|
The White Rabbit put on his spectacles. "Where
shall I begin, please your Majesty?" he asked. "Begin at the
beginning," the King said gravely, "and go on till you come to
the end: then stop." (Alice's Adventures in Wonderland,
Chapter
12)
|
The full programs above for primary and junior high school quantitative
skill development describe the start and a possible middle for
mathematics education. Now the question becomes how to how end
mathematics education. Many stop due to failure and thus a poor
view of mathematics or their own skills in it. Governments may want
to train engineers, scientist and mathematicians and even commerce
students in some or many elements of advanced mathematics. But before any
focus on formal or advanced knowledge of mathematics in school,
mathematics teaching needs to development skills and concepts in
mathematics and logic likely to have take-home value for students, so
that students are prepared to solve routine problems. For that methods
may be learnt and taught without or with full explanation of why they
work. The aim is observable and verifiable skill development so that
students are equipped to face common needs in reading, writing and
arithmetic. In that, the careful evaluation of formulas is
considered to be part of arithmetic.
In mathematics education, the take-home value of skills and concepts
should be explicitly identified - obvious or not; and long-term reasons
and context for skill development should be explicitly
identified as a guide for instruction and studies for the sake of
transparency for better or worse. Mathematics education should stop
(or go into maintenance and refinement mode) when further skill
development is seen to be too hard for a student or for the available
teaching corp. In the latter case, it better to stop instruction
and say the subject cannot be taught in place of misleading
students. Or, in place of misleading students , instructors should
describe what they know and do not know, carefully and precisely, so that
students understand the instruction given is honestly done. While
mathematics education may continue indefinitely in the face of
success, some how we need to find a way to stop mathematics
instruction at a point where students have developed observable and
verifiable abilities.
Schooling may develop skills and concepts with take-home
value. Reading, writing and arithmetic provide examples. That
kind of education is very positive. Schooling in competitive arts
and disciplines may provide students with an chance to succeed, but not
guarantee it. That kind of education is positive for students who want
to compete and are able to do. The third kind of schooling
is not to my liking. It is bureaucratic. It appears when topics are
covered in class without any comprehension of why they covered, except
that a final examination will require them, while long-term reasons for
them are unclear or absent. While it appears certain that primary
and junior high school mathematics should provide skills and concepts
likely to serve common needs of students and their families, sooner or
later. That should include mastery of logic and arithmetic
because one or both are needed to develop or improve work and studies
skills, and because there is need for self-interest, self-defense
included, to understand the words and arithmetic present in agreements
involving work, property and money matters. Beyond that ends and
values for mathematics education needed to be clarified. Site pages
do not that fully.
While many schools give mathematics education, that education becomes
bullshit when and when or where skill mastery becomes a bureaucratic
formality with ends and values unclear to parents, students and teachers.
Learning and teaching mathematics should continue or resume when or
if skill development and maintenance is justified by clear ends and
values. That being said, there is bullshit in education when students in
need of remedial instruction in basic mathematics are placed in courses
covering topics unrelated to their likely academic and work
destinations. Invest instead in a review of primary school and
junior school mathematics with the aim of showing how to develop and
perfect skills and concepts at their level, so that when or if they
become parents, they may set the stage for their children to do well in
mathematics. With that, fewer students may be seen to school by
parents whose last image of mathematics was failure.
|
|