LAMP Implementation - Ends, Values & Means

Appetizers and Lessons for Mathematics and Reason ( Français)
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Logic mastery is key to easing or avoiding learning difficulties in work & studies.

LAMP includes a context for each skill and context in it, or an explanation of why each skill and concept in it should be mastered, albeit the explanation why need not please everyone. The aim is a practical and operational command of mathematics - that needed in every day life for home and work in town or out on land or sea. Yet there is cultural bias in this. The basic quantitative skills and concepts developed here reflect the cumulative agricultural, trading, construction and travel needs of ancient to present day societies where for better or worse work, production and distribution is divided in a multi-layered manner between in-town and out-of-town activities.

Besides mastery of mathematical methods through practice, by rote if need-be in basic instruction, and through the thought-based development of skills and concepts in both basic and advanced instruction, the LAMP program aims for operational command of skills and concepts in a practical, observable, repeatable, reproducible and verifiable manner.

Skills and confidence is based on an operational command of step-by-step methods in arithmetic, geometry and algebra. Those methods followed with care should give repeatable, reproducible, observable and hence verifiable or correctable results. Thought based development of skills and concepts is available for students who want it, and optional except in situation that development aids mastery of operations.

Anticipation: Guides and course material for this program should be clearly written so that students, parents and teachers able to read and write at a college, or better yet at a senior high school or secondary or even lower level, may easily understand and explain all details. Guides and courses materials will be checked by mathematicians for logical development, consistency and completeness of exposition; by editors for grammar and proper diction; by teachers, students and parents for readability, clarity and usability. In guides and course materials, small step methods are provided for instruction which each skill and concept is a consequence of a sequence of smaller steps, each for independent development and verification. Guides and course material include step, skill and concept checklists for student, parent and teachers use. All is written in accordance with inductive principles for instruction.

Guides and course materials for this program should be based on inductive principles for instruction which eliminate or reduce the need for natural talent (the ability to understand when not all is explained) by providing smaller steps for learning and teaching. Ease of comprehension and effectiveness will be criteria for iterative trial and testing, refinement, and eventually replacement of this program and its materials.

The development of mathematics for TCPITS in LAMP basic and advance levels is lean as it focuses on skills and topics likely to be of interest or service to students in their current or adult lives. The emphasis here is on mastery of formulas and methods with repeatable and reproducible results to build skills and confidence with comprehension of reasons why the methods work, desirable but optional. For TCPITS benefit, delay or prolong the preparation for calculus by covering and describing as completely as is possible, the situations in which arithmetic, algebraic and geometric figuring is likely to be of service in home, work, society and monetary matters. That should give greater satisfaction and turn TCPITs into an advocate of basic skill and concept development for others, his or her children included. That may end a vicious cycle in mathematics education, and begin a pleasant one Mathematics for TCPITs includes ends, values and means for that.

In modern life, imagine if numbers were not present. There would be no clocks to tell us the time of day; no numbering of the days of the month from 0 to 28, 29, 30 or 31; there would be no bus nor train schedules; there would no number-based coins and bills (money) for the buying and selling of goods and services, and the payment of duties and taxes; and there no measures of length, time and amounta (weights or masses) at home in the kitchen, in market places and in garages. Numbers everywhere keep us on time and help track our activities.

The study of logic is valued for that combination and for its contribution to precision reading and writing, two aids or musts for work and study in all disciplines. The great emphasis is in part deliberate and in part a consequence of grouping together in in so-called advanced instruction, those skills and concepts where that emphasis appear to be required for full mastery and comprehension. An operational or applied mathematics style, thought-based development of mathematics with the aid of logic, arithmetic and drawings provides a story or stories (theories if you like) to tell and follow in a repeatable and reproducible manner for the sake of a greater and fuller account, explanation and connection of skills and concepts.

The preparation for calculus in the advance portion of LAMP is also lean. It stems from a critical path viewpoint of skill and concept development, so that calculus prerequisites are clearly identified and topics not strictly needed are identified as optional.

The optional parts of LAMP of value in themselves also have some value in strengthening and reinforcing arithmetic, algebraic and logic abilities. The difficulty of these optional parts of LAMP is not greater than other parts that student are likely to meet and master. These optional parts should do no harm and have some benefit.

Simply put, calculus is the key to college level studies in accounting, business, heath, engineering, science and mathematics. It requires the study and mastery of topic not of immediate use to TCPITS. Those topics are clearly identified, so students know why they are present - have at least one reason for the study of those topics. Readers may see further reason not yet known to this author. LAMP briefly describes for the sake of some completeness and for the sake of providing advice and directions, topics that are archaic or add needless difficulties or hurdles in to objectives of providing TCPITs with a practical command of mathematics and, if desired, with preparation for calculus.

LAMP also follows a just in time philosophy. Elements of mathematics needed after calculus are not covered or marked as extras. But LAMP also has a cross-curricula component. It covers, develops or mentions algebraic skills and concepts likely to be met in the pre-calculus study of science and (?) technology. LAMP points outs connections between application - how mathematics in one situation is similar to that in another.