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LAMP Prequel - Previous InstructionIn the first years of education, primary school and even before, children in well-protected environments may be enthused, initial reluctant aside, about going to school to learn and growing up to follow in the footsteps of their parents or guardians. For students with sight, learning to read, write and do arithmetic is based on our ability to recognize shapes as different or similar, and to draw or write those shapes on paper. Elementary or primary education may or should introduce students to decimal notation; to associated place-value methods for the arithmetic operations of addition, subtraction, multiplication and short & long division; to the meaning of fractions and arithmetic operations with them; to measures and calculations - more addition, subtraction, multiplication and division - with whole and fractional units of time, length, area, volume, money and mass (or weight) present in our cultures. As time permits, parents and teachers of children may expose students to planning and making meals; to following daily, weekly and longer schedules; to buying and selling goods and services in many situations - travel, work and restaurants. Applications: Book that teaches another language, say French, may describe people or a family in situations at home, at work, in town, on the land, at seas or in air, course designs and materials and in that description introduce to associated vocabulary. Likewise, course materials in mathematics may describe the calculation present in common place situations and activities with simplest ones first. Examples in primary and secondary school years could place students in the mathematical shoes of buyers and sellers, carpenters, painters, construction workers, health workers, taxpayers, wage earners, business operators, investors, bankers, planners, navigators, surveyors, and so on. The description of mathematical reasoning would provide a context and motivation for mathematics learning and teaching whose extent depends on local culture and conditions. The mathematics of activities that are not in local favour - a favor that depends on time, place and culture - should be presented so that students can recognize what to avoid.
Put Performance First. That is to say or suggest, skills and confidence in arithmetic may follow in the first instance from a rote or near rote mastery of calculation methods, so that results are obtained in a repeatable, reproducible and hence verifiable manner. While thought based development and comprehension of operations on whole numbers and fractions, including place value methods for operations on decimals, is preferable. It may aid mastery of arithmetic operations and should be emphasized for that, but any further comprehension of why operations work need not be required. In the first instance, skill and confidence may be produced by emphasizing drill and practices, so that students figuring skills becomes automatic. However, for students who refuse to apply methods before understanding the origins or justifications, the course materials should provide explanations in an appendix for the sake of completeness. |
LAMP
(first
draft, June 2008) a program for adult
and teen mathematics education Musings - More Ideas For further musings or thoughts see site books.
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