Three Ways to be a Better Student

Appetizers and Lessons for Mathematics and Reason (www.whyslopes.com) Entrance Level \|\|Définition d'une variable \|\| Algèbre \|\| Arithmetique \|\| Logique \|\|La raison basée sur les règles et modelés\|\|
Online Volumes 1, Elements of Reason. 1A. Pattern Based Reason 1B. Math Curriculum Notes 2. Three Skills for Algebra 3. Why Slopes & More Math (Optional Book Orders)	More Site Areas 1. Help Your Child or Teen Learn 2. Solving Linear Equations 3. Fractions Ratios Rates Proportions & Units 4. Euclidean Geometry 5. Analytic Geometry/Functions 6. Number Theory. 7. More Calculus	More Site Areas 8. Complex Numbers 9. Qc Maths Education 10. Secondary IV(?) maths 11. Real Analysis 12. LaTeX2HotEqn: 13. Electric Circuits Etc 14. Français 15. Algebra, Odds & Ends, Etc	More Site Areas 16. Math Education Essays 17. Telling & Working with Time 18. Maps, Plans & Drawings 19. Quantitative Skills for home and work, etc, etc 20. Statistics . ** Means Under-construction. Test the Twiddla Whiteboard
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Identify what you want or need to master.

Sit down and study, test yourself by writing answers in full on paper, and ask for help when you have difficulty.

Show your written work to others - instructors, tutors, fellow students or parents - and ask where it is wrong or can be improved. Others cannot read your mind, but they can see and correct what you write.

Site pages cover many skills and concepts at the senior high school and junior college level mathematics and logic. See what is different. See what is clearer or simpler than what you have seen before.

Suggestion: Start with Volume 2, Three Skills for Algebra. Its wordy logic chapters offer a different way to develop precision reading and writing - two musts forv work and study. Further, wordy algebra chapters 8 to 14 and a wordy postscript what is a variable offer a different path for easing or removing common difficulties.. Arithmetic review questions in chapter 7 test key skills developed in high school and needed in calculus. More postscripts, Short videos in Real Player format with low-bandwidth, review exact calculations with whole numbers, fractions, LCDs, GCDs and primes.

For coming or current calculus studies, see Volume 3, Why Slopes and More Math, chapters 1 to 6, for a Geometric preview (postscript) and skill building algebraic perspective. The algebraic way of writing and reasoning is employed in full strength in calculus in manners students find difficult. When first written, Volume 2, Chapters 1 to 14, and Volume 3, Chapters 1 to 6 plus Chapters 14 to 18 offer a unique perspective or solution. See what works.

A skill and concept is fully mastered only when you know how to explain that mastery or develop it for another. There-in lies your stopping rule for each skill and concept you need or want to master. Online lessons here or elsewhere may help. Good luck.

Suggestion: Start with the logic chapters of Volume 2 above, or read about site books and areas, and other sites, below.

Three Ways to be a Better Instructor

Identify clearly the skills and concepts your students need to master.

Develop or find lessons and lessons plans to clearly and firmly develop those skills and concepts.

Observe student work to correct errors and react to them - when a student or students have difficulty, take the student or students back before the likely source to rebuild skills and confidence, to remove the source and then to proceed.

In my high school days 1966-9, I suspected difficulties in learning & teaching came from steps too large and words missing in the introduction of algebra. I watched carefully for fuller introductions to algebra to appear in my courses and textbooks. None did. Then in fall 1983 as a novice instructor, I invented three lessons three skills for algebra, why slopes and two logic puzzles to make algebra alone & in calculus simpler to understand and explain; to strengthen reading, writing & reasoning; and to hint at the role of logic in mathematics. The usual success of these starter lessons in filling skill and concept gaps for students led to their repetition in classes & tutorial sessions and the puzzle of why they were effective with many but not all. Those lessons and further site material also spring from unifying inductive standards or principles met in 1981 not in mathematics; and from the earlier example of guest speakers, mathematicians and one physicist 1975-80 at McGill University. Those speakers made what was hard, easier, and implied the exposition of mathematics could be questioned. Masters of mathematical induction know how induction in logic and by analogy in instruction may fail due to steps undefined or unreachable.

Site material in 900 pages ranges from new or recycled exposition of key skills and concepts to more theoretical discussion of instruction, methods, ends and evaluation. That being said, writing is an iterative affair. Site material will be useful or very useful, but I am not satisfied with it. There is a possibility and a requirement of setting forth course designs or pathways for instruction to provide clear practical and theoretical ends which build skills and confidence, and prepare for further instruction. The study of mathematics is not endless in time and purpose. There-in would lie a context for inductive standards and principles for instruction. Lessons effective or likely to be effective in the classroom need to be developed and shared systematically and without prejudice. Bon Appetite.

While national curricula and standards may call for communication skills in mathematics, those curricula and standards were written without a knowledge of the first skill for algebra - this site emphasis of the ability to talk about and describe numbers and quantities with words before and then besides symbols. The high level discussion of mathematics education and general principles or directions for instruction is supported in site pages by the details - the low level discussion of what to teach and how.

Suggestion: See Chapters 1 to 14 of Volume 2 and the site areas on solving linear equations, or see the descriptions and appetizers for site books and further site areas below. To learn more, see site ideas for instruction,, lessons and lesson plans included, Also in the English National Curriculum, also see mathematics key stages 3 and 4 and attainment levels 5 to exceptional performance - altogether they describe secondary school level prerequisites for calculus.

Primary School Instructors: For mathematics instruction, year by year, see site area for parents and see site lesson plans for secondary I and II. The advice and lesson plans give discipline based aims for your mathematics lessons. In the English National Curriculum, also see key stages 1 and 2 and attainment levels 1 to 5 for mathematics.