Entrance Level
Adopt whyslopes.com/search/
for internet searches.
Proper notation & format
makes the hard easier.
Show a student how to learn and that helps one. Show a teacher or tutor how to make skills and concepts easier for students and that helps many.
Miscellaneous
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
What may be learnt and when depends on how skills and concepts are developed. Making the hard easier and clearer will allow earlier & richer development of skills and concepts.
|
YOU are better than YOU think. Show yourself how:
|
-/[]\- |
Help Me Learn/Teach;
- Algebra
words before symbols - direct & indirect use of formula, numerical versus algebraic solutions - what is a variable (more words) - Arithmetic
-new Arithmetic Folder
- 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
Site History and Content
Site reviews below, a subset of more, give a third party views of site development.
-
Math Forum June 1995 Hot Spot: Three Skills For Algebra (a first image of mathematics after arithmetic - why letters or symbols are favored in algebra in place of numbers); Two logic puzzles to show the difference between a one-way and a two-way rule; Painless Theorem Proving; Longer Chains of Reason: What is Mathematical Induction?; Complex numbers Etc. - A geometrical story based on the addition and multiplication of arrows in the plane; Chains of Reason - math-free examples of rule-based reasoning; How Logic or Rule-Based Reason Appears in Math; ...
-
Cornell Theory Center, Fall1995. Several puzzles and short discussions to help students understand algebra and proofs. If you don't like the first one you look at, try another; they're all quite different.
The Cornell Theory Center and the Math Forum provided the first two links to this site.
-
Magellan, the McKinley Internet Directory, 1996: Mathphobics, this site may ease your fears of the subject, perhaps even help you enjoy it. The tone of the little lessons and "appetizers" on math and logic is unintimidating, sometimes funny and very clear. There are a number of different angles offered, and you do not need to follow any linear lesson plan. Just pick and peck. The site also offers some reflections on teaching, so that teachers can not only use the site as part of their lesson, but also learn from it
-
Math Forum News Letter, November 25, 1996 .... mathematics appetizers range over arithmetic review problems, notions of what variables are, skills leading to algebra, painless theorem proving, complex numbers with some trig, the importance of slope (some calculus), a decimal perspective of error control and continuity (more calculus), and renaming the greater than sign (back to algebra). // Advice on how to read, how to learn, why go to school, etc. ... included. The tone is sometimes funny, and the writing is dense, rich, and intriguing. There are reflections on teaching, so these materials can be used in the classroom and as a place for teachers to learn. // ... explanations of mathematical concepts using words and stories are particularly strong. ...
-
Education Planet Newsletter, top math sites, 2001: ... The commentary and online books available at this site provide a very rich guide to mathematical reasoning and high school math to calculus. The emphasis here is on the thinking part of math rather than the actual manipulations themselves. There is also information here for parents as well as teachers. Now you can help your students gain insight into mathematics rather than just helping them memorize formulas.
-
Math
Forum News Letter: Aug, 2001. ... new sections on Complex
Numbers and the Distributive Law for Complex Numbers offer a
short way to reach and explain:
-
trigonometry
-
the Pythagorean theorem
-
trig formulas for dot- and cross-products
-
the cosine law
-
a converse to the Pythagorean Theorem
There are five different ways for learning and teaching complex numbers and trig in site pages.
-
-
The NSDL Scout Report for Mathematics, Engineering, & Technology -- Vol. 1, No. 8 (May 2002) Math resources for both students and teachers are given on this site, spanning the general topics of arithmetic, logic, algebra, calculus, complex numbers, and Euclidean geometry. Lessons and how-tos with clear descriptions of many important concepts provide a good foundation for high school and college level mathematics. There are sample problems that can help students prepare for exams, or teachers can make their own assignments based on the problems. Everything presented on the site is not only educational, but interesting as well. There is certainly plenty of material; however, [criticism] This does not take away from the quality of the information, though.
-
The NSDL Scout Report for Mathematics Engineering and Technology-- Vo. 4, No. 4 (Feb. 2005) [A new] section of the website, offers lesson ideas for teaching linear equations in high school or college. .... The approach uses stick diagrams to solve linear equations because they "provide a concrete or visual context for many of the rules or patterns for solving equations, a context that may develop equation solving skills and confidence." The idea is to build up student confidence in problem solving before presenting any formal algebraic statement of the rule and patterns for solving equations. Links to related [online] chapters ... are also provided.
-
The World-Wide Web Virtual Library Education by Country - Canada, Nov. 2005. Why Slopes: This online classroom offers appetizers and lessons for math from arithmetic to calculus or why slopes; for deductive reason (logic) and critical thinking; and for learning in general. Included here are opinions on the communication of skills and mathematics instruction. The logic appetizers are math free. Each appetizer is different. If one is not to your liking try another. Most are from three books on understanding and explaining math and reason.