| ||||||||||||||||||||||||||||||||
| For Better Study Skills |
First Steps in Logic | Arithmetic & Fractions |
| A
Appendices B How to Learn C How to Read D What to do in School and Why E. How to Study Mathematics |
1.
Introduction 2. Implication Rules 3. Chains of Reason 4. Induction (Longer Chains) 5 Knowledge Islands Indirect Logic |
Arithmetic
WebVideos 7 Arithmetic Review Problems See Solving Equations with stick diagrams if your fraction skills and sense need improvement |
| If you plan to study calculus, do the Arithmetic Review Problems and have them corrected by another. Problems like these catch errors that slow or undo too many students entering calculus. Ouch. | ||
Altogether, the logic chapters provide a unique mathematics-free introduction to the direct and indirect definition and rule-based thinking that appeared in Euclid's work a long time ago (2300 years ago)
|
First Steps in Algebra |
||
| 8
The Three Skills 9 First Skill What is a Variables 10 Two More Skills 11 Why Shorthand 12 Shorthand Usage 13 What's Next 14 Compound Interest 15_Solving_Linear_Equations 16 Painless Proofs 17 Pythagoras |
Fractions and Solving Equations with stick diagrams (spring 2005 postscript) - | |
| A.
Letters & Lengths B. Stick Diagrams C. Beyond Sticks D..Almost One E. Binary Systems F. Larger Systems |
Stick
Diagram Examples 2x + 5 = 20 3x + 10 = 32 5a + 16 = 3a+ 24 (½)x + 8 = 24½ (¾)a + 16 = (¼)a+ 24 (¾)q + 17 = 32 |
|
| Stick diagrams give a visual introduction to algebra which develops fraction sense and skills. Try them before or besides chapter 15, Solving Linear Equations, whatever works | ||
| Teachers: Here some algebra lesson plans for the more effective development of the shorthand ways of writing and reasoning. | ||
|
Finite Mathematics |
||
| 21
What's Next 22. Geometric and Arithmetic Sums 23 Summation Notation 24 Investments, Loans, Pensions - Personal Money Calculations 25 Mathematical Induction and Recursion Proofs, Product Notation, & Factorial Notation |
26
What's Next 27 Pronouns in Logic 28 Occurrence Tables 29 Contrapositive 30 Truth Tables 31 Indirect Reason |
Some of this logic chapters may be used in the above treatment of analytic geometry. |
Algebra, Odds & Ends,
Odd and Ends, Essays
|
|
-/[]\- |
|