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Bedlam with BODMAS and BEDMAS

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Mefiante
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« Reply #15 on: May 20, 2014, 15:55:36 PM »

It’s the introduction of the “of” construct in mathematical/arithmetical expressions that is the problem.  It is completely artificial and exists only in the strangely contorted OCD minds of postmodern maths teachers and educational authorities whose megalomania vastly exceeds their numeracy.  In the substantially more real world inhabited by mathematicians and mathematically literate professionals, such forms are NEVER used.  (Is that sufficient emphasis?)  And they are NEVER used precisely because they are ambiguous, and ambiguity goes with maths the way cheese goes with barbed wire.

4x4-4x4+4-4x4=?
–12.  (4×4 – 4×4 + 4 – 4×4 = 16 – 16 + 4 – 16 = 0 + 4 – 16 = –12.)

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Brian
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« Reply #16 on: May 20, 2014, 16:19:23 PM »

sorry my bad: the original quiz was: 4x4+4x4+4-4x4=?? 20 or 320 according to some. I was taught that multiplying and dividing take predence over +/-....in other words the order is key.
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cr1t
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« Reply #17 on: May 20, 2014, 16:24:09 PM »

sorry my bad: the original quiz was: 4x4+4x4+4-4x4=?? 20 or 320 according to some. I was taught that multiplying and dividing take predence over +/-....in other words the order is key.

Yes that is what I was thought as well , how the hell do they get to 320?
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Mefiante
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« Reply #18 on: May 20, 2014, 17:13:55 PM »

4x4+4x4+4-4x4 = ??
20.  (4×4 + 4×4 + 4 – 4×4 = 16 + 16 + 4 – 16 = 20.)

In naïve left-to-right reading order, the result obtained is wrong:
4×4 + 4×4 + 4 – 4×4
= 16 + 4×4 + 4 – 4×4
= 20×4 + 4 – 4×4
= 80 + 4 – 4×4
= 84 – 4×4
= 80×4
= 320.

'Luthon64
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brianvds
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« Reply #19 on: May 20, 2014, 17:25:42 PM »

It’s the introduction of the “of” construct in mathematical/arithmetical expressions that is the problem.  It is completely artificial and exists only in the strangely contorted OCD minds of postmodern maths teachers and educational authorities whose megalomania vastly exceeds their numeracy.  In the substantially more real world inhabited by mathematicians and mathematically literate professionals, such forms are NEVER used.  (Is that sufficient emphasis?)  And they are NEVER used precisely because they are ambiguous, and ambiguity goes with maths the way cheese goes with barbed wire.


Yes, it is kind of difficult to imagine many real world problems where the "of" construct would be used, except perhaps in things like "only 12% of the 300 math educators could do elementary multiplication." :-)

Now I am lucky enough to work for an independent school, and we do not absolutely have to do whatever the education department wants, but we nevertheless try to remain fairly close to the official syllabus because the students will eventually have to pass a government exam. Also, as I have pointed out before, if one of our students go to another school, or we get students from other schools, it can create difficulties if the two schools followed too radically different syllabuses.

Hmm, reading around on the web, I now see a new twist in the tale. When I was in school, they told us the O in BODMAS stands for "of". But according to some pages, such as this one:

http://thehalltruth.com/tag/bodmas/

it actually stands for orders - also known as exponents. I.e. BODMAS and BEDMAS are not two conflicting rules. They are the same thing. I.e. my grade 8 teacher was just an uneducated moron. As if the fact that he was also a sadistic psychopath wasn't bad enough.

One more data point in my theory that we need teachers who are educated in the subjects they teach, rather than in education, and that closing down the teachers' colleges might well have been the one rational thing the ANC did in its quest for better education. :-)

PS: I also get -12 on that thing with the long string of multiplied, subtracted and added 4s... :-)
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Mefiante
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« Reply #20 on: May 20, 2014, 17:33:04 PM »

Aha, difficulty solved!  I wasn’t aware that you thought the “O” in BODMAS stood for “Of” instead of “Orders” (which is the archaic form of “exponents”, although still used today when describing polynomials “of order n” where n is the highest power that occurs in the polynomial).  If “Of” is to be read as a multiplication operator (as logic dictates it must) then it would be pointless to include it alongside “D” and “M” because all three are at the same precedence level.

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brianvds
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« Reply #21 on: May 20, 2014, 18:02:32 PM »

Aha, difficulty solved!  I wasn’t aware that you thought the “O” in BODMAS stood for “Of” instead of “Orders” (which is the archaic form of “exponents”, although still used today when describing polynomials “of order n” where n is the highest power that occurs in the polynomial).  If “Of” is to be read as a multiplication operator (as logic dictates it must) then it would be pointless to include it alongside “D” and “M” because all three are at the same precedence level.

Indeed. Of course, after grade 8, we never, ever again saw problems with the "of" construct, so I cheerfully forgot about it, and order of operations was just never an issue again, until I got confronted by it once again in primary school materials! But it now seems I was quite simply fed completely false information by a high school teacher, way back in the early 14th century. Whatever else I teach my own students, I really must get this into their heads: never, ever, blindly believe a teacher. :-)

I wonder whether it was only my own high school though, or whether that crap was taught to an entire generation of students. I should ask around some teens of my acquaintance and find out whether they perhaps STILL teach it that way...

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Rigil Kent
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« Reply #22 on: May 20, 2014, 18:44:26 PM »

It looks like public opinion remains divided as to what the "O" in BODMAS stands for. https://answers.yahoo.com/question/index?qid=20090413141638AA0xR8p. So at some point the idea of "of" must have snuck in.

I recall my teacher applying the Brackets, Addition, Division, Angular Substitution and Simplification approach. Tongue

r.
« Last Edit: May 21, 2014, 06:20:08 AM by Rigil Kent » Logged
brianvds
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« Reply #23 on: May 21, 2014, 04:21:33 AM »

It looks like public opinion remains divided as to what the "O" in BODMAS stands for. https://answers.yahoo.com/question/index?qid=20090413141638AA0xR8p. So at some point the idea of "of" must have snuck in.

Hmm, yes, lots of people apparently think the O stands for "of", so one must presume that at some point, this is what schools taught. One wonders how that happened. There may be a whole interesting book there. At least I got the right information eventually, even though my hair is graying, and despite my schooling.

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Brian
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« Reply #24 on: May 21, 2014, 07:51:28 AM »

Quote
At least I got the right information eventually, even though my hair is graying, and despite my schooling
      Yes sometimes I wonder that we actually survived. I had a German teacher who was quite adamant that the whole manned space satellites thing in the early 60's was a scam, but then again I had a brilliant Afrikaans and Math teacher (my math was abysmal)in Affies, Pretoria.
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