Help Your Child or teen Learn

Helping Your Child or Teen Learn

Authority - Use it or Lose it: Parents & teachers need to PRACTICE say no for small things of little consequence to build and maintain authority to say no for larger matters. Help Elsewhere: http://www.bbc.co.uk/schools/parents/

Advice and Directions
for Mathematics Education

General Advice
All Ages - Easiest to Read

Aiming for observable and hence verifiable & correctable mastery of skills and methods gives a tangible, material, concrete goals and pathways for instruction and self-instruction - lean, critical or just in time, as you like. A do-this, do-that approach for instruction from elementary to advance levels with the focus on skill development, one small step at a time, one small step after another, could build confidence and give a viable, accessible, operational command of mathematics and logic at many levels

For each year of secondary, primary and preschool, I bought mathematics booklets to review to understand what skills and concepts should be taught or developed. . For preschool and grades 1 to 8 (ages 3+ to 12, 13 or 14), use of 19 below should easy for most adults to follow and supervise. In general, it easier to acquire the books and use them to check skill mastery than it is to read a list of skill and concept objectives.

Eleven Mathematics Work Booklets for PreSchool and Grades 1 to 3 Three site pages review booklet contents: [Pre-K (ages 3+)] [Kindergarten (ages 4 & 5 say)] [Grades 1 and 2 (ages 5, 6 and 7 say)]

Eight Mathematics Work Booklets Grades 4 to 8 - I have yet to write chapter by chapter reviews of book contents

Use the booklets appropriate for your child's or teen's age and performance. If you have an older child of who has fallen behind because of poor schooling, acquire the books at or below his or her age level, so that he or she can catch up.

If you are pre-school, primary school or junior high school teacher of mathematics, the above books and the examples in them will identify the key skills and concepts you need to test or develop and they provide a progressive path for that development. You may asked to cover further topics in mathematics (graphing, data collections, statistics) but for the sake of your students, the first priority should be the key skill and concepts covered in these booklets for the sake of ordinary or remedial instruction.

Junior High School Arithmetic - What should be taught and how site material may help. Well-done. Immediately Useful.
Junior High School Algebra - What might be taught and how site material may help. Well-done. Immediately Useful.
Junior High School Geometry - Topics or Skill Development Steps for tomorrows mathematics education.
Sets and Probability (Grade 8 plus)

In my estimation, the 12 to 14 year old who masters the grade 7 and 8 level booklets here will have a strong based for the foregoing.

Speaking Skills suggests how to improve the speaking and listening skills of your child.
Reading & Writing offers ideas for the development of these skills.
Preparing for science -Teaching a boy or girl to cook or to follow any multi-step method precisely, in a repeatable and reproducible manner, will help in science and all area of work and study.
Learning Takes Time and Effort: Four Things for a Student to Know. Quote in full of an article from Speaking of Learning that refers back to words at this site, no longer online.
Patience Please. Reflects the inductive idea that learning takes time. If you see a difficulty, you need to identify the source and retreat before it in order to practice skills that restore confidence and then to practice skills that remove the source of the difficulty. Teaching, tutoring or parenting takes time and patience. Good luck. Nothing is certain.
Who is in Charge? For better or worse, you the parent or guardian may be the first and longest term instructor of your child. Do your best

Parents and teachers need to say no for small things of little consequence to build and maintain authority to say no for larger matters. Parental authority: use it or lose it.
Student Motivation Here a discussion of the challenge. Not the solution.

Students with parents who say mathematics mastery is important, or education in general is important, will often have more goals, more will and more staying power in school and college - no guarantees here -but is part of the solution.
Talk to Your Child or Teen. For many, those without learning difficulties, the will to learn is often more important than ability. Encourage the will. That is part of the solution.
Discipline in Schools
Work & Study Ends, Values and Methods. These appear to be missing in schools.
More Work & Study Ends, Values & Methods
Parents Need to Follow & Supervise the Education of their Child or Teen.

If your child falls behind, provide extra help during the school year or during summer vacations. Ask your school for a list of observable skills that it and you should be verify. If there is no list, form one alone or with other parents. If there is no list of observable skills, your child school system has no idea where it is heading. It is lost.

~~Senior High School or First Year College Mathematics~~

~~Each part below may serve as an end or as a base for further instruction.~~

a natural stopping point for students who would like to would end their mathematics, with some topics and skill that have take-home value - serve common need - while a quick view of the role of logic in mathematics. There is more to mathematics than being given a method and data to use in it; and

a base for further studies for students who plan to pursue intermediate or advance studies in mathematics, science, engineering and commerce at an intermediate or advanced level.

The curriculum is written step by step with the two fold aim of providing skills and concepts with take-home value and providing skills needed to study calculus, all in a way that might provide closure for the mathematical studies of some, and a base for a more rigorous treatment.

~~preparation for a light form of calculus.~~

a light form of calculus sufficient as end in itself, or as an
appetizer for those going on to the strong form

Here I assume a calculus teacher can follow the directions.

~~Calculus with proofs~~

~~preparation for calculus with proofs.~~

Calculus at full strength and preparation for it, plus some physics, mechanics and incidentally optimization oriented geometry: conic sections, the further geometry of circles, their tangent lines and their chords.

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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Helping Your Child or Teen Learn

Senior High School or First Year College Mathematics

Help your child or
teen learn