1. Adice for Parents: Improving or Practicing Speaking and Social Skills

Speaking Skills

Explain to your child, that every object in the home and in the street has a name. In pointing to objects, in your spare moments, you can ask your child to identify or name them. This can be done before or besides lessons on reading and writing. (This is done accidentally while your child is hearing the conversation in your house.) Identification should a game with rewards (a treat, a smile or the word good perhaps, but no penalties).

Once a week, it could be an ongoing game or task to introduce say three or several new words to your child. In this game, you say a word. If your child can say what the word means, you provide a small reward, and if not, you explain it. Playing this game may require a dictionary as an aid, if the game lasts a long-time. Feel free to introduce unexpected words, ones not in use locally or in the present time, or ones for which are several possible meanings. (You may also explain how the meaning of words changes. To be brave today has a noble meaning, but in previous centuries, to be called brave was to be called a fool. Meanings do change.) Note in some school districts, an elementary school teacher who with good intentions introduces new vocabulary weeks or a year before it is scheduled to be introduced may be cautioned or fired. This word game might fill a gap in your child's education.

Speaking and listening skills can also be developed by reading or telling your child or children, a short story, and then asking him or her to summarized it. Around a table with many children, you may ask one or more to summarize or repeat the main points of a story just told or read. Later summaries may improve or corrupt the story. The changes in detail may be most interesting or amusing -- politeness required. The youngest children present may be asked first, or given a chance to improve their stories by giving their summaries after an older individual. After all the summaries, the short story can be read in full, once more yourself or one of the older children. Have fun. Once children have learnt to read and write, this speaking activity should be retained as a family gathering, but variations may be tried. Listeners can write their summaries or notes down before reading them aloud. But the game lies in the presentation of the summaries. Beyond this, game children or those present can be asked to create stories, or repeat others from memory.

The communication of ideas is based on story telling. The story can be fiction, nonfiction or, in a stretch, it can describe how to do this or that. A repertoire of stories, those of others in the first place, provide examples for the development of further stories. Stories provide a second hand experience of this or that real or imagined situation.

Speaking and listening skills may also be improved by asking your children around the dinner table, after supper or before: what happened in school today, what was unusual, what new ideas and words were met and understood, what words or ideas were met and not understood. This questions can be applied to English courses, history courses, science courses and mathematics courses etc. This habit of reporting what has pasted the day should be cultivated or introduced slowly, not suddenly. Each child should be given a chance to speak, and should be listened to, politely.

Again, reporting and summarizing what was met or learnt in school could be and should be introduced and cultivated slowly as a pleasant duty. Negative reactions might require your backing off. With luck, older children may lead the discussion and allow parents to depart. Children or teens from neighboring families could also come together in study groups. Your home could be a one room, supplementary school house. Good luck. (The demands of modern life and TV watching may be a distraction, and meeting once a week instead of everyday may well be necessary.

A. More Arithmetic a must for algebra etc

D. Logic In Mathematics

G. Algebra with Take Home Value

I. Vectors & Functions

Decimal Lesson - Reference
Counting & Addition   (8 lessons)
Comparison to Subtraction (9 lessons)
Multiplication ( 11 lessons)
Long Division (12 lessons)
Decimals and Primes (8 lessons)
-Primes & Composites
-Primes Factorization
-Greatest Common Divisors & Multiples.
-Prime Factorization Aids (Learn how to find factors quickly)
-Prime Factorization Examples
-Counting & Generating. Factors.
-Divisibility Rules and Remainders for Division by 2, 3, 5, 9 and 11.
Integers (12 lessons) Intro to Signed Numbers
Fractions (< 20 lessons)  Essential Skills & Concepts
Ratios & Fractions (3 lessons): Similarities & Differences
Units in calculations Fractions with Units

B. Basic Algebra

Solving Linear Equations
- in one unknown. Intro with stick diagrams?
the normal way & with good nttn. (the nttn that reappears in Gaussian Elimination. |
-in more unknowns: simultaneous equations essentially one unknown. the let algebra do the work view of word problems.
- still in more unknowns: Gaussian Elimination via substitution, by equality or comparison, by operations on equations.

C. More Algebra

Words before symbols: See if U like the lengthy chapters 8 to 12 in Volume 2, Three Skills for Algebra
What is a Variable. The answer here is a simple prequel to the modern mathematics viewpoint.

First, every rule & pattern U meet in math, logic & science will be used forwards and backwards. Get a head start with this theme by reading Chapter 14 in Three Skills for Algebra. Second, in the study of Proportionality Relations (3 dense lessons here) finding the proportionality constant gives an initial backward use of the proportionality formula.

