Chapter 5, Four References
Volume 1B, Mathematics Curriculum Notes
Applications of mathematics in money computations, geometry,
navigation, surveying and so on, are found in the following encyclopedia –
one reference for subjects for further inquiry.
|
The VNR Concise Encyclopedia of Mathematics by W.
Gellert, H. Küstner, M. Hellwich & H. Kästner, Van Nostrand
Reinhold Company, 1975 (or 1977). 450 West 33rd Street, New York,
N.Y. 10001 (circa 1977) 750+ pages. ISBN: 0-442-22646-2 (hard
cover) and ISBN:0-442-22647-0 (paperback).
|
This is a beautiful work. It has many colored pages and many
diagrams. This work gives a broad overview of mathematical ideas from
advanced high school to specialized studies in college or university. It
contains many worked examples. Every high school math and science teacher
should own or have access to a copy of this encyclopedia. So should every
gifted student taking mathematics at the high school level and above. A
copy of it should be in every school and community library. If not,
strongly suggest that one should be ordered[1].
[1]
This work is now out of print. The Thompson publishing company, telephone
1-800-865-5840 in North America, now has the rights to the work, or its
successor with a different ISBN number. This author hopes that the work
will be reprinted, hardcover, with multi-coloured pages as before.
VNR also produced the James and James, VNR Mathematics
Dictionary, third edition of 1968. This may also be of interest.
The first edition appeared in 1942. (VNR has or had a remarkable collection
of works in science and mathematics. Their issuance was a public service.)
2. Historical Topics for the Mathematics Classroom
Providing information about the origin of terms and methods is one way
to nurture a knowledge of mathematics and its origins. An effort in this
direction is provided by the book
|
Historical Topics for the Mathematics Classroom,
by J. K. Baumgart et al, published by the National Council of
Teachers of Mathematics, 1969, second edition 1989, 1906
Association Drive, Reston, Virginia, USA 22091.
|
In this reference, two sections or articles provide background
information which support, I think, the perspectives on algebra and the
development of mathematics given in this work and its companions. 1. The
elementary section: The History of Algebra, an Overview, by J. K.
Baumgart. This section briefly mentions the transition of algebraic thought
from words only to symbolic. 2. The less elementary section:
Development of Modern Mathematics, an Overview, by R. L. Wilder.
This section briefly indicates that from 1930 to 1950, the set-theory
perspective went from a curious part to an essential part of mathematics.
The bibliographies A and B in this book, one more recent than the other,
provide further references for the study of mathematics or its instruction.
3. Secondary School Mathematics
The previously mentioned work, the 1965 book Secondary School
Mathematics by J. J. Kinsella, published by The Center for Applied
Research in Education, Inc., New York, is another reference. It
describes mathematics instruction from the early 1900s to the 1960s in
North America. Many of its comments are still valid.
4. Mathematical Thought From Ancient to Modern Times
Morris Kline’s work Mathematical Thought from Ancient to Modern
Times, today appears as three volumes (1990, published by Oxford
University Press). It was first published as one book in 1972 by the same
press. This work gives an overview of the discipline, the strands of reason
and geometric thought that entered into it in rigorous and not so rigorous
fashion. This work describes the changing nature of mathematics.
Mathematics apart from geometry was not a deductive exercise. In
particular, the symbolic reasoning of algebra, also called analysis from
1700 to 1900 was a tool with useful results – faith in it would
follow usage. There was no rigorous and no precise thought-based
foundation. The material underlying algebraic or symbolic analysis
treatment of calculation, that is the concept of number (whole, fractional,
negative, imaginary, complex) was only clarified gradually. This work
describes mathematical knowledge before its deductive codification, that
is, its derivation in an axiomatic framework for sets and arithmetic. This
reference is more technical than the rest, and may need to be sampled
rather than read from end to end in the first instance. Its eventual
comprehension could be the target of a college student specializing in
mathematics.
|
|
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.
|
|
Return to Page Top
Home < - Volume 1B Mathematics Curriculum Notes << Chapter 5 Four References
[1] [2] [3] [4] [5] [6][7] [8] [9] [10] [11] [12] [13] [14] [15] [16]
All trademarks and copyrights in this are owned by their
respective owners.
Copyright to comments & contributions are owned by the Poster.
The Rest
© 1995-2011, by site author, Alan Selby, Ph. D., Montreal,
All Rights Reserved ---
Skype
or Email to contact.
|