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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.
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