Chapter 2. For and Against Mathematics
Volume 1B, Mathematics Curriculum Notes
Motivations from philosophy, daily life and science or technology or
business can be offered for the study of mathematics. They are
described next with some links to reason. This chapter ends with
paragraphs which discusses why students avoid mathematics.
- For some past philosophers and thinkers, the definitions and
conclusion reaching methods in Euclid's books on geometry provided the
most certain model for rule-based reason, or how to argue if you must.
Geometric knowledge was based on rules, patterns and definitions which
seemed self-evident once said or described. Euclid's books or elements
were composed two thousand years ago. Modern translations of them exist.
The translations are recommended to specialists in geometry only, as
today newer presentations of geometry and other ideas of mathematics are
favoured in the classroom. For students wanting to understand whatever
they may be doing, if not why, the Euclidean organization of mathematical
disciplines can be attractive. This is a link to the love of rule-based
reason, if not knowledge.
- For the person in the street a few centuries ago, writing, reading
and figuring skills were signs of knowledge or education. Before the
seventeenth century A.D., if not later, the absence of a good
notation for arithmetic made figuring hard, except perhaps in areas where
the abacus was readily available. Since the seventeenth century the
development of the printing press and of arithmetic based on decimal
notation, the skills of writing, reading and figuring have become common.
For the person in the street, these skills are useful in correspondence
and in the buying and selling of goods, property and services. Counting,
decimal arithmetic and the use of simple formulas provide people with
repeatable and therefore verifiable rules for arriving at conclusions.
Figuring on paper or in the head is also part of rule-based thought and
reason. This link to rule-based reason needs to be remembered.
- The decision of what or how to calculate in business, science and
technology often depends on an algebraic way of writing and
thinking for describing (or changing) calculations, numbers and
quantities. The latter appears as a reasoning tool. But this tool is part
of the mystery surrounding mathematics and reason for many people in
school and out. Implication rules with the algebraic way of writing and
thinking, if clearly explained, provide a foundation for both
mathematical thought and also rule-based reason in all disciplines. A
student may be encouraged to study mathematics in the hope of
understanding whatever he or she might be doing and why, and to have the
option of mastering numerical disciplines in science, technology or
commerce. For better or worse, this is a link to rule-based reason in
modern life.
At least four further motivations for studying mathematics exist. First,
teachers and writers in all disciplines may have the goal of identifying
and imparting some worthwhile knowledge - an incentive for this writer.
Second, researchers in mathematics may identify the goal of extending the
boundaries and form of mathematical thought. Third, some people were
attracted to mathematics instruction and research just as a means to a
livelihood in some shape or manner. Fourth, some find an enthusiasm for
mathematical thought or mathematical recreations sufficient.
No single motivation can satisfy everyone. A motivation that is
meaningful for one may seem vacuous to another, and some motivations are
not positive.
In modern society or times, science and technology are used to justify
ecological and ethical acts which appall some students. Students see that
the environment is under threat. Many leading elements of our society
busily trying to survive today have the attitude that tomorrow does not
count. Students see the use of technology and science in the creation of
war machines. Students fear that there will be no jobs regardless of what
they study. And students excelling in literature and word-based subjects
may find the symbolic and algebraic exposition of mathematics itself and
of quantitative disciplines alienating – an abstract art. Their teachers
in schools and colleges may be powerless and insecure cogs in
bureaucracies that go forward without allowing initiative. Not all is
well. Schools may be like assembly lines, impersonally processing
students or livestock to be moved on and out. Given the fears that
students may acquire, many rational students will turn away in despair
from studies or planning for the future. [1]
[1] As a student and then
as an adult I had a fear and despaired of the ever-present possibility
of nuclear war. Much to my own surprise, thirty years later in 1996, I
am still alive but have refrained from having children. This refrain
may continue due to my ecological pessimism.
In education and society, give students hope or pay the consequences in
the classroom, in the streets and in the morgue – circumstances hopeless
or lacking purpose may lead students to harm (glue sniffing, drugs, crime
or suicide). Compulsory education is absurd and pointless without care
for these other factors.
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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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