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YOU are better than YOU think. Show
yourself how:
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Logic
chapters 1 to 5 re- appear not in sequence, as is or longer,
in Volume 1A, Pattern Based
Reason, Bon Appetite.
Logic
Mastery
Amazing, Amusing, Amorous, Delicious, Delightful, Edifying,
Strengthening Elixir.
It eases work & learning difficulties Makes the hard easier. Opens eyes.
Leads to greater precision.
in reading and
writing
Logic
mastery makes the hard, easier. Logic
mastery leads to better, stronger and richer comprehension. Logic
mastery improves reading and writing. Logic
mastery ease learning difficulties. Logic
mastery gives a headstart. In sum, logic
mastery will develops critical thinking, improve reading and writing,
and give a firmer base for work and studies at many levels. Good luck.
After logic,
(a) continue reading Three
Skills for Algebra, chapters 8 to 14 and do so alongside site area on solving
liinear Equations ; or (b) see this calculus
starter lesson and Volume 3, Why
Slopes & More Math, chapters 2 to 6;
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Caution: Site advice is approximately
correct, for some circumstances, not all. That leaves room for thought |
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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.
Try the Twiddla
Whiteboard. In principle, it allows
to people to draw and chat together online on a copy of this webpage or a clean
sheet. The chat may be via text or audio. Visit www.twiddla.com
to set up whiteboards to work with the webpage of your choice.
For online automated help in senior high school maths & calculus,
visit quickmath.com For Automatic
Calculus and Algebra Help with derivatives, integrals, graphs, linear equations,
matrix algebra, visit calc101.com
With overlap, each site quickmath
& calc101offers a different range of
services, some free, some not, all based on webmathematica. Good luck.
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Mathematics From
Primary School to College
[ Ages 5 or 6 ] [ Ages 6 or 7 ] [ Ages 7 or 8 ] [ Ages 8 to 9 ] [ Ages 10 to 13 ] [ Age 14 ] [ Where is it going ] (These links also appear in the left
margin)
Setting clear goals, identifying what should be mastered and
testing knowledge of those goals, is the key to good mathematics
education. Parents, teachers and students need logical, tested guides
to what should be learnt and why. Instruction needs to provides steps
small enough so that most (preferably all) can follow alone or with
help.
Warning: If the text and workbooks
provided by school authorities are not clear to parents, they will not be
clear to teachers - the mathematics background of most primary school teaches
and many high school mathematics teachers is often equal or inferior to that
of parents. . Unfortunately, modern theories of
education in English lands appear to be based on subjective psychological or
cognitive theories of knowledge which contradict the essentially objective
rule- and pattern- based view of mathematics held by university mathematics
professors. So there is a division of labour in which professors of
mathematics in leading universities are excluded from math teaching training
and course content decisions at the primary and secondary school level.
So mathematics lessons in secondary school and primary school has become
diluted with subject matter and standards not endorsed or not supervised by
mathematicians. At the primary and secondary level, mathematics lessons may be
given by people with a weak knowledge of mathematics. At the college level,
math-teacher training programs may be led by professors of education whose
technical knowledge of mathematics is less than that recommended by
mathematics societies for high school teachers.
Primary and secondary teachers could buy large-print
math workbooks for grades 1 to 6 (Primary School Mathematics) in duplicate
to post their pages on walls under the title tutor training program
for students to see and review what they should know from present or
earlier studies. Students in difficulty can be asked to explore the posted
material to regain confidence and fill gaps in their knowledge. The JumpMath
books described next are not big-print.
Elementary Mathematics: To learn to
read, write and spell, students need to master the alphabet - learn it and not
forget it. Anything less would lead to difficulties or fear in or of reading,
writing and spelling. Likewise, to learn high school and college
mathematics, and to avoid fears and difficulties,, algebra, geometry, trig and
even calculus, students need to master the following efficiently and fully to
the point of automation, the how with and if necessary without comprehension
of why: addition and times tables, decimal methods for arithmetic; angle,
length and time telling or measurement; fraction skills and sense
besides calculator usage skills. Alone or with help, parents, teachers and
older students, those taking charge of their own education, need to
check mastery, develop the missing ones, or verify the missing
ones are being develop in school.
