Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Building Site Map || Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling, with chapters on Logic and Pattern Based Reason to inform and amuse.

Logic 5 Chapters Arithmetic 10 Steps Algebra 12 Starter Steps & 5 Advanced Steps
Work & Study 23 Tips Geometry 15 Steps Calculus 70 Lessons

Ages 15+: Why study slopes Polynomials Quadratics Why factor polynomials Logarithms Functions
What is similarity Euclidean geometry leanly Coordinates + complex no.s Vectors DC Electric Circuits

Ages 12+: Prime factorization Written work formats Decimal place value Extend arithmetic skills orally
What is a variable 5. Fraction Operations by Raising Terms Solving Linear Equations: Take I Take II


Online Volumes: 1 - Elements of Reason, 2 - 3 Skills For Algebra, 3 - Why Slopes and
More Math
, 1A - Pattern Based Reason, 1B - Skill Development Principles + Troubles

Welcome:Site material may develop critical thinking, improve reading and writing, and build mathematics and pattern based reasoning skills. Online Volumes 1, 1A and 2 give avid readers in school and out the best places to begin.

Teachers & Tutors: This December 2011, 5-phase framework offers a context for mathematics & logic education. Phases 1 to 3 focus on skills with actual or potential local value for adult & daily life. College-oriented phases 5 & 4 focus on calculus & preparation for it. Phases 1 to 4 may also serve trades & professions not dependent on calculus.

Site Review: Math resources ... span ... arithmetic, logic, algebra, calculus, complex numbers, and Euclidean geometry. Lessons and how-tos .... provide a good foundation for high school and college ... mathematics. Read more.

Home < Parent Center << 8 The Effect of Negative Remarks

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Negative Talk May Harm Motivation

In a 1988 junior college mathematics course, I found myself facing a student whose aim in my class to obtain the borderline mark of 60% to pass. In challenging his lack of effort directly and trying to explain why he needed to study mathematics for his future plans to become a police officer, I found that I was the first to confront him on his lack of will and effort and that his mother had said mathematics after arithmetic was a waste of time.

The latter remark is understandable. In course design and delivery reaps what it has sown. For too many years, secondary mathematics in covering mathematics after arithmetic has had technical difficulties in introducing algebra. Secondary mathematics has immersed students in skills and concepts whose presentation when done well may be algebraically and logically correct, but whose presentation is unclear because of a lack of systematic development of algebraic and logical skills. For many students and many of their mathematics teachers, many unversed in mathematics, the sole apparent reason for skill and concept mastery is preparation for the next final examination. Year after year, decade after decade, The latter has left a poor impression of mathematics education on high school leavers and graduates - the parents of today's high school and college students included. So aversion to mathematics may be inherited. Site ideas on emphasizing skills and practices with clearer value for adult and daily life may ease or remove that aversion and lack of context for mathematics education.

For Positive and Active Learnings

Talk to your children and teens. Ask them about their school days. See if they are passive learners - working to rule - doing the least amount possible, or opposing their own instruction. Regardless, encourage your offspring to be positive, independent, self-directed learners, learners actively and deliberately seeking to obtain and perfect skills and knowledge - alone or with help from readings, tutors and teachers. Teachers may meet dozens or hundreds of students each week, and so have not the time nor inclination to be personal tutors. So active cooperation with attention to details, the will to listen and try instead of passive or overt opposition or resistance to education, will all help your charges in school and out.

Your children and teens have decisions to make. Whether to try or not, to cooperate in their own education is one of them. The proper choice may be harder when a teacher is not charming but the decision still has to be made. So talk to your children and teens. Ask them about their school days, and guide them if you can. In raising kids, if you are unlucky, there may be two difficult even stormy periods during the horrible two's and the horrible teen years. Wait for the storms to pass, if you can. Giving your child or teen the will to learn counts more for his or her education than being well-educated yourself. Students with limited gifts or abilities with the will to learn and to keeping trying may go further than student with many gifts. Much depends on will, effort and the chance to study, preferably with clear material.

Do not be Negative - Find a silver lineing.

