www.whyslopes.com >> LAMP (an
abandonned mathematics education program) >> Maths
Cultural Origins [ Back ]
[ Next ]
|
|
|
LAMP - Motivation
The role of cultural ends and values in
mathematics education
Ends, values and reasons for mathematics education are culturally
dependent. They represent the needs and elements of city,
agricultural and intercity trade. They reflect reflects life in all
it forms for better or worse from ancient times where agricultural,
trading practices began to the present day in which home life,
buying and selling goods and services involve amounts, quantities,
time and/or money. Quantitative skills and concepts are
everywhere. Describing and explaining them provides
motivation, direction and content for mathematics education in an
applied and operational manner from primary school to college level
in many, but not all societies. For such societies,
skill and concepts represent common ground and in a sense, a
universal language for their common culture.
Mathematics is not a universal language for all.
While many generations has been connected with city and
agricultural life, and quantitative activities there-in, some ethic
groups are newcomers to or strangers to these activities. As a
result, there is a clash of cultures. In that there are
decisions to made or not, without a full knowledge of what is
involve and of all the consequences. In particular, many
parents and cultures send their children and teens to school in the
hope of a better future, without full understanding what
skills and values schooling will give. There-in lies another
clash of values.
Cultural Ends or Values in LLAMP
The primary aim of LLAMP phase I core topics is to provide an
operational command of drawing and figuring methods.
In phase I, the thought based development or
explanation of the methods is optional except when it clearly
aids method mastery. For students for whom the thought-based
development of skills and concept is a burden, skill
and confidence will be based on the repeatable, reproducible
nature of results. That being said, the full thought based
development of skills and concepts will be available for students
who need that greater confidence in drawing and figuring met
during instruction or self-instruction. That be said, seeing how
rules and patterns being applied one at a time, one after
another, alone and in combination in developing an operational
command of mathematics may in time provide students with the
ability to appreciate the full details of a thought-based
development. An operational command of mathematics, and examples
of mathematics in action in scenes and situation from daily life
and work may raise students expectations for themselves and
others, future offspring included, in the definition of what
should be common knowledge in mathematics and mathematics
education from primary school to the LLAMP phase I level.
Is it possible for LLAMP phase I to define a lower bound for
the common knowledge of arithmetic, geometry, algebra, and
applications there-of in daily life?
Motivation and Context for Quantitative Skills
Mathematics study is encouraged or required for many reasons -
cultural and practical. Basic or primary schooling once aimed for
3Rs: reading, writing and arithmetic skills. The fourth R for
reason might be added to this basic list.
The study of mathematics, if it not to be aimless, needs to be
based on ends and values. Calculation, geometric and logic skills
and concepts appear in many, many aspects of merchant, agricultural
and industrial life, a life that is familiar to many, but not all
people in the world. That being said, cultures around the world in
secular and religious classrooms include the study of mathematics,
basic & beyond, for the sake of activities in daily from daily
buying and selling to trades, personal banking, personal
investments, and business matters; for the sake of logic
mastery and for college level mathematics - calculus required for
entry for skills and comprehension in accounting, engineering,
science and mathematics.
Students do not enter mathematics lessons or courses with a
knowledge of why its study is advocated and required year after
year. In societies where schooling has been a
multi-generation affair, parents unhappy with their studies may
tell their children mathematics after arithmetic is without
value. Course designs and course materials need with some
modesty to set or offer ends, values and means for learning and
teaching mathematical skills and concepts in primary, secondary and
tertiary education at home, classrooms and work environments.
Course designs that cover and include topics for reason long
forgotten lead to bureaucratic environment in which learning and
teaching is guided and motivated by marks and the prospect of a
diploma or degree, but no love of learning. I have taught
high school courses where preparation for final examinations
is the only obvious reason for covering and mastering skills and
concepts of little value to students while the opportunity to
review and cover skills and concepts likely to be value is
missed.
Course designs and materials should be very clear on the short- and
long-term goals, values and ends of instruction. Course designs
based on meeting the immediate- or short-term needs of students
with say examples of calculations etc whose short and long-term
value is clear and immediate to students and teachers may succeed
in providing a context for mathematics and the work (drill and
practice and correction) needed to master it rules and
patterns. Each topic or set of skills and concepts in a
course should be accompanied by a statement of short, intermediate
and long-term reasons for it, practical or
intellectual. Reasons and connections should be given
in course design and materials so that student, parents and
teachers hear why a rule, pattern or topic is studied. The
statement of why may involve some values and ends, short- or
long-term. The statement of reasons and connections would
lead to greater clarity and transparency for mathematics studies,
year after year.
The reasons and connections given need not appeal to all. For
example, when wood was more abundant than metals, woodwork
(carpentry) as a trade is more relevant that metalwork.
Modern times since the 1500s say has led to time tracking and
telling with the use of mechanical and then digital clocks.
Counting and measuring without and then with standard units
(culturally based) has been present at the start, in and at the end
of many societies and their transitions. There-in lies a
context and motivation for primary school mathematics.
Geometry itself stems from land (geo) measurements (metrics) and
principles for that. While Euclid Elements codifies geometry
etc [ to do - describe the etc] in an intellectual manner,
the then and further development of mathematics has been driven by
applications in social and technical affairs in monetary,
construction, drawing and with regrets (value judgment) military
ends. The development of mathematics has been driven by
intellectual or religious ends, and the search for greater
certainty by codifying more and more mathematics in the rule and
pattern based fashion set forth by Euclid 's work, his
Elements. In recent times, arithmetic skill with whole numbers
and fractions has been regarded as a sign of intelligence. That
being said, the advent of electronic calculators and fervor in
favor of technology has led schools to favour decimal arithmetic
done by the electronic calculators.
|
|
|
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 < Archives < LAMP - Lean Applied Mathematics Program << C LAMP Introduction Culture in Mathematics Education
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11][12] [13] [14] [15] [16] [17] [18] [19] [20]
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.
|