Talking about words before symbols and the forward and backward use of formulas gives words to make algebra simpler & clearer.

If you can not read or write precisely, you will have difficulty in following instructions. One wordy remedy is given by chapters 2 to 5 in Three Skills for Algebra. Where does Logic or a geometric model for reason Appear in Mathematics? The answer lies in Euclidean-Geometry In North America, Euclidean Geometry disappeared from high school mathematics as it was too hard. The light treatment here is a possible remedy.

E. More Geometry

The Pythagorean Theorem. Chapter 17 from in Three Skills for Algebra uses algebra and geometry   to show why the Pythagorean equation for right triangles holds. Its forward and backward use is common exercise.. At a more theoretical level, the Pythagorean theorem leads the discovery that not all lengths can be fractional multiples of a unit length. That geometrically implies a need for and even existence of irrational numbers.
Analytic Geometry: Common Practices with Maps and Plans drawn to scale give coordinate-dependent base for senior high school development of similarity, trig, vectors and straight lines.
Complex Numbers: This lesson on Complex Numbers draws on Euclidean and Analytic geometry. Sbortcuts simplifiy trig identities, the cosine law; and   trig formulas for 2D dot- and cross-products.

F. Logarithms, Exponentials,
Roots & Powers

Logarithms, exponentials, rational and real powers for secondary students. This complete Operational Viewpoint. (Sufficient for the precalculus forward and backward use of compound growth and decay formulas in biology, physics, chemistry, personal finance, and calculus. To learn more, if you study calculus, see chapter 19 of Volume 3, Why Slopes and More.Math

In Volume 2, Three Skills for Algebra, chapters

identify methods useful in money computations, methods needed for calculus. Your teachers or other writer may present the same ideas with greater clarity and detail - A site to do.

H. Polynomial & Quadratics

Analytic Geometry: - Slopes and Lines - Take 1.   Take 2 appears in site section Maps and Plans.   Two views are better than one. I may combine them later. -In my school days, slopes appeared year after year.   This Why Slopes calculus preview on graphs of functions y = f(x) explains why. Enjoy.
Quadratics and Polynomials: - Operations on Polynomials: Meet a light and ultraquick geometric introduction to multiplication, addition and subtraction of polynomials. Then see how the foregoing combine to permit long division of polynomials. Compare Fractions with Units. Enrichment: A Plus: The Geometric introduction here gives or is almost identical to a justification for column methods in decimal arithmetic.
Geometric Derivation of the Quadratic Formula:   The account here gives a starter lesson for the more algebraically harder geometric-free derivation. If you study physics, chemistry or trigonometry, you will need to know about quadratics, their factorization and the quadratic formula.
Technical Value: The study of polynomials high school mathematics has technical value as part of the senior high school mathematics preparation for calculus. This simple account of Why Factor Polynomials   (Chapters 2 to 6 in Volume 3 .Why.Slopes.&.More.Math.) will give a context for the study of polynomials, their factorization, and sign analysis of functions, all in a way that should improve your algebraic thinking and reasoning skills.

Vectors in the Plane (2 simple lessons)
- Navigation with vectors or arrows
- Sum of Motions
- more lessons to be added later.
Operations on movement or vectors along the line and in the plane have value in mathematics in defining and implying the properties of real and complex numbers before the assumption of those properties as axioms. Vectors and their properties appear in physics, its mathematical description and formulation.
- Functions - Forwards & Backwards. Here is a full technical reference (24 lessons) for use in a calculus or precalculus course as needed. In it, the set viewpoint of functions expression of modern pure mathematics. comes from the set-based codification and
In the mathematics education reforms of the 1960s in North America, primary and secondary school mathematics were expressed in terms of sets. That expression has now retreated from primary and secondary school texts. But it still lingers on, and can be very useful, a source of clarity and precision, in the situations where it should be retained: Counting with the aid of sets and functions; the description of functions; the high school account of probability theory; and in the discussion or illustration of ideas in logic.

J. Pre-Calculus Skill Check

- Arithmetic Skill Check. In the calculus courses I taught 1983-89, too many students had weak skills in arithmetic. I would give and carefully correct these exercises to tell students what they needed to review and master.
- All the skills and concepts in Chapters 1 to 24 or Volume 2, Three Skills for Algebra: Look for those you do not understand and fill the gaps. Do so quickly while balancing this advice with your other duties. Good luck.

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Speaking Skills

Help your child or teen learn

Help your child or
teen learn