A teenager planning to become a policeman said he did not work at learning mathematics, that he was doing the least possible (in fact less) to pass, since his mother had told him, mathematics after arithmetic was a waste of time. My late or too late objection to that came as a surprise - no earlier teacher had done that. For students to do better in school, they need parents who value education and say so repeatedly for the sake of motivation, especially when and where immediate take-home value is missing - not self-evident. While I disliked writing essays and book reports as a teen, had difficulty deciding what to writing, I would not today tell any child of mine that reading and writing skills, and understanding the characters in book or play, is unimportant. With the passage of time, I might have acquired the maturity to do well and avoid the misery of my earlier high school days in expressive and creative subjects.

Help your child with Mthematics and Essays

Help your child with homework without always doing it for them. With school work, your objective should be for the child or teen to write as much as possible alone, or with a few kind hints, while you encourage the greatest possible independence. In mathematics, the vertical alignment of equal signs in evaluatio of formulas and arithmetic expressions provides a pattern to follow and encourage. For good work habits, it will help your teenager or pre-teen do and record work in steps that can be seen and checked, and make the domino effects of care and mistakes easier to see and correct.

When you child or teens writes an essay, point out mistakes in spelling and sentence structure. Say when sentences are too long, run on and on, or include too many ideas. While writing that, I fear that the advice is not always not followed in site material. So do as I say, not as I do. Writing essays will be easier for teen or pre-teen if there is a story to tell. In the case of a writing block, ask your son or daughter leading questions: Do they have a story, a chain of reason, a chain of instructional steps to present, or a collection of examples, to present in an organized manner. In writing as in packing a suitcase, the order of packing is not important as long as all is packed. Other times, sequence is important. Further say, if the son or daughter cannot answer the question posed by their teacher, than they should improvise by picking a topic, close or far, to demonstrate and practice their writing and story-telling skills, fictional or not, in a technical or non-techical area. In that the aim is to produce a work of art, fiction being easier and requiring less rigour than non-fiction. If you teen is lucky, his or her teacher may accept a good essay, on topic or close. As a rule of thumb, producing one is better than producing none.

Learning from and Correcting Mistakes - Before Submission

How to limit your help. For the sake of your sons or daughters mark, you or a tutor may help more initially. But eventually, your son or daughter should do more and more. In doing writing for mathematics or for producing an essay, the objective is for your son or daughter to eventually learn how to independently produce so well in correct, well-formated manner. You or tutor may help by identifying errors in form, content and logic well-ahead of the homework or assignment due date. You son or daughter may have to learn that not corrrecting the errors will lead to lower mark.

Remember on tests and final examinations in school, your son or daughter will be alone. So the aim of help from a parent, sibling or tutor should be independence - show how to mathematics and write essays alone, and identify errors small and large. The aim is for your son or daughter to learn from them in order for errors to be caught and corrected before submission and in order for like errors to be avoided in future written work. Good luck.

Postscript: Advice-Summary for Young Writers

Teachers are not interested in what you say or think. They are interest in developing and/or observing skill. You do not have to put your heart into your words - use your head instead: Teachers are interested in how you write: Do your words tell a story or present a theory which others can follow in steps or pieces that other may follow? Are your words presented carefully without spelling and grammatical errors?

You are presenting written work to teachers not only for grades or marks, but also for corrections, to learn where you are making mistakes in content and format. But that learning from mistakes could take place before you hand in your work if you ask others to identify errors, small or large, in your work that you may correct before giving your work to your teacher, and mistake or lack of quality penalized. The reward for this extra attention to detail may be higher marks, justified we hope by the fact that have learnt from correction or feedback of others.

And in essay writing, if you have a mental block for an assigned topic, you have nothing clear to say about it, talk to others to see if you can unblock, and failing that write about another topic to exercise and demonstrate your story or argument telling or development skills, and to exercise demonstrate your spelling and grammatical skills, all in the hope that your instructor kind - preface the essay with words to say you had a writing block. The foregoing advice is more easily followed in writing essays than it is in answer given mathematics questions. That's life.

