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OnlineVolumes
1, Elements of Reason.
-with foreword for all volumes
1A. Pattern Based Reason
- striving for objectivity, etc
1B. Math Curriculum
Notes
inductive principles etc
2. Three Skills for
Algebra
- unifying themes + study skills
3. Why
Slopes & More Math - previews & starter lessons for
elementary & advanced calculus.
See Volume 2 and 3 if you are preparing kids for calculus.
More Site Areas
1. Help Your Child or Teen
Learn.
2. Linear Equations
& Fraction Skills - Sec I to V level
3. Fractions Ratios
Rates Proportions Units - Sec I & II
4. Euclidean
Geometry - Sec IV
5. Analytic Geometry -Sec
IV & V
6. Number Theory. Sec V
&VI
7. More Calculus Sec V
& VI
8. Complex Numbers Sec
II to VI
9. Qc Maths Education
10. Secondary IV(?) math
11.Real
Analysis College level
12. LaTeX2HotEqn College level
13. Electric Circuits Etc
Sec IV+
14 Français - Sec III +
15. www.whyslopes.com Entrance
Level Pages:
This Calculus Preview and Chapters 2 to 6 in Volume 3 offer lessons to make the hard easier at the start of calculus, or to provide a context for the study of slopes and factored polynomials before calculus.
Your IP
Address &
how to use it
Three Links for Teachers:
(i) First
Year High School Math - Lesson Plans with Fraction Focus
(ii) Second
Year High School Math - Lesson Plans with an algebra focus
(iii) Algebra Lesson
Plans
Parents: Site Area Helping Your Child or Teen Learn covers 1. Speaking Skills, 2. Reading & Writing, 3. Preparing for Science, 4. Math Work Books, 5.Books for Parents, 6. Mathematics for ages 6 to 14, 7. Having Patience -you'll need it. Chaperone your sons and daughters through jumpMath workbooks for grades 3 to 8 along side site lessons for grades 7 to college and material elsewhere. Parents and teachers need to say no for small things of little consequence to build and maintain authority to say no for larger matters. Parental authority: use it or lose it, but do not abuse it.
Lesson Plans and lessons
Secondary I - fractions
& allied concepts (decimals, percentages)
Secondary II - Algebra (arithmetic versus algebraic methods, backward
use of formulas and proportionality equations)
Secondary III - to come(?)
Secondary IV - Functions to Trig & Statistics
Algebra Lesson Notes & Ideas for All levels
Euclidean Model for development of an art or discipline: More than two thousand years ago, the works of Euclid in Geometry gave a model for a clear, full, logical development and application of rules and patterns in an or a nearly authoritative manner.
Application to Education & Skill Development: Pattern Based Reason is not always authoritative due to gambles or approximations in it. Skilful and empirical mastery of rule and pattern based thought and action, modulo limitations, is one aim, we hope, of school and college education in rational "method-based" arts and disciplines. Learning to apply rules and patterns in a repeatable and reproducible manner is or should be part of education.
Teachers & Parents: Compare and combine site ideas with those available elsewhere. For example, the Mathematics portion of English National Curriculum, a site for teachers, is well-written and well-put. Yet content shifts might improve it. An empirical focus on what works or well or should would improve education. Site material stemmed from a perception of older gaps in course materials and design, gaps not deliberate but still present. Asking students to discover ideas by themselves is fine as long as the ideas in question are not critical for further instruction.
Curriculum Shifts - Undoing the Damage
The constructivist view of education calls for authentic, realistic, engaging activities in the classroom - that call is great except for my lack of imagination, so details how are required. Many arts and discipline develop by trial and error, with nature as direct teacher correcting the reasoning and methods of the developers. The element of the constructivist view of education which calls for mathematics, science and complicated rule- and pattern based arts and disciplines in general to be understood in the classroom via student discovery and construction of the underlying concepts without the teacher being an authority figure, so that student chains of reason or their consequences are accepted as valid and not judged nor corrected is empirically absurd. Instructors of long developed arts and disciplines, arts and disciplines corrected by nature, need to identify and empirically verify student mastery and comprehension of previously discovered methods, so that students empirically learn how to arrive at results in a repeatable, reproducible and therefore verifiable fashion. Where instruction is an empirical art, teachers judge and guide students by observing and correcting their writings or activities. In complicated arts and disciplines, long-developed, there is insufficient time for students to rediscover and verify the rules, patterns and working practices of the disciplines. So direct summaries and skilful direct instruction with skill practice and empirical concept verification is required. The instruction may range from learning via practice and rote to learning via practice and Euclidean, logic-based, developments.
In some primary and secondary classroom, mathematics lessons are giving students concrete metaphors as building blocks for their comprehension of the subject. Those metaphors are not incorrect. They complement the views I have met as a students and teacher of elementary to advanced mathematics. But if mathematics mastery is to be art that is repeatable and reproducible, there is also a need for an operational and logical command of key skills and concepts in high school, say those needed for calculus, in more old-fashioned manner, at least until the metaphors provide a complete path.
1B, Mathematics Curriculum Notes, Chapters 1 to 12
Chapter 11: Primary School Mathematics
-Inductive principles for course design & delivery require a clear description of where and how skills and concepts may rest on earlier ones, so that difficulties may be explained and remedied by looking for what was missed or forgotten in earlier studies.
Mathematics is a demanding subject. All errors in notation and comprehension need to be identified and corrected. In reading, spelling and writing, students have to learn all the letters in the alphabet, not just some. and memorize spelling. Anything less implies difficulty.
Likewise in mathematics, students have to master key skills and concepts, one at a time and one after another. Anything less implies difficulty.
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free. While talking online, we may scribble on Yahoo, MSN,
Skype or
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teachers and tutors in general to import webpages and explore/scribble on
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