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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
More On Constructivism:
Education: Reform in haste, repent at leisure. Top down planning may be in haste if implementation begins before key material and concepts are in place. The business model, make the sale, worry about the implementation later, should not be the model for education reform. Changes in teaching style do not necessary remedy content difficulties.
The logical connection and development of high school mathematics and calculus springs from the minds of many - key individual included. The foregoing defines paths for understanding, individually followed, but developed and refined over decades or centuries. To avoid re-inventing the wheel time and time again, students and teachers need expositions which define and develop skills and concepts clearly and directly. Problem solving in mathematics is enhanced by the identification and mastery of key skills and concepts, and the emphasis of a jigsaw puzzle approaches in which the easiest parts of a puzzle are identified and tackled first. While the ability to construct comprehension directly from hands-on activities is important, the ability to learn from second-hand experience, that summarized in hopefully direct and clear expositions or lessons, is also important. Education may involve a mix of student inquiry plus teacher direction or feedback, with the latter being authoritative as teacher provide evaluation and marks. Student need to learn how to do and reason in a repeatable and reproducible manner. Anything less points to an inconsistent mastery of know-how and know-why. And students need to be corrected. The notion that student notions and answers are valid because they are individually constructed represents a low standard for education. Learning by trial and error is an authentic, realistic and essential part of business, science, technology and decision-making. Where errors are not identified, learning will not occur.
The modern constructivist views of instruction and knowledge need to be consistent with the rule- and pattern-based reason met in mathematics, science and society and they need to acknowledge and address content difficulties and gaps in the earlier expositions of each subject.
The modern constructivist view of education includes some fine calls for realistic, authentic, genuine, hands-on and appealing course design and delivery accompanied by a lack of detail for how, the how is the responsibility of teacher with or without training, and accompanied by a theory of knowledge which is subjective in place of objective. But mathematics, science and technology for better or worse are oriented towards rule and pattern knowledge with repeatable, reproducible and verifiable results. The subjective orientation of constructivist in saying we can gauge student understanding of a discipline what a students does or writes supports anarchy and the end of systematic methods for training and instruction. Instruction is an empirical art in which theories are fine, but repeatable and reproducible improvements are better.
Peer review in mathematic, science and technology works because the results described in journals are verifiable. Modern constructivism in saying knowledge is individual and subjective, and thus not verifiable removes quality control from the peer review process.
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.
| for online sessions by chance when I am
online or appointment when I am off. The first session (saying hello) is
free. While talking online, we may scribble on Yahoo, MSN,
Skype or
whiteboards. The twiddla whiteboards has a built-in browser for students,
teachers and tutors in general to import webpages and explore/scribble on
them together. It also has audio in theory. [Session
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