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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
Grouping students according to abilities and their individual cooperation in their own education is out of style. Instead instructor are required to teach multilevel classrooms with an engaging style and engaging content. Mathematical skills and concepts can be employed in many different directions. The general development of critical thinking and problem solving skills provides a principle to follow in but not to dominate instruction. Some students in leaving school early, earlier than desired, might be kept in school by concrete examples of mathematics in society - cost of living, cost of credit and business or shopkeeper arithmetic. Where as for others who plan to continue in school, those concrete examples may be too early. The KISS principle is not applied to mathematics education. Yet it should be.
One way to keep mathematics education focused and even it shorten it, so that too many topics do not overwhelm learning and teaching, is to emphasis the full mastery of arithmetic, logic, algebra, geometry, trig and eventually functions required by a first course in calculus, and to give exercises that illustrate or suggest the utility the required skills in society and technical trades. Courses given before calculus should not be overfilled with topics with topic that may come after a first course in calculus. No context will please all, but keeping the context simple and teaching at a high level, the least amount of mathematics needed for entry into calculus might lessen the pain and be more effective.
Food for thought: The one-size-fits-all criticism of direct instruction in mathematics course design could be a criticism of the removal of streaming or the grouping of students by their level of cooperation in school with education. Without streaming and without focus, requiring longer and longer periods of education could be a form of imprisonment. While we hope that constructivist advocates can provide methods or activities, applications and situations, to engage all students in class, regardless of their knowledge or skill level, the one-size-fits-all method today of keeping students of the same age, but at multiple levels of ability, is a criticism that can be applied to the end of streaming. Streaming should return if only to separate the students who value education from those who do not. Students 14 to 18 who want to work should be allowed, and given a voucher for the completion of high school leaving requirements later, when they have the time and will, when hormones have subsided. The foregoing is food for thought, not a prescription.
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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