Secondary Mathematics for Ages 11+, A Practical Approach for home-tutoring or -schooling, or for schools & colleges with local curriculum control. Study how to include site content - its skill development how-TOs and innovations into present or future lesson plans - some reading required.

Road Safety Messages and Questions: When and why should you face traffic when walking along a road or cycle path? Is it a good idea to hang limbs outside of cars etc? What gives more protection in a crash: a car, motorbike or bicycle? See too, the BBC-Belgium story Texting and Driving - texting & the impossible test - the article links to a gruesome utube video on the subject

The Logic of Injustice: How Texas sent an innocent man to his death - The wrong Carlos. Some judgments are irreversible. Procescution: Where and when prosectors play to win rather than for justice, guilt beyond a reasonable doubt goes unrespected due to prosecutors who putting winning first, those innocence before the law may be convicted. Some procescutors offices in continuing to accuse after a pardon due to reasonable doubt or innocent being shown, may sucessfully oppose compensaton for false convictions by asserting a pardon individual is still under suspicion. Then the pardoned individual or the latter's estate is not compensation for years or decade of improper or false imprisonment, or for execution. Site chapters on Logic
and some in Pattern Based Reason may slowly lead to greater precision in reading, applying and writing laws.

May 2012, Composition Starting: Pre-School and Primary Mathematics - Quantitative Skills, An Intellectual View, Feedback Welcome:

The 8 Most Popular Site Inlinks

20 Times Table - the most popular site page - popular pages - unexpected.
Fractions & Ratios - with lesson on raising terms to introduce & justify times, division & comparison as well addition & subtraction
Parent Center - See below
Volume 1, Elements of Reason - Intro to all site books.
What is a Variable - best for ages 13+
Written work formats for Arithmetic and Algebra - a skill method and standard!
Complex Numbers Visually - best for ages 13+
Natural Logs, Exponentials, Powers, Roots

Division of Labour: This site offers advice and directions with pointers to resources elsewhere, if known, when they help or lessen the need to write more.

Parent Center: Help your child or teen learn:

Parent-friendly Work Booklets for ages 3+ to 13 Use these or others to check or build skills. Other booklets are available but these booklets allow parents unsure of themselves in mathematics to help their children. The selection acquired in Canada is published in the USA. So it has a US orientation. In retrospect, the selection shows parents what to check with the booklets or by other ways, the choice is theirs. But in retrospect, the selection does not cover integral and fractions liquid weights and measures - ask the publishers to correct that! For ages 9 to 12 say, parents may compensate by showing boys and girls how to use weights or mass, and further measures in food preparation. Beyond that children may be shown how to measure and calculate angles, lengths and areas [proportional amounts too] directly or by using maps and plans drawns to scale. Learning how to gather and measure all the ingredients, pots and pans for a dish or a meal, along with cleaning up sets the stage for like activities or experiments in science courses, and in developing organizational skills, gives boys and girls a head start. Good luck. At the other extreme, more comprehensive than light, if your motto is McCainian: drill, drill, drill then Toronto mathematician and actor John Mighton's jump math organization has jump math workbooks for at least grades 3 to 8 for at-home and in-school use - training sessions for teachers available. Jump math has been expanding to cover older students. Jump Math Samples: plus Fractions for Grades 3-4 & Grades 5-6 [Read] Free Resources grades 1 to 8 [unread - likely to be good]. and

Mathematics Skills For Ages 3 to 14 - technical!

Skills with take home value - A few ideas

Basic skills include time-date-calendar Matters; money matters; map, plan and scale diagram matters;counting, measuring and figuring; decision making with logic and likelyhood; being careful and being aware of the domino effect of mistakes; reading and writing with precision.

Is your child able to add, subtract and multiply amounts of money, work with fractions, work with clocks and calendars, work with maps and plans, and measure length, weight-mass and volume? Schools may promote your son or daughter without providing basic skills in reading, writing and arithmetic.

