Whoops. Thanks for spotting - maybe I'm allowed just one typo at 5am ?
I've corrected it!
Kind Regards, John
'Surprisingly' (to me) low PF of gadgets
- Thread starter JohnW2
- Start date
I've corrected it!
Kind Regards, John
Deleted - quoted instead of edited, yet again!
Dunno. Mine did, ~35 years ago, even though a lot of other aspects of teaching had changed dramatically by then - but it may have 'got worse', since (i.e. suffered from further 'improvements').
Indeed. If I recall, we had to 'recite' most, if not all, of the "times tales" first thing every morning, for a year or two. I'm talking about the late 50s, so the question of "not being allowed calculators" obviously didn't arise
I think one more recent improvement is that I think the clock has been turned back a little and calculators banned in at least some 'lower school' exams, maybe even GCSEs.It was so drummed into me all those years ago that I think I can probably still fairly easily remember everything up to 12 x 12 plus some of '13' and (for specific reasons) a fair bit of '16' - plus a few other fairly random ones (like 17 x 3 - don't ask me
), not to mention 'squares' (and some 'cubes') up to about 25.Very much so, particularly at A-Level. In my day, the issue wasn't calculators (which didn't exist) but slide rules (as well as log tables), which didn't even pretend to tell one "where to put the decimal point", let alone whether one's answer was even vaguely sensible. For A-Level exams, we were generally expected to 'show' our approximate calculations and, in relevant cases of expressions, to also show rough 'sketch graphs' of functions, both of which, I think, were 'marked'. Indeed, even if one got the answers wrong, a lot of credit was given for 'the working'.
My daughters did do this approximating for GCSE, when they obviously were using calculators.
If we did, that wouldn't really be fair on them, since we are talking about the ways in which the system has 'improved' teaching methods over the years.Is this the point where we start moaning about "kids today"
Not really 'my fields' at all, but (although I think they have probably gone too far), the way that subjects like History, Geography, Religious Studies etc. are now taught in schools has changed dramatically, and is now more like university education in those subjects, focussing much more on concepts/principles, sources (and critical evaluation of sources) than on rote learning of lists of names, dates etc. etc. They probably would not have a clue as to the significance of "1066", but could probably have an intelligent discussion about "evidence of when the Battle of Hastings actually happened". Even science subjects, much closer to my heart, now major more on concepts/principles than just 'fact learning'.
Kind Regards, John
All as it should be. I never knew how fascinating history was until after I left school.
Indeed - the lists of names, dates, etc. etc. (many of which were probably from being 'certain facts', even though we were expected to 'just believe' them) which we were expected to 'learn by heart' really did very little to give us a useful understanding of the subject. Indeed, I recall getting into all sorts of trouble for daring to question whether some of the 'facts' we were being taught were necessarily correct (and the less said about what was called "religious education" or "religious instruction" in those days, the better!).
Kind Regards, John
Yes indeed.
My mother was a teacher (junior & infant) many years ago. Several times we'd be watching some report on the news of some "new" teaching method that someone's come up with - and she'd point out that "that's what we used to call ... 30 years ago"
It seems that every few decades, a new batch of experts grows up unaware of what's been done before - and re-invent it.It does - but 'worse', I get the impression that some of the things which they re-invent are ones which were abandoned fairly soon after they were first invented (a long time ago) because they proved to be so disastrous!
Kind Regards, John
Overall, and for all its imperfections, I don't reckon that the teaching we got back then (mid 50s - mid/late 60s in my case) was all that bad, particularly in the early years of schooling, so I do wonder to what extent all the 'improvements' (many of which appear to have proved to be anything but!) were actually needed!Indeed so, and then another generation of students suffers
Kind Regards, John
I think you are confusing algebra (and conventional algebraic notation) with the order of application of operators during calculation. Everything you write above is true in terms of algebra, and conventional algebraic notation. That is because writing (in algebra), say ....
1
------
2πFC
is conventional algebraic notation for (in computational or operational notation) ....
1 / (2*π*F*C)
... which will evaluate in the manner you intend by your algebra (applying the rules of BODMAS). The reason for that is that the algebraic notation ...
wxyz .... is actually conventional algebraic shorthand for .... (w*x*y*z)
If someone presented you (or a computer) with ...
1 / 2 * π * F * C
... what would you (or the computer) be expected to do? Had you yourself translated from the algebraic notation above, you would, as above, have written it as
1 / (2*π*F*C)
... which is not ambiguous. However, there is no way you (or the computer) would know to do that without that 'insider knowledge', so there has to be a conventional set of rules to tell one what to do in the absence of clarifying information in the expression (particularly brackets). Those rules are BODMAS, and would result in "1 / 2 * π * F * C" being evaluated as ....
(1 /2) * π * F * C
... which, of course, is not what you would actually work. In other words, if one is telling one's computer, calculator or brain (to do it 'manually') how to do the calculation, one has to translate the notation of the algebraic expression into computational instructions - and if one leaves any ambiguities (less than a 'full' set of brackets), then BODMAS is used to decide what to do about those ambiguities.
This applies to even very simple expressions. Even "a+b*c" is computationally ambiguous, since it could mean "(a+b)*c" or "a+(b*c)". BODMAS assumes the latter meaning, as does the algebraic notation "a+bc".
Kind Regards, John
Top marks for the most comprehensive and logical explanation of BODMAS rules (so far) regarding division before multiplication
Thank you, kind Sir. You're welcome.
It was only really whilst I was writing last night that I realised why this probably only rarely arises as 'an issue'. When we write things in algebraic notation, we generally know (and anyone else looking at it knows) what is intended computationally. In other words, when SUNRAY writes or sees
1
-----
2πFC
... he knows exactly what is meant in terms of computation - so, if he were given values for F and C, he could evaluate the expression 'correctly' ('as intended'). In contrast, few, if any mainstream computer languages would know what was meant by "2πFC", so we would have to instruct the computer with something like "2*π*F*C" - but if we then did not include brackets to clarify, what the computer would be seeing would be the ambiguous expression
1 / 2 * π * F * C
... hence the need for it to have some set of rules (i.e. BODMAS) to tell it what to do when there is such an ambiguity. The only alternative would be for it to throw up an error message ("cannot do - expression is ambiguous").
The same is true if computation is by calculator or by hand. Again, we 'know' what SUNRAY's algebraic expression means/intends computationally, so we do the right thing.
Accordingly, it's probably only really if one is confronted, without any context, with a potentially ambiguous expression (as in the video) that any of these 'problems' or apparent 'anomalies' usually arise, and they only arise because of the ambiguity. Put another way, the expression which started all this [ 6 ÷ 2(1+2) ] is not really a 'fully defined' (some would say 'not valid') algebraic expression.
As I implied before, even the workers in fish and chip shops are aware of this sort of ambiguity, and will often seek clarification. If I go into my local chippy and ask for "two cod and chips" they will nearly always reply " cod and chip twice?" (the alternative interpretation being 'two cods and one helping of chips').
Kind Regards, John
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