Were
it not for convoluted language, plenty of lawyers would be out of work.
Educators, though, shouldn't be subjected to such torture.
William McCallum, one of CCSSI’s authors, wrote in the comments section of an article appearing on The Atlantic Magazine website, written by Barry Garelick,
``I agree with you that there is a lot of misreading of the standards
out there in the field, and this is a problem.’’ Such arrogance. The
real problem is that CCSSI is poorly written, not only substantively, but
also in its lack of clarity.
7.G.2’s ``Focus on constructing triangles from three measures of angles or sides...‘’
is at best, ambiguous. Writing intelligible English is not the same as
constructing logic gates, where the definition of ``or’’ invariably includes the
possibility of both. The parallelism in the sentence implies you are
given either 3 angles or 3 sides, but we suspect it’s supposed to mean
the following: ``Focus on constructing triangles given various
combinations of three angles and/or sides.’’
CCSSI 7.G.2 states, ``Draw
(freehand, with ruler and protractor, and with technology) geometric
shapes with given conditions. Focus on constructing triangles from three
measures of angles or sides, noticing when the conditions determine a
unique triangle, more than one triangle, or no triangle.’’
Some preliminaries before we parse this standard.
Protractors
We
here at ccssimath.blogspot.com LOVE protractors. The way we see it, a
(non-toxic, teething) protractor should be given to every newborn in
their bassinet (thanks to Charles Schulz for the inspiration); perhaps
the first one can be hanging from a mobile. A protractor (like a banjo) is a happy
thing: it’s a smile, or a big letter D. A protractor is easy to hold,
it’s too big to choke on, and it’s covered with numbers. It even has
mystery and intrigue, for why would the numbers run in opposite
directions? Rulers, in contrast, though useful, are dangerous things;
they fit in the mouth and can be brandished as swords.
In
legal argument, every assertion cites authority: when lawyers know they
are losing, they attempt to cloak weak arguments in language such as
``it is clear that’’, glossing over the insufficient basis for why;
strong assertions cite controlling authority, such as a prior ruling of
the U.S. Supreme Court. The same citation requirements hold true for
judicial opinions. The American common law system is grounded in its
constitutions and legislation, but also on the principle of stare decisis,
which means a strong legal opinion will cite another, preferably
higher, controlling authority for coming down on one side or another.
In the absence of binding authority, non-binding or persuasive
authority is relied on: someone made an argument that won a case in
another jurisdiction, the judge cites that decision and the law expands
to a new jurisdiction. Opponents of such decisions with weak legal
precedent may deride them as ``judicial activism’’, but judge-made law
is a fundamental component of how our system works, and indeed, how the
legal system has managed to survive. Of course, a judge may instead
reject another non-controlling decision and cite an alternative argument
for ruling differently. Thus, competing legal doctrines scatter like
leaves in the wind until a higher court decides to consolidate and
resolve contradictory rulings. It is often possible (and enlightening)
to trace a winning argument in a high court ruling down through various
lower court decisions and ultimately arrive at the original language
source, which can be the unprecedented argument of a jurist publishing
research (and personal opinions) in some obscure law journal. Thus
judge-made law, sometimes with questionable origins, becomes the law of the
land and not always for the better.