Toronto JumpMath
Work Books (Grades 3 to 8) for home and school
The jumpMath home
and school mathematics program asserts the following:
One feature
distinguishes our workbooks from regular math textbooks, however: in the
JUMP workbooks, teachers are consistently shown how to help students who
are having trouble moving forward by breaking mathematical concepts and
operations into the most basic elements of understanding and perception
in its Teacher Manual -
Fractions, page 2. The jumpmath
publication page offers a downloadable fraction unit and describes
workbooks for home and school (grades 3 to 8). Copies of the workbooks for
grades 3 and 4 bought for inspection are well-done. The workbooks may
cover more than necessary.
-
The jumpmath program
publication page offers a downloadable fraction unit and describes
workbooks for home and school (grades 3 to 8) - Schools should see the
bulk order prices. Parents should consider chaperoning their children,
grades 3 to 8, through the home version of the workbooks.
The jumpMath program
(created by a mathematician) appears to cover the middle years of primary
and high school instruction well. So I recommend its consideration besides
any other program parents and teachers choose for students in grades 3 to
8 in school or for remedial instruction. See what is what is
best.
Older Site Mateial Questions and activities in
the webpages
[ Ages 5 or 6 ] [ Ages 6 or 7 ] [ Ages 7 or 8 ] [ Ages 8 to 9 ] [ Ages 10 to 13 ] [ Age 14 ] [ Where is it going ]
will allow you to judge the mathematics and logic
skills of your charges in primary school and high school instruction.
A simpler route may be to acquire the jumpmath workbooks for home
schooling (I have seen those for grades 3 and 4) and chaperone your
offspring through them - time and patience required.
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Secondary School Mathematics
The page Where is it going
gives or suggest reasons for high school that seem to have been
forgotten.
Teens and pre-teens need to obtain fraction sense and an efficient command of
operations with fractions and whole number without a calculator. If that
is not done, all further mathematics instruction is sabotage or
suboptimal. The teacher who finds his or her students do not have the
prerequisite for the current course needs to review and consolidate those
prerequisites - not doing so may turn instruction into a formality. The
new site area Solving
Linear Equations with Stick Diagrams and Fractions introduces
algebra while illustrating and reinforcing fraction sense and skills. As parent,
you could take your son or daughter through it carefully.
The ability to add, subtract, multiply and divide fractions whose
denominators and numerators range from 1 to 100 say is sufficient provided
students also have a good command of what is a fraction. That be said,
fraction sense and skill is needed to understand and do algebra beyond being
given a formula and numbers to use in it. The algebraic way of writing and
reasoning needed the further or proper mastery of analytic geometry,
trigonometry and calculus relies on fraction sense and skills. While some
students and teachers unfamilar with the next level in mathematics may object to
or not know the foregoing, the efficient mastery of fraction sense, what they
are, and fraction skills is a must for going further in high school
mathematics. That mastery should be consolidated between ages 10 to 13
say. Anything less slows or stops learning. All topics before students
talk about solving equations may be used to emphasize fractions and allied
concepts: ratios and proportions. The aim of site areas in fractions,
algebra, geometry and so on is to provide students or their teachers and
tutors (parents included) clear directions for understanding and explaining
mathematics and its logic.
Site books (online in full so you do not
have to acquire them) may help some students 14 plus to adult learn
mathematics and logic, and parents guide their children.
The advice offered here is approximately correct, for some
circumstances not all. Pick and choose that which applies to yours.
- Learning takes time and effort. Your child or teen should know that or be
told, especially if you have succeeded in protecting them from worry. Do not
assume he or she knows that learning takes time and effort. Marks in schools
may be too generous to the extent that students do not receive this
message from teachers. I am a skeptic.
