Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Development How-TOs Site Map || Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling; and for avid readers not in school

Logic 5 Chapters Arithmetic 10 Steps Algebra 12 Starter Steps & 5 Advanced Steps
Work & Study 23 Tips Geometry 15 Steps Calculus 70 Lessons

Ages 15+: Why study slopes Polynomials Quadratics Why factor polynomials Logarithms Functions
What is similarity Euclidean geometry leanly Coordinates + complex no.s Vectors DC Electric Circuits
Ages 12+: Prime factorization Written work formats Decimal place value Extend arithmetic skills orally
What is a variable 5. Fraction Operations by Raising Terms Solving Linear Equations: Take I Take II


Online Volumes: 1 - Elements of Reason, 2 - 3 Skills For Algebra, 3 - Why Slopes and
More Math
, 1A - Pattern Based Reason, 1B - Skill Development Principles + Troubles

Welcome: Site content may develop critical thinking, improve reading and writing, and build mathematics skills. See online chapters on on logic and pattern based reason.

Teachers: This December 2011, 5-phase framework offers a context for mathematics & logic instruction. Phases 1 to 3 focus on skills with actual or potential value for adult & daily life. College-oriented phases 5 & 4 focus on calculus & preparation for it. Phases 1 to 4 may also serve trades & professions not dependent on calculus.

Site Review: Math resources ... span ... arithmetic, logic, algebra, calculus, complex numbers, and Euclidean geometry. Lessons and how-tos .... provide a good foundation for high school and college ... mathematics. Read more.

Home < Archives < LAMP - Lean Applied Mathematics Program << A Introduction Objectives

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www.whyslopes.com >> LAMP (an abandonned mathematics education program)  >>   More About LAMP     Back ] Next ]

LAMP  Implementation - Ends, Values & Means

 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. 

  1. 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. 
  2. 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. 
  3. 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.

  4. 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.

Secondary Mathematics for Ages 11+, A Practical Approach for home-tutoring or -schooling, or for schools & colleges with local curriculum control. Study how to include site content - its skill development how-TOs and innovations into present or future lesson plans - some reading required.

Road Safety Messages and Questions: When and why should you face traffic when walking along a road or cycle path? Is it a good idea to hang limbs outside of cars etc? What gives more protection in a crash: a car, motorbike or bicycle? See too, the BBC-Belgium story Texting and Driving - texting & the impossible test - the article links to a gruesome utube video on the subject

The Logic of Injustice: How Texas sent an innocent man to his death - The wrong Carlos. Some judgments are irreversible. Procescution: Where and when prosectors play to win rather than for justice, guilt beyond a reasonable doubt goes unrespected due to prosecutors who putting winning first, those innocence before the law may be convicted. Some procescutors offices in continuing to accuse after a pardon due to reasonable doubt or innocent being shown, may sucessfully oppose compensaton for false convictions by asserting a pardon individual is still under suspicion. Then the pardoned individual or the latter's estate is not compensation for years or decade of improper or false imprisonment, or for execution. Site chapters on Logic
and some in Pattern Based Reason may slowly lead to greater precision in reading, applying and writing laws.

May 2012, Composition Starting: Pre-School and Primary Mathematics - Quantitative Skills, An Intellectual View, Feedback Welcome:

The 8 Most Popular Site Inlinks

20 Times Table - the most popular site page - popular pages - unexpected.
Fractions & Ratios - with lesson on raising terms to introduce & justify times, division & comparison as well addition & subtraction
Parent Center - See below
Volume 1, Elements of Reason - Intro to all site books.
What is a Variable - best for ages 13+
Written work formats for Arithmetic and Algebra - a skill method and standard!
Complex Numbers Visually - best for ages 13+
Natural Logs, Exponentials, Powers, Roots

Division of Labour: This site offers advice and directions with pointers to resources elsewhere, if known, when they help or lessen the need to write more.

Parent Center: Help your child or teen learn:

Parent-friendly Work Booklets for ages 3+ to 13 Use these or others to check or build skills. Other booklets are available but these booklets allow parents unsure of themselves in mathematics to help their children. The selection acquired in Canada is published in the USA. So it has a US orientation. In retrospect, the selection shows parents what to check with the booklets or by other ways, the choice is theirs. But in retrospect, the selection does not cover integral and fractions liquid weights and measures - ask the publishers to correct that! For ages 9 to 12 say, parents may compensate by showing boys and girls how to use weights or mass, and further measures in food preparation. Beyond that children may be shown how to measure and calculate angles, lengths and areas [proportional amounts too] directly or by using maps and plans drawns to scale. Learning how to gather and measure all the ingredients, pots and pans for a dish or a meal, along with cleaning up sets the stage for like activities or experiments in science courses, and in developing organizational skills, gives boys and girls a head start. Good luck. At the other extreme, more comprehensive than light, if your motto is McCainian: drill, drill, drill then Toronto mathematician and actor John Mighton's jump math organization has jump math workbooks for at least grades 3 to 8 for at-home and in-school use - training sessions for teachers available. Jump math has been expanding to cover older students. Jump Math Samples: plus Fractions for Grades 3-4 & Grades 5-6 [Read] Free Resources grades 1 to 8 [unread - likely to be good]. and

Mathematics Skills For Ages 3 to 14 - technical!

