|
Five Decades make a difference: Site material
parallels and re-invents a small subset of the following texts and
several more. With some zeal, these texts gave or reflected set
oriented course design and delivery in the late 1950s and
early1960's.
-
Report of the Commission on Mathematics,
Appendices,College Entrance Examination Board, New York
1959. Here is a technical base for the senior high school
presentation of many concept. VG
-
Secondary Mathematics, A Functional Approach for
Teachers, H. F. Fehr, Teachers College, Columbia
University. 1951 D. C Heath and Company. A wealth of
technical know-how for course design - senior level. VG
-
The Growth of Mathematical Ideas, Grades K-12,
Twenty-Fourth Yearbook, The National Council of Teachers of
Mathematics, Washington, D. C. USA 1959. Not my cup of tea.
The site introduction
via examples of a variable as a number or quantity which may vary
may be easily woven into the placeholder view of what is a variable,
but that introduction appears to be clearer for
students.
Five decades ago, there was much discussion of what should
be in primary and secondary mathematics to train engineers, scientist,
mathematicians and math teachers - university oriented types; and to help
the remaining "terminal students". In the great
discussion of what should be done and how, the algebraic way of writing
and reasoning was employed with a partial rather than a full progressive
development of its skills and concepts. The development of trig
with the aid of complex numbers was seen as advantageous, but it was not
implemented may be due to the question of how to introduce complex
numbers in a simple manner.
Cold War Motivation in the 1950s: Sputnik went up
and around the globe. Western societies responded with a thrust to form
or train scientists, engineers and mathematicians with great
zeal. The space (and arms) race was on. Until Gorbachev,
there was an imminent threat of global nuclear
annihilation.. The sputnik motivated,
pre-university secondary mathematics omitted skills and concepts that
might have been useful to "terminal" students - those not
heading for university. Motivation in the pre-university
stream was given in part by the maths in chemistry and physics.
In the last decades, students in the pre-university stream was
widened to include more students -parents wanted their kids to
have chance to go and not be excluded. But in the pre-university
stream, the study of polynomials and radian measure have
not immediate value, save for preparation for calculus. Besides
old and continuing gaps in the progressive or inductive development of
skills and concepts, there has been a motivation gap, a lack of purpose
in and communication of ends & values of instruction, save
for the annual bureaucratic goal of preparing for final
examinations.
Site
methods for the progressive development of algebraic skills
(comprehension of the shorthand role of letters and symbols) upto and
including calculus, continuing with site ideas for basing trig and trig
formulas on a development of complex numbers from Euclidean geometry,
continuing with site introduction of analytic geometry, and site calculus
previews offer a quicker, more accessible and stronger base for students
taking or aiming for calculus. The development of algebra skills, those
related to money matters, will help students aiming for calculus or
not. Course design may be based on the dynamic
programming optimization question of how to maximize the value of each
year of school for students who might not continue while
progressively developing skills and concepts in an observable and
verifiable manner. The terminal rather than the pre-university
stream should be widened to give students as much as possible, a thorough
empirical grounding not in the mathematics needed for academic
studies, but in skills that could be needed or useful in
life, daily or yearly, sooner or later. Even students who are
pre-university need that know-how sooner or later.
|
|
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.
|
|