- Your charge also needs to be told that notes and work for doing problems,
written on paper, needs to be written precisely. Ideas or work written
incorrectly will be a source of error. For instance, methods for arithmetic
(addition, multiplication, subtraction, and long divisions) rely on numbers
being written in the proper place or column. Imprecision in location or
alignment of numbers is a common source of error due to a change in meaning
or interpretation between writing and reading. Likewise, the algebraic
way of writing and reasoning requires a proper and precise command of
notation, otherwise what is meant or intended at time of writing will not be
misinterpreted a moment or period later at the time of reading or further
reasoning.
- Too many high school and college students not interested in mathematics
believe arithmetic should be left to decimal computations with
electronic calculators. They forget how to do arithmetic by hand met
if not learnt in earlier years. But in algebra and beyond, operations
with fractions appear and they need to be done exactly - the decimal
approximations provided by electronic calculators cannot be used for the
exact derivation of formulas. At the high school and college level,
please check whether or not your son or daughter can add, multiply and
simplify fractions efficiently. You may be surprised, sorry.
- Online help in reading, writing or mathematics has one limitation at the
moment. The written work of students needs to be seen and corrected
repeatedly for errors in presentation and notation. In mathematics
especially, a student may master an idea (almost) without being to write
arithmetic or algebraic calculations precisely and exactly on paper. The
errors here in notation are dangerous. A student may write one thing
while meaning another, and then later read what is written inexactly.
Imprecision in reading what is written is accompanied by an imprecision in
writing mathematical thoughts or calculations on paper. Imprecision in one
implies imprecision in the other. The written work of students needs
to be read and marked carefully, so that imprecision in writing (notation)
is corrected. Here if there are few errors all should be identified, but if
there are many, the most important ones should be identified and some left
uncorrected in order not to discourage a student too much.
[ Ages 5 or 6 ] [ Ages 6 or 7 ] [ Ages 7 or 8 ] [ Ages 8 to 9 ] [ Ages 10 to 13 ] [ Age 14 ] [ Where is it going ] (These links also appear in the left
margin)
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www.whyslopes.com
Help your Child or Teen Learn:
Area Intro
1. Speaking Skills
2. Reading & Writing
3. Preparing for Science
4. Learning Takes Time and Effort
5. Math Books: kids & teens
6. Math Books: teens & adults
7. Readings for Parents
8. Patience Please
9. Who is in Charge
10. Motivation
11. Will to Learn
12. Math K1-20
13. Links For Parents
14. JumpMath WorkBooks
15. Discipline in Schools
Maths for Ages 5+
Ages 5 or 6
Ages 6 or 7
Ages 7 or 8
Ages 8 to 9
Ages 10 to 13
Age 14
Where is it going
D
What to do in School & Why
E.How to Study Mathematics
To read, write and spell, your children need to
learn and memorize the alphabet. Anything less would be absurd. That being
said, learning and using mathematics demands that your children meet key
skills and concepts, and not skip any. Where local schools do not provide the
latter, you need to provide remedies.
Care and Precision: If your child can learn
to follow multi-step methods carefully and precisely in arithmetic, he or she
may do so in other subjects, as well. Get your child or teen, if you
can, to sit down and study. Suggest he or she aim for skill and concept
development and perfection for their own sake, not that of their teachers.
The will to learn is the key to success in
school. Parents do have to be educated to support or guide their
children and teens. What matters more is support for the will to learn, for
children and teens to be told to try to learn and to ask teachers, their
schools or classmates for help and more help, as needed. Teachers and parents
need to push students, help them find the will to learn, teamwork helps.
The main reason and focus for high school
mathematics is or should be preparation for calculus. That requires skill and
knowledge perfection with fractions, algebra, geometry, trig and functions.
Many high school programs do not provide this. Make sure alone or with
help that your children and teens have a good command of
fractions.
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