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Original Site Title: Appetizers and Lessons for Mathematics and
Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept
Development with How-TOs Français: 26
pages
for college students,
gifted teens, home-tutoring and K1-12 schooling. Avid readers in school and out may like Site Volumes.
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Logic
5 Chapters Arithmetic 10 Steps
Algebra 12
Starter Steps & 5
Advanced Steps
Work & Study 23 Tips Geometry
15
Steps Calculus 70 Lessons. See Site
Map
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Why study slopes Polynomials
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What is similarity
Euclidean geometry leanly
Coordinates + complex no.s
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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
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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.
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Home < Archives < LAMP - Lean Applied Mathematics Program << E LAMP Introduction Modern Mathematics
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www.whyslopes.com >> LAMP (an
abandonned mathematics education program) >> Modern
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LAMP and Modern Mathematics
The modern mathematics curricula of the period mid-1950s to 1980s
determined what would be taught and how, at least to the advent
of the constructivist approach and dogma for instruction in
mathematics and science.
LAMP could be have been named LEMP, an acronym for Lean
Extrinsic Mathematics Program.
LAMP offers an extrinsic rather than intrinsic
development in which quantitative skills, concepts and
principles (patterns or axioms) are derived or inferred from
figuring and drawing practices in daily life that appear to give
repeatable and reproducible results.
LAMP offers a replacement for the modern mathematics curricula in
secondary instruction from arithmetic to advanced calculus. Yet in
doing so, it provide an extrinsic context and the
algebraic-deductive maturity (we hope) to enable interested
students to obtain a clearer and better understanding of modern
mathematics.
Mathematics originated from extrinsic
considerations before its more rigorous, intrinsic, pure
mathematics codification in terms of axiomatic set theory - the
basis of modern mathematics and the motivation for modern
mathematics curricula. The intrinsic or context-free view
of pure mathematics starts with axioms for sets or real numbers
to provide a logic-based codification and development,
context-free. So extrinsic considerations - the drawing of
diagram as in Euclid's elements or its successors - are excluded
from advanced mathematics for the sake of rigour. The
modern mathematics curricula duplicated some of that rigour its
course designs and materials, but did so inconsistently without
stating nor acknowledging the tacit assumptions needed to
illustrate and apply mathematics.
The LLAMP extrinsic development envelopes the tacit assumptions
needed to apply mathematics and in doing so arrives extrinsically
at the field properties of real numbers, in other words,
axioms for real numbers assumed in the modern mathematics
curricula. LAMP does more. It arrives extrinsically or
geometrically at the field properties of complex numbers. The
extrinsic development in LLAMP is no less and no more rigourous
than the extrinsic development of geometry and trigonometry present
in the modern mathematics curricula. Further LLAMP adopts and
sanctions the decimal representation of real numbers from first use
to the discussion of limits and convergence in calculus where as
the modern mathematics curricula avoided all mention of decimals in
its theoretical development while employing a mastery of
decimals in the representation of irrational numbers and in the
numerical evaluation of function and limits from trig to
calculus. Whence the adherence of the modern mathematics
curricula to an intrinsic (context-free) development was
inconsistent.
This LLAMP approach furthers implies the algebraic and deductive
maturity needed for a later mastery of intrinsic axiomatic
development of mathematics from assumptions about real numbers or
sets. The LLAMP extrinsic approach also provides a context
and motivation for the intrinsic axiomatic approach. Yet LLAMP
alone may be sufficient for people without the time and
inclination to meet and master pure mathematics.
Summary: The modern mathematics curricula intrinsic
approach to mathematics was mixed with extrinsic approaches to real
numbers, to geometry, trig and calculus inconsistent with the
intrinsic or context free approach to modern mathematics and
represented in the algebra portion of modern mathematics curricula.
That realization in fall 2007 led to the notion of providing a
replacement LLAMP based on inductive principles for skill and
concept mastery from arithmetic to calculus in ways that will be
supported by and be motivated by applications and the availability,
but not imposition, of a thought-based development of all or almost
skills and concepts.
Remark: For students for whom calculus
preparation is not a possibility or not wanted, the thought-based
development is optional. Yet the operational mastery of rules and
patterns, one at a time, one after another, alone or in
combination, may eventually make the thought-based
development accessible to those for whom it initial
imposition may be a burden.
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Teachers & Tutors: Site pages offer better or best practices for providing skills -
simpler than expected & comprehensive but for exercises. For your charges, your duty is to study them alone or in
groups and develop skill building exercises & activities to share. Start now. The effort here is the best I can do.
Others are welcome to refine or exceed it. Please do.
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
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
Geometry
- maps plans trigonometry vectors
More
Algebra
70
Calculus Starter Lessons
Calculus Lessons Elsewhere:
-
How to Ace Calculus: Street Wise Guide - Mostly
Text.
-
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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