Arithmetic and Number Theory Skills

Algebra Starter Lessons

1 Working With Sets
2 Formula Forward Use - Evaluation
3 Solving Linear Equations - Skip first step with students able to solve 1 eqn in 1 unknown.
4 Computation Rules and Function Notation
5 Real Numbers
6 More Less Greater Than Inequalities and Comparison
7 Axioms Logic and Equivalent Equations
8 Unifying Theme For Algebra
9 Proportionality Backwards and Forwards
10 Examples of Algebraic Reasoning
A Origins of Counting and Figuring Methods
B Real Numbers Extrinsic Development


Site coverage of formuala evaluation format, of computation rules and axioms, and of the forward and backward use of formulas and proportionality relations lessens the amount of natural talent needed to understand and explain algebra.

Geometry - maps plans trigonometry vectors

1 Maps Plans Measurement
2 Euclidean Geometry - Constructions + extras
3 Cartesian and Polar Coordinates
4 Lines and Slopes Take 1
5 What is Similarity
6 Trigonometry first steps
7 Complex Numbers
8 Unit-Circle Trigonometry
9 Lines and Slopes Take 2 with tangent function
10 Intersecting Straight Lines and Transversals
11 Parallel Straight Lines and Transversals
12 Function Translating and Rescaling
13 Vectors
14 Degrees to Radians and Radians to Degrees
15 Arc or Inverse Trigonometric Function

Pre-Teen and young teen mastery of skills and practices which should be common with map-plans-diagrams drawn to scale, contour interpretation included, has actual or potential take-home value for daily- and adult-life in solving routine problems. Elevating some practices to principles, axioms or postualates, provides a base for analytic and Euclidean geometry, an analytic view of similarity, and an efficient mastery of trigonometry and complex numbers. Right triangle trigonometry provide an analytic alternative to solving geometric problems by drawing diagrams to scale.

More Algebra

Natural-Logarithms Exponentials Powers Roots
Five Polynomial Operations
Quadratics Geometrically
Functions
5 Factored Polynomial Sign Analysis Examples
Rewriting algebraic substitution as function substitutions

The first topic leads to a full high school level theory for the forward and backward mastery of growth and decay models and for definition, range and domains of radicals, roots and powers. The next two topics make quadratics and polynomials easier to learn and teach. Site coverage of functions turns vertical and horizontal line rules into computation methods for evaluating functions.

70 Calculus Starter Lessons

Calculus Lessons Elsewhere:

  1. How to Ace Calculus: Street Wise Guide - Mostly Text.

  2. Flash Video for Calculus Phobics

They cover basic topics in ways likely to complement your notes, your textbooks and site material. When Goldilocks trespassed in the house of the three bears, she found three bowls of porridge, two not to her liking, and one just right. Different bears have different tastes. As invited guest here and elsewhere, if one or more explanations is not to liking, try another. It may be better or just right.

Unsolicited Advice

Learning to do and high marks if it comes to easy is often deceptive - light rather than deep. For that reason, students with learning difficulties determined not to let it get in their way may go deeper and farther than those with none. High marks, if the come easy, may be deceptive - provide a too light and not a deep mastery. That could have been your problem in secondary school, one that leads to comprehension shock or difficulties in calculus and more generally in the first year of college. Bon Appetite.


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Home < Parent Center << 8 The Effect of Negative Remarks

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Logic-Reason for all
Careful Thinking
Chains of Reason
Mathematical Induction
Responsibility
Bodies-of-Knowledge

Arithmetic - Ages 10+
1. Deciml Place Value - fun
2. Decimals for Tutors
3. Prime Factors - quickly
4. Fractions + Ratios
5. Arith with units - science

Geometry
1 Maps + Plans Use
2 Euclidean Geometry
3 Rct +Polr Coordinates
4 Lines-Slopes [I]
5. What is Similarity
Algebra Starters - the base
1. Better Work Format
2. Solve Linear Eqns
3. Computation Rules
4. Axioms, Item 3 Viewpnt
5. Formulas Backwards
More Algebra
Logarithms-ax & m/nth roots
Five Polynomial Operations
Quadratics Geometrically
Functions || Vectors too
Arith. Skill Check+Answers
Calculus Prep/Preview
What is a Variable
Why study slopes
Why factor polynomials
Complex Numbers
Limits + Continuity

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