Work and Study Tips
How to Build Skills and Confidence
A. Skill has to be seen to believed
B. Domino effect of errors
C. Domino effect of being careful
D. Check work - a must with a caution
E. When and how to correct errors
F. The student teacher tutor feedback loop
G. Written work formats for developing and showing skill
H Jigsaw puzzles and problem solving
H more - Routine to non-routine problem solving
I. Logic and language skills
J. More on written work and showing skill
N Improving Marks on Tests and Finals
L Skills with take home value
M Words to extend arithmetic
N Mathematics - Prepare for College Studies
O On Learning Mathematics and Science
P Exact Arithmetic With Whole Numbers and Fractions
Q How Logic and Proofs extend Show Work Practices
R Why Learn Mathematics Skills
S Adding words to algebra
V Reasons and Motivations for Logic and Mathematics
1 Links to Online Resources Elsewhere Take 1
The tips above reflect ends and values for work and studies.
Site material covers
elements of logic and of high school and college
mathematics from arithmetic to advance calculus. Site material may help in learning, review or revision just before tests or final examinations - the time
when most are the most keen to learn.
If you cannot find a topic you need, try a site keyword search.
Food for thought
In many high schools, the question of why this or that is in a
mathematics course has the answer: Preparation for final
examinations. This answer turns students and teachers alike into
bureaucrats: Ours is but to learn or teach without understanding
why.
"Would you tell me, please, which way I ought to go
from here?"
"That depends a good deal on where you want to get to," said the Cat.
"I don't much care where--" said Alice.
"Then it doesn't matter which way you go," said the Cat.
"--so long as I get SOMEWHERE," Alice added as an explanation.
"Oh, you're sure to do that," said the Cat, "if you only walk long
enough."
(Alice's Adventures in Wonderland, Chapter 6
If you do not care where you are going, if you do not have ends and
values, then any path will do. In instruction, I have had to teach
mathematical topics because questions on them might appear on forthcoming
final examinations. I would have preferred to teach skills and topics to
fill gaps in their know-how of mathematics with take-home value.
Mathematics may be taught to give skills and concepts useful for life
in the street. For that, see existing cnline chapters on logic and
future site pages on application areas: time and date matters, on
money matters, on counting, measuring and figuring, on on maps and
plans and on decision-making (chance) when not all is certain.
Study of the foregoing areas will take time and effort.
In primary school, you may have met mathematics with take-home value
for daily and adult life. And in many primary schools, there is no
guarantee that basic reading, writing and figuring skills are taught. I
have met primary school graduates who cannot figure with fractions
because they were not taught how, and because their teachers and
parents did not know better. Central planning and central control can
lead to substandard practices in education. Central planning and
central control needs to do better. Otherwise, home schooling becomes a
better and stronger choice. If you become a parent, watch for
substandard practices or substandard skill development and try to
remedy or avoid that in the education of your child - good luck.
But