Skills with take home value - A few ideas

Basic skills include time-date-calendar Matters; money matters; map, plan and scale diagram matters;counting, measuring and figuring; decision making with logic and likelyhood; being careful and being aware of the domino effect of mistakes; reading and writing with precision.

Is your child able to add, subtract and multiply amounts of money, work with fractions, work with clocks and calendars, work with maps and plans, and measure length, weight-mass and volume? Schools may promote your son or daughter without providing basic skills in reading, writing and arithmetic.

Arithmetic and Number Theory Skills

Algebra Starter Lessons

1 Working With Sets
2 Formula Forward Use - Evaluation
3 Solving Linear Equations - Skip first step with students able to solve 1 eqn in 1 unknown.
4 Computation Rules and Function Notation
5 Real Numbers
6 More Less Greater Than Inequalities and Comparison
7 Axioms Logic and Equivalent Equations
8 Unifying Theme For Algebra
9 Proportionality Backwards and Forwards
10 Examples of Algebraic Reasoning
A Origins of Counting and Figuring Methods
B Real Numbers Extrinsic Development


Site coverage of formuala evaluation format, of computation rules and axioms, and of the forward and backward use of formulas and proportionality relations lessens the amount of natural talent needed to understand and explain algebra.

Geometry - maps plans trigonometry vectors

1 Maps Plans Measurement
2 Euclidean Geometry - Constructions + extras
3 Cartesian and Polar Coordinates
4 Lines and Slopes Take 1
5 What is Similarity
6 Trigonometry first steps
7 Complex Numbers
8 Unit-Circle Trigonometry
9 Lines and Slopes Take 2 with tangent function
10 Intersecting Straight Lines and Transversals
11 Parallel Straight Lines and Transversals
12 Function Translating and Rescaling
13 Vectors
14 Degrees to Radians and Radians to Degrees
15 Arc or Inverse Trigonometric Function

Pre-Teen and young teen mastery of skills and practices which should be common with map-plans-diagrams drawn to scale, contour interpretation included, has actual or potential take-home value for daily- and adult-life in solving routine problems. Elevating some practices to principles, axioms or postualates, provides a base for analytic and Euclidean geometry, an analytic view of similarity, and an efficient mastery of trigonometry and complex numbers. Right triangle trigonometry provide an analytic alternative to solving geometric problems by drawing diagrams to scale.

More Algebra

Natural-Logarithms Exponentials Powers Roots
Five Polynomial Operations
Quadratics Geometrically
Functions
5 Factored Polynomial Sign Analysis Examples
Rewriting algebraic substitution as function substitutions

The first topic leads to a full high school level theory for the forward and backward mastery of growth and decay models and for definition, range and domains of radicals, roots and powers. The next two topics make quadratics and polynomials easier to learn and teach. Site coverage of functions turns vertical and horizontal line rules into computation methods for evaluating functions.

70 Calculus Starter Lessons

Calculus Lessons Elsewhere:

  1. How to Ace Calculus: Street Wise Guide - Mostly Text.

  2. Flash Video for Calculus Phobics

They cover basic topics in ways likely to complement your notes, your textbooks and site material. When Goldilocks trespassed in the house of the three bears, she found three bowls of porridge, two not to her liking, and one just right. Different bears have different tastes. As invited guest here and elsewhere, if one or more explanations is not to liking, try another. It may be better or just right.

Unsolicited Advice

Learning to do and high marks if it comes to easy is often deceptive - light rather than deep. For that reason, students with learning difficulties determined not to let it get in their way may go deeper and farther than those with none. High marks, if the come easy, may be deceptive - provide a too light and not a deep mastery. That could have been your problem in secondary school, one that leads to comprehension shock or difficulties in calculus and more generally in the first year of college. Bon Appetite.


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Home < Archives < LAMP - Lean Applied Mathematics Program << A Introduction Objectives

[1] [2] [3] [4] [5] [6] [7] [8] [9][10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]


Logic-Reason for all
Careful Thinking
Chains of Reason
Mathematical Induction
Responsibility
Bodies-of-Knowledge

Arithmetic - Ages 10+
1. Deciml Place Value - fun
2. Decimals for Tutors
3. Prime Factors - quickly
4. Fractions + Ratios
5. Arith with units - science

Geometry
1 Maps + Plans Use
2 Euclidean Geometry
3 Rct +Polr Coordinates
4 Lines-Slopes [I]
5. What is Similarity
Algebra Starters - the base
1. Better Work Format
2. Solve Linear Eqns
3. Computation Rules
4. Axioms, Item 3 Viewpnt
5. Formulas Backwards
More Algebra
Logarithms-ax & m/nth roots
Five Polynomial Operations
Quadratics Geometrically
Functions || Vectors too
Arith. Skill Check+Answers
Calculus Prep/Preview
What is a Variable
Why study slopes
Why factor polynomials
Complex Numbers
Limits + Continuity

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