23 May
2021
23 May
'21
9:12 p.m.
Anno domini 2021 Sun, 23 May 13:46:58 +1000
Steven D'Aprano via tde-users scripsit:
On Sat, May 22, 2021 at 08:05:03AM +0200, Dr. Nikolaus
Klepp wrote:
I teach mathematics, and I'm curious what you mean by this. What year
level is Junior studying, what topics?
(Also, in Australia, "PITA" means Pain In The Arse. What do you mean by
it?)
In English-speaking countries, it has been traditional for the last 40
or so years to make maths relevant to the kiddies, with lots of real-
world topics, examples and questions. Especially in primary school
maths, years 1 to 6, but also into secondary school, which is my area.
For example, lots of business maths (interest, annuities, depreciation,
loans, etc); applications of trigonometry to navigation; maths applied
to practical problems like working out the cost of items using
simultaneous equations, etc.
Of course there is still pure mathematics taught with no applications
given. In Australia, our senior year (Year 12) of secondary school has
four mathematics streams:
- Specialist Maths (pure mathematics, heavy on calculus and advanced
algebra, very abstract);
- Maths Methods (mix of pure and applied maths, some calculus);
- Further Maths (practical applied maths: finance, statistics, etc,
very light on algebra);
- Foundation Maths (remedial mathematics, heavy on practical
applications like cooking, sport, finance, measurement, speed and
distances, etc, virtually no algebra).
Most kids do Methods or Further Maths.
What is the situation like in your country?
Once upon a time in the 80s and eary 90s the situation was quite simillar. But then came
"Schüssel I" and with it the decline of the education system which is still
ongoing. In the days long gone the A level was not centralized, but you were allowed at
any university - and the knowledge you gained at school was sufficient to enable you to
follow the lectures at university. Then the conservatives started "optimizing"
or "reforming" the education system. A level certificate is now centralised (a
great "improvement") and prepared by some private company. Additionally there is
a regular school certificate. Stuff taught for A level is plain useless at a univerity, so
all universities introduced entry exams and "trial" semesters.
But to give you a rel live examples from 5. class (age ~ 15, still 3 years to go for A
level):
- Pupils are told how prime factorization works. They are not told what to do with it -
never.
- Comes "Linear equations", 6 months later 2D vectors. They are not told that
these 2 things are the same.
- Geometry, "2 lines may be parallel or have one intesecting point or none".
Then they learn a methode to find "the" line that does not intersect with a
given line. They are not told that there are infinite non-intersecting lines, nor are they
told the correct way to build a inequality to describe all non-intersecting lines.
- Trigonometry: taught sine theorem and cosine theorem, but not a single word that they
need 3 independent specifications to define an triangle and why and when to use sin/cosine
theorem to get the other 3 specs.
- They are never told how to solve a problem by using or combining prior knowledge - this
is the absolute nogo for universities. And its quite astouning how the schoolbooks mange
to not-teach this vital skill.
To sum it up: Austrian school system is totally broken nowadays. Funny thing is, in the
80s austrian school system was superior to german, now its the other way round - but not
because Germany did real improvements, on the contrary, they are just slower with
"improving".
Nik
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Anno domini 2021 Fri, 21 May 18:14:42 -0500
J Leslie Turriff scripsit:
[...]
Yeah.
Good luck getting today's teachers to teach how to learn instead of how to
memorize.
That's impossible. Checked juniors math books this week: they are full
of descriptions what different kinds of hammers are around, but not a
single line on what you use a hammer for. Just PITA.