|
YOU are better than YOU think. Show yourself how:
|
-/[]\-
Logic
Mastery Do not leave here without it - Logic mastery will develops critical thinking, improve reading and writing, and give a firmer base for work and studies at many levels. Good luck.
|
-/[]\- After logic, (a) continue reading Three Skills for Algebra, chapters 8 to 14 and do so alongside site area on solving linear2007 Equations ; or (b) see this calculus starter lesson and Volume 3, Why Slopes & More Math, chapters 2 to 6; For online automated help in senior high school maths & calculus, visit quickmath.com For Automatic Calculus and Algebra Help with derivatives, integrals, graphs, linear equations, matrix algebra, visit calc101.com With overlap, each site quickmath & calc101offers a different range of services, some free, some not, all based on webmathematica. Good luck. |
How Letters Appear
Letters appear in geometry to name or locate points and to give the lengths of sides and hieghts in formulas for areas of rectangles and triangles. As a student, you will accept the use of a letter as a length of a side or line segment. The letter than has meaning.
Formulas for perimeters, areas and volumes provide introduce the algebraic role of letters as placeholders for physical or geometric amounts and quantities.
The site area on solving linear equation with and without stick diagrams uses letters to denote the length of a line segment. But the length is unknown. The stick diagram shows how to find the unknown length by adding, subtracting, duplicating and dividing stick diagrams. The stick diagram three column format also introduces the algebraic view of solving linear equations along the diagrams.
The stick diagrams are used here to introduce and build your algebraic writing and reasoning skills and sense. And after seeing and do several examples with the stick diagram method, you should be able to solve linear equations without stick diagrams. Then the algebraic idea of letting a letter stand for an unknown numbers instead of an unknown length will have been understood, we hope. Good luck.
www.whyslopes.com
Mathematics Education Essays, 57 or so
Area Entrance & Hub Ideas for Better Instruction 4 Ways to Improve Reform Theory of Knowledge Peer Review The Trouble With Algebra Course Design and Delivery How Letters Appear Sit Down & Study Modern Education Key Notes and Themes Site Lesson Plans How This Site Differs Site Origins Math & Logic Puzzles Comments on site content.
Words For Instructors Inductive Principles Fairness Principles Apprentices & Masters Three Remarks For a Leaner Curriculum Mixed Maths Curricula Cultivating Intelligence Reason - 3 kinds in maths Logic in Mathematics Science Education Maths Instruction in General Operational View & Values Standards Ends and Values Goals & Unifying Themes Algebra Lesson Plans Algebra, Geometrically Mathematics Curriculum Shifts Teaching Tips - Fractions to Calculus Math Ed Perils Talk the algebra talk Sec I - Fraction Focus Sec II - algebra focus Sec III - Focus on Slopes Maps-Plans-Drawings Math Wall Posters Education, Empirical Art Damage Reversal North American Math Curriculum Managing Reform Essay January 2007 Educational Follies Contructivism Incomplete Missing the Point I Mathematics in Context What and When, A Challenge Grouping Students Teacher Certification Education of Math Ed. Professors Site Eurekas Links Help Me Learn/Teach;
- Algebra
words before symbols - direct & indirect use of formula, numerical versus algebraic solutions - what is a variable (more words)- Arithmetic
- exercises
- with fractions
- videos on primes, lcm, gcm,lcd, square roots etc- Calculus - geometric preview, algebraic preview,
3 study guides,
much more- Complex numbers
-starter lesson with java applet - easy consequences for trig & vectors in the plane- Education
- Empirical Course Design & Delivery- Fractions
- alone
- by rote
- with algebra
- videos
- Functions - introduction
hindsight - composition aka
substitution -- Geometry, Euclidean - Correspondence of triangles, Triangle construction, duplication & Isometry - Failure of ASA & the // line postulate - angle sum in triangles -// grams - Triangle Similarity
- Geometry- Analytic - functions, polynomials, complex numbers, unit circle trigonometry
- Logic
- First Steps -
Symbols in Logic -
Occurrence & Truth Tables - Indirect Reason -Indirect Reason More- Proportionality
- Definition - Direct & Indirect Use - Numerical versus Algebraic Solutions- Real Analysis
- Decimal View of concepts and of proofs- Rules &Patterns in Science, Technology & Society - Pattern Based Reason
- Mathematical Reasoning, empirical, inductive or deductive
- Units
- in rates & slopes & (?) derivatives
- in ratios & proportions - slopes & rates included- Complex Numbers & Vectors & Trig
- trig expression for dot & cross - cosine law