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LAMP Instructional Concepts
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 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.
- Communication is represented by developing and recording thoughts on
papers with the aid of words, equations and diagrams.
- Reason is dependent on communication, and calls for the ability to show
work or the steps followed in a method in legible and clear format.
- Problem solving is represented first by the ability to solve routine
problems via standard method, and then by the ability to combine rules and
patterns in creative, opportunistic or speculative ways, and in doing so
arrive at solution that is clearly described, with steps are easily followed
and consistent with earlier rules and procedures for arriving at
conclusions.
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. |
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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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