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 << 7 Student Motivation

[1] [2] [3] [4] [5] [6] [7][8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31]


Student Motivation

Some students study because they do well with their marks or because they like learning. Many more become cynical about the value of education. How do we help them?   

An advisor should not give direct advice. The advisor instead offers open or multi-choice problems for others, interested parties, students, sons or daughters,  to solve.  Then they have a say in what to do.  No one likes to be told. 

 Here are a few questions or problems for your teen to consider.

D What to do in School and Why  
E. How to Study  Mathematics

While some teenagers may skip the terrible teens and remain polite and serious, the terrible teens arrive sooner or later for most. During that period parents can do no right.  And during that period if not before,  school may become less attractive.  Elementary students may be motivated by the notion that school attendance helps them grow-up or mature, but after several years of schooling from ages 6 to 13 say, school loses it appeal.  It is compulsory, parent and teachers may not be say clearly why school is necessary except for bureaucratic need for a high school graduation as a ticket to further studies if not employment. 

Compulsory instructions may seem pointless for some students. The question of why go or why stay does not have a clear nor immediate answer.  The reward if any lies in the future. 

One way to motivate students is to say that studying is a job and to support that view with pay or pocket money for performance and attitude.  That is, students could be given an immediate reward for their effort. (As an instructor, I would not object to informing students that their pay in my class depends on their work habits and work presentation - In the presence of a demanding and rigourous curriculum, students may not see point of the long preparation. Some way to get students to behave in class with motivation would be welcome. 

My subject properly taught can be rather dry despite efforts on my part to lighten the subject and provide a context for it. Kid who lack motivation slow learning for themselves and will sooner or later not cooperate in their own education,. and may even rebel.  

Students in the past and today have been expected to bring their own motivation. That motivation may be inherited from parents.  Students with motivation, regardless of source, will go further than students with out.  The will to learn is important. 

Teachers and school may provide encouragement. Instruction in not leading to definite ends,  but in leading to general ends cannot say to a student in concrete terms why he or she should work at their studies and take those studies seriously.  General statements of the importance of education may lack specifics. So education itself may mean following a dream or path with no definite aims nor ends.  And in those circumstances, loss of interest in school may be a sign of intelligence. Parents and Course Designers need to consider the question of leadership, the question of how to  provide motivation for learning.  

Attempt to provide motivation are provided by the appendices in site volume three skills for algebra on what to do in school and why, and on how to study mathematics and why.  Besides those appendices, parents may give their teens and younger charges a message, namely that mastery of logic and arithmetic (fraction sense) is provides the intelligence needed to follow multi-step methods in many arts and disciplines at school, home and work.  The knowledge that an error in one step makes all that follow wrong or likely to be wrong is a sign of intelligence and application provided by the mastery of logic and arithmetic. 

Postscript November 2011

If your child were to say, there are too many letters in the alphabet to remember, you would explain otherwise. Likewise, if your child or teenager complains mastery of counting, measuring and figuring skills with numbers, maps-plans-diagrams drawn to scale and algebra is pointless, you need to explain otherwise. Site material will describe -today or eventually - writing is an iterative affair - how mastery of arithmetic, algebra, geometry and logic may serve the needs of adult and daily life, and also prepare for college studies.

One may say that mathematics in particular provides a language for the correct and incorrect description of ideas and calculations in business, science, technology, engineering and further mathematical disciplines. Beyond your present knowledge of this language, you need to understand more to see where is its used exactly or not, and to understand the approximations or errors in its use.

Since writing the advice above more thought has been given to the question of context or motivation for mathematics and logic education.

  • There is more context and motivation for primary than secondary education. Primary education in reading, writing and arithmetic has clear value for adult and daily-life. It is practical. Secondary education in mathematics today often emphasizes skills and topics with long-term value for college programs involving calculus or STEM: Science, Technology, Engineering and Mathematics. Many accounting or business activities involve mathematics or statistics for better or worse - insurance, stock market, credit card activites, marketing. But the latter form of secondary mathematics from the first year of secondary schooling to the end is too remote from the practical needs of adult and daily life, serves only the few - 10 to 20% who will succeed in college programs involving calculus and STEM, and does not serve common needs of all. The site general remedy for that in early and mid-secondary schooling is to focus mathematics and logic-language skills and activities with actual or potential value for adult and daily-life before preparation for college programs in calculus & STEM begins in ernest. Then when the latter begins, those skills and practices with even the slightest amount of take-home value for adult or daily life will be put first. Finally, when such skills and practices are exhausted, the remaining pure mathematics topics - those needed for calculus etc - will be covered. The general remedy is flexible - different schools may implement it in different ways. But the general remedy is a prescription for leaving a good impression by putting take-home value first and long-term value secondary, all combined with site steps for simplifying and enriching skill and concept mastery in logic and mathematics. The proof is in the details.

  • In North America and Europe, modern educational pyschology in the form of contructivism and cognitive theory holds that true knowledge is located in the mind apart from observable and material skill development. Because of that teacher training programs and school systems are telling teachers, reflection is more important than observable skill mastery. That contradicts the common assumption that skill has been seen to be believed.

    Because of that school systems may be advocating an immaterial and subjective view of knowledge contrary to the tenets and practices of mathematics and the empirical sciences. Where the latter accept is not all is certain in their useful theories and practices, educational pyschology in the form of constructivism and cognitive theory is saying the only true path to knowledge is through reflection and personal discovery in any manner not subject to peers nor teachers. Thus when your child or teen in school looks for a clear and direction explanation - make life simple for me, teachers following school dictates may try help indirectly and suggest how your child or teen may discover what they want. That year after years is not only tedious, but also problematic. This site refines the art of direct instruction in mathematics and logic by showing how to provide skills and concept directly and clearly - the aim of writing was to fill gaps in the process - make it simpler and clearer for teachers not fully versed in mathematics. However, the newer art of indirect explanation is not fully documented. Post-modern school systems in providing course designs that call for teachers half-trained or unversed in a mathematical discipline to employ the indirect U-discover-it approach and course materials in their instruction are putting dogma before practice. It very good to have students who think, who have discovered skills and practices by themselves, but those students and society need observable skill mastery in an empirical manner far more than they need nebulous, unverified and invisible reflection skills. That lack of attention to skill mastery and its pre-requisites, combined with olde skill development difficulties present in earlier instruction, explains in part how students in "rich" countries may graduate from primary and secondary schools without a strong mastery of reading, writing and arithmetic.

The underlying causes of student difficulty and alienation in course design and delivery will not be corrected in schools overnight. But parents may help at home by providing home-tutoring to complement or replace in-school studies in mathematics and language skills. Site support is not immediate for that. There is a difference between seeing what needs to be done and actually doing it.

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.


Return to Page Top

Home < Parent Center << 7 Student Motivation

[1] [2] [3] [4] [5] [6] [7][8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31]


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

All trademarks and copyrights in this are owned by their respective owners.
Copyright to comments & contributions are owned by the Poster.
The Rest © 1995-2011, by site author, Alan Selby, Ph. D., Montreal,
All Rights Reserved --- Skype or Email to contact.