Math Ed Perils

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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, shopping and work 20. Statistics Useful, or Not. Test the Twiddla Whiteboard
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Mathematics Education Perils

Improper notation in mathematics points to and leads to difficulties. If your teacher solves equations ¾ = (¼)x by writing =3 besides the x, transfer to another class. Proper notation allows you to record, develop and report arithmetic and algebraic ideas in writing instead of in your head. If you cannot write mathematics properly, your mathematics education is at risk.

A) Arithmetic Troubles. People have difficulty in mathematics due to a poor command of arithmetic - See these arithmetic problems with hints of algebra. If you have trouble with them see the RealPlayer webvideos in Three Skills for Algebra. For further help leave this site to explore aaamath. and Purplemath carefully and then return. the following Math League Help Topics (help from another Ph. D in math for grades 4 to 8) provide more site exits.

|| Whole numbers & their basic properties || Decimals, whole numbers & exponents || Using data and statistics || Fractions || Geometry || Ratio and proportion || Percent and probability || Integers || Metric units & measurement || Introduction to algebra || Positive & negative numbers || (help topics here go beyond arithmetic, and may be useful by themselves or with site coverage of similar topics).

Novices: The ability to do arithmetic with whole numbers and fractions not in your head but on paper efficiently and written with proper notation is needed in algebra, geometry, trig and probability. Mastery of fractions and radical without a calculator may not be useful in daily life but it is required for further learning in mathematics. Old curriculums in mathematics said mastery of arithmetic was needed for algebra. But today requiring less points to folly in mathematics instruction with many victims - high marks in mathematics courses where arithmetic skills are not developed mislead students and lead to to remedial mathematics courses for many first year students in North American colleges and universities.

Arithmetic skills should lead to unique results - In arithmetic, if you regularly obtain different results than others then your arithmetic skills need urgent repair.

B) Algebra Troubles. Intelligent people have difficulty with algebraic reason, the shorthand roles of letters and symbols in mathematics, due to awkward or absence explanations - too much is assumed and not enough is explained.

The following site pages offer a remedy which requires arithmetic skills slowly and not suddenly - so student weak in arithmetic may follow most immediately.

Logic Chapters (3 Chains of Reason 4 Longer Chains 2 Logic Puzzles 5 Knowledge Islands) Algebra Chapters ( 8 Three Skills for Algebra 9 The First Skill 10.Two.More.Skills 11 Why Shorthand) Essay: What is a Variable Algebra Chapter: 14, Compound Interest, Arithmetic Skills (Problems & More Problems, Solving Linear Equations) Algebra Chapters (Solving linear Equation - a second go, 16 Painless Theorem Proving 17 Pythagorean Theorem - Chinese Square Proof)

The remedy begins with logic chapters to test or develop reading, writing and study skills. Strong reading and writing are needed in mathematics and for learning in general. The remedy continues with lessons and insights not found elsewhere to provide a fuller and clearer view of algebra. The First Skill for algebra and the essay What is a Variable offer a simpler and clearer ways to understand not only symbols but also words in mathematics from arithmetic to calculus and beyond. Remember: Fraction sense (comprehension) and arithmetic with fractions is needed for algebra.

C) Calculus Troubles - Students starting calculus often have difficulties with algebra, arithmetic and logic skills. Calculus courses may compound difficulties by demanding not only well developed arithmetic skills, but also algebraic ways of writing and reasoning at full strength too quickly. Site links and site pages point to remedies to ease or avoid difficulties, besides further topics to enrich skills and knowledge.

Site pages on algebra, arithmetic, logic, better learning in general, reason, theorem proving and complex numbers offer appetizers and lessons that may be added to the start or middle of calculus to ease or avoid perils. Some may be met before calculus to provide a context for slopes and polynomials. All gradually introduce the full strength role of algebra in elementary to advance topics in a ways that may avoid difficulties and enrich knowledge.

Calculus is the subject of slope related computations, direct or reversed, along with interpretations and applications. Many formulas for perimeters, areas and volumes met before calculus can be justified by slope (a.k.a derivative) computations, direct and reversed.