Extent and Need for Quantitative Skills depends on your society

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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.