The Motivation Problem:
By the end of primary schools students and their parents may not see
great value in mastering more mathematics. But arithmetic is needed for
buying and selling goods and services (consumer & merchant math).
Formulas are used directly & indirectly in business, science,
engineering & technology. Measurement & Geometry appears in map
and plan reading & making. Arithmetic & further mathematics
demands and practices the ability to follow steps, one at a time, and one
after another, carefully, patiently and precisely. Parents &
teachers have a responsibility to emphasize that ability and its value in
all tasks, at home and at work, where steps will have to be followed with
care.
While I would like to see a leaner math curriculum focused on practical
ends and an efficient preparation for calculus, the mathematical key to
college studies in business, science and engineering, and while the
practical ends need to be identified clearly - a to do for site content -
site content and advice serve the needs of calculus, what it requires
from primary and secondary school mathematics. The question of how to
provide a clearer context and path for primary & secondary school
mathematics from counting to calculus remains open.
Cultures with weights, measure, counting, commerce and
clocks in common use and appreciated provide a firmer base for
primary school mathematics. First Nation & Aboriginal
Societies: Cultures now meeting fast lane, modern, pollution
age civilizations will have to help themselves, no one else will
do that for them, in adopting notation and adopting or coining
words and concepts to preserve, extend and refine existing
elements of mathematics in their societies. For better or worse, do not
ask what is right, old ways may be lost - so record them. Good
luck.
The importance and extent of numerical and quantitative
skills and concepts may depend on society needs or their development.
Today many societies work by the clock instead of the sun or sundial.
So time telling and using for appointments and duration of activities
appears in homes, schools and business. Everything is schedule
according time during and over hours, days, weeks and months. Whence
time telling and using is a quantitative skills that appears in school
and even before, as parents try to schedule the day of their charges
and say how long to wait. The concepts of counting and division,
fair shares and fractions, may appear in home when eating and when
dealing with money matters. Primary school mathematics has to build on
skills and concepts familiar to students from local culture or home
environments. Cultures which depend on numerical and quantitative
skills and concepts will develop words and/or written methods for
communicating those key skills and concepts. Local languages will
reflect key numerical and quantitative skills and concepts. However
some societies and languages are more quantitative and numerical than
others in the home and in the occupations of parents. The city child,
the farmland child and the hunting society child will all see different
ways of measuring and discussing amounts, time and distance. There can
be great variation within a single society between such ways and even
greater variation between societies. If a society does not employ or
did not a skill or concept in the past that society may lack the
words, oral and written, to discuss the skill and concept. Whence some
invention or adoption of terms may be needed.
Further Readings: See the current or forthcoming site discussion
of inductive principles for instruction, of critical paths for
course design, of ends, means and values for mathematics education,
and of theme based instruction. The themes may develop application
areas (time, maps and plans, money matters, game playing, ...
) or technical elements of mathematics in parallel, but as
independently as possible, to minimize the barriers to comprehension in
anyone theme or thread of skill and concept development.
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