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LAMP Instructional Concepts
LAMP like the modern mathematics curricula of the 1950s provides a very structured view of mathematics. In that view, mathematics is an art or discipline in which the steps or reasons for results or conclusions are recorded and developed on paper in observable and verifiable manner using methods which have invented and passed-on or inherited as is or in transformed form. For example, Euclid Elements is an invention from 300 B.C. while decimal notation and decimal methods for arithmetic are inventions and refinements from the period 1500 to 1800 A. D. So mathematics skills and concept have a long history with twist and turns that may have been forgotten. Mathematics is mastered or has been mastered and required for cultural reasons. Those reasons are not all obvious. Mathematics also consists of methods, or rules and patterns, for figuring, for geometrical reasoning and logic which are not obvious, which have been slowly found and consolidated over time through the work and writings of many individuals. Before constructivism, the description and use of rules and patterns, one at a time, one after another, alone and in combination to understand more mathematics or solve standard or routine problems on paper in an observable and correctable manner was part of mathematics and a measure of it mastery. Mathematics is based on communication, reason and problem solving.
There-in lies a rigorous and demanding structure for using and extending mathematics in an objective manner. In this process, individuals may have their private thoughts and in those thoughts entertain many possibilities. But the test and proof of comprehension lies in the ability to record and communicate steps and reasons in an observable and correctable manner. Here the writer may do correction after correction until the communication is ready for peer and/or teacher review. LAMP reflects the view that mastery of rules and patterns as indicated by their statement and application on demand, one a time, one after another, alone or in combination in an observable, on-paper, repeatable and reproducible manner is the essence of mathematics and mathematics education. While instructors cannot read the mind of students, instructors can read their work, and provide feedback. While we can do some mathematics mentally, the use of paper to write equations and draw figures extends our memories and provides a place to represent and record our thoughts - wordy or visual. Like a picture, the use of paper to record and develop thoughts is worth a thousand words. The intellectual part of mathematics with its complications is based on the ability to present and record on paper, our thoughts in a repeatable, reproducible and legible, logical format for review by ourselves and our peers. Thus mathematics consists of observable and verifiable activities. |
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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