An approach to algebra shaping up via the Oregon Curriculum
Network is more geared towards computers than calculators, with
the 'function' concept tied more closely to that of 'operator'
(e.g. via the calculator keys, which we survey when introducing
'unary and binary' operators) and 'program' or 'algorithm'
introduced as sequences of operators, along with control logic
(looping and branching).
In this picture, the domain and range may be linked to the
concept of 'records' with the program outputting the latter
using the former as input. To sort or alphabetize a telephone
directory is an operation or function.
Variables get tied to the concept of 'parameter' early on such
that f(x) might be written myObject.f(x), where f is a method
interior to myObject. Likely we don't just write 'f' though
-- we discourage one-letter names for methods as underinformative,
unless the point is to be as generic as possible (or to be
backward compatible with pre-computerite text books).
The distinction between 'function' and 'relation' is still
provided: functions carry a domain input to a single output
whereas relations may return more than one value per a single
input.
The idea of multiple parameters is introduced early, with
emphasis on the idea of building a library of functional
routines, and wanting to keep these generic enough by not 'hard
coding' things you might as well parameterize. Parameters get
linked to the notion of 'stored data' or 'properties' within an
'object' or 'class'.
In sum, we're aiming to converge algebra with the already
well-developed paradigm of object oriented computing
languages. The two may be taught in tandem to good effect.
This does not replace or displace the need to study solutions
to equations (techniques) or the formal notions of linear
versus exponential, slope, factoring or simplification.
Instead, the goal is to provide an alternative notational
framework which gets away from text book notations as the only
apparatus for making the relevance and importance (and
convenience) of symbolic manipulation come alive.
Kirby
Curriculum writer
4D Solutions
Background reading:
http://www.inetarena.com/~pdx4d/ocn/outline0.html
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