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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
Words for Teachers
Students need an operational command of fractions, logic, algebra, geometry, trig and calculus. Seeing how to follow multi-step methods to obtain and present results in a repeatable, reproducible, readable and therefore verifiable (right or wrong) manner may be source of confidence in the reliability of mathematics and a source of abilities or a sign of intelligence for further work and studies.
For students with no immediate interest in the know-why, a focus on the practice, an operational command of key skills and concepts may make comprehension later of the know-why easier and more appealing. For high school mathematics and calculus, fraction sense and an efficient command of arithmetic with fractions is more important than full comprehension of why the calculation methods work, but seeing the why, depending on the student, may help with the practice. Logic or chains of reason appear in many places in mathematics. A mix of logic and rote learning may be optimal.
In mathematics, skill and confidence begins with arithmetic methods with repeatable and reproducible results - so answers are right or wrong, and so that student acquire the discipline to follow steps carefully. Drill and practice in whole numbers and fraction arithmetic and meaning (number sense) until second nature is needed in moderation. Explanations why arithmetic methods work may be presented in part as aids to their mastery, where not too complicated nor too alienating for students. The fact that a method works may be sufficient empirically and hence intellectually for many. The further development of mathematics (algebra, logic, geometry, trig, calculus) after arithmetic provides opportunities to emphasize the thinking part of the subject, at which point some, not all, may revisit arithmetic methods to see why they work, but for marking and evaluation, an operational command is sufficient. Tutoring, or checklist approach to skill and comprehension development and tracking for each student, may go further.
In skill and concept based subjects, I would like to see instructors track for each student, which skills and concepts have been mastered and to what level, so that students and teachers have a clearer guide for what needs to be reviewed or learnt. Keeping such a checklist might allow a teacher to say to student, you may skip these question, but you have to do or try those. That may lead to more thought in direction of studies and less work in marking in mathematics or science courses alone and in sequence. That may also provide an objective evaluation of a students skill and concept level.
The thought-based development of applied mathematics present in site pages may stand alone or be seen as platform for further studies in modern mathematics, pure or applied. High school mathematics with its reliance on diagrams and coordinates for its comprehension and development is mixed rather than pure mathematics.
The exposition of mathematics, the introduction of algebra or the shorthand roles of letters and symbols has been confusing in the past for many literate students, skilled and intelligent outside of mathematics. Innovations in site material may make existing mathematics courses easier while setting the stage, trust but verify please, for expositional or content changes in high school mathematics and calculus
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Talking about three skills for algebra and what is a variable may provide a remedy.
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The role of logic in mathematics may be seen more easily if logic ideas are introduced and clarified alone.
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Algebra shocks in calculus can be eased or avoided by re-arranging calculus to put some easier ideas first. Rigour can come later.
The implications or scope of site material grew from just a few ideas to submit to educational authorities to a full, self-contained theory for changing and improving mathematics education, all driven by the inductive principles for instruction and by reports of poor results in high school mathematics. Writing began in 1991 to report and develop further fall 1983 starter lessons for logic, algebra and calculus which had been useful in easing or avoiding difficulties in college classrooms 1983-89, lessons which had been motivated by a sense of incompleteness in the introduction of skills and concepts.
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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