematics

In my limited experience, slightly under half instantly give the wrong answer, and are difficult to persuade there might even be a question. A clued up minority ask where the parentheses are, and are then realise they've forgotten the normal laws of arithmetic. Very few confidently give the right answer.

I now see that excel, as well as other software do things differently to convention, but these can be mitigated through use of parentheses.

Yup, that's the point.

[0culus]

I have noticed a lot of threads that deal with education or the basics of engineering/mathematics have this air of "in my day things were better" from the older generation.  Of course people are going to think that, because otherwise it implies that their education - and by extension, themselves - is/was substandard or outdated.

I have noticed a lot of people trying to explain away simple and widely acknowledged facts by insinuating that they exist only in imaginations of fragile egos.

Things were NOT better.  My grandson and I were working through one of his physics problems the other night and it involved a rather ugly polynomial.  We took one look and decided to just set it up in MATLAB.  Turns out one of his other classes is MATLAB - a forward thinking university that requires a MATLAB course.  We kind of laughed when he asked how I would have solved it back in the early '70s.  I moved my hands around in a familiar 'slide rule' fashion and mimicked writing intermediate results.

I could imagine being able to learn the various material with much more depth and understanding if I wasn't bogged down doing arithmetic.  Just compare solving a 5x5 matrix by hand versus dropping it into MATLAB.  Statics was a fun class but it will be more fun with MATLAB.  He can spend more time understanding WHY elements are in tension or compression and not wondering if he dropped a sign.

Things were NOT better!  The tools, the online tutorials, even the textbooks are far superior to what the 'old folks' had.  I wish I were back in college!  I would eat that stuff up.

I agree. I think there is a certain value to learning to manipulate 2x2 and 3x3 systems by hand...beyond that it's pure drudgery and you'll spend more time correcting mistakes than you do understanding the problem.