Standards for Course Material
How to Identify or Avoid Nonsense in Mathematics Texts
Ideally students will have clear and precise reading material, that
is text and exercises, to follow or do, one at a time
and one after another. Albeit, some school authorities may impose
math textbooks of the scatter-brained type on teachers and students, a
professional embarrassment for the teachers which puts students and
parents. Not all is ideal. To help improve school
textbooks, ask local mathematicians, domain experts with doctorates
in mathematics to identify in public newspapers and in university
mathematics department websites, the rational and irrational elements in
local mathematics textbooks for local schools, primary to
secondary. Do some muckraking. Math textbooks that are not
self-contained with important terms high lighted or bold faces are like
legal documents in which key terms and phrases are not explained.
Confusion follows.
Remark: A monopoly on course design and text composition by
professors of education more familiar with teaching style than
substance - that is, the content and fine points (and limitations) of
technical subjects and their exposition - can lead to nonsense.
Hence there is a need to involve university professors outside of
education in the development and monitoring of course design and
delivery. What education requires are course designs and lesson plans
easily understood and followed by instructors.
Since the 1990's, I have been looking at the plans of educational
authorities and organizations in Quebec and the rest of North
America with the intent of understanding them. But until recently, those
plans or standards for mathematics education offer edu-babble, that is,
general directions for instruction based on assumptions about the role of
technology and based on assumptions about how students learn or should
learn, without clear and full consideration of the underlying
course content. With the details of what should be taught in
mathematics inherited without much reflection, as is or weakened
from earlier days. Content-related difficulties in the exposition
or development of skills and concepts are persevered or compounded.
An individual who done well in calculus should be able to read and
understand the curricula or course design for primacy and secondary
school mathematics before calculus. Anything less points to a
lack of clarity and intelligence in North American course
design and delivery. And in all this, mathematicians have no say in
course design delivery due to their aversion to edubabble and the
emphasis there-in of style over substance. The question where is
the content and what should be taught needs to be well-understood before
delivery styles are applied. Education is or should be an empirical
matter in which hypotheses about how student learn and what to cover
should be tried and tested on a small scale, before central planning, if
any, begins.
People who advocate education reform should try and test those reforms
in ideal to less than ideal situations, and then report how or
where their ideas and material worked. Teachers parachuted
into subject they have never taught before need materials,
well-prepared and tested, to provide a lower bound for their
instruction. Education reforms with directions, fresh and not
tested, for instruction invite failure.
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