Appetizers and Lessons for Mathematics and Reason  ( Français)  
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 Logic mastery is key to easing or avoiding learning difficulties in work & studies. 

Online Volumes (Book Orders)
1,  Elements of Reason. 1996
1A. Pattern Based Reason  1995
1B. Math Curriculum Notes 1996
2. Three Skills for Algebra  1995
3.
Why Slopes & More Math 1995

Site  Folders for Instructors & Adults
A. Public Policy Essays
B.  Mathematics  Education Essays  2006-7
C -Logic & Applied Math Program  
    for education,  June 22, 2008 
D. Quebec English Math Ed -  Standards to
 avoid  in course design & teacher education 
E. Help your child or teen
How TOs/ Ref.-08- 2008
1. Arithmetic Reference
2. Algebra 
3. More Algebra 
4. Geometry  
5. More Geometry
6. Calculus
7. Logics in Maths
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.  

 

LAMP (first draft, June 2008) a program for adult  and teen mathematics education

Mathematics education standards implied by calculus should be a factor, not the only one, yet not a forgotten nor hidden one in course design 

Area Intro
Introduction
Arithmetic
Geometry
Algebra
Logic
Calculus

Musings - More Ideas

More About LAMP
Evaluation
Maths Cultural Origins
First Nation Education
Modern Mathematics
Before LAMP
Problem Solving Skills Routine to Non
Instructional Concepts
Student Cooperation
Maths Extrinsic Origins
Science Education

For further musings or thoughts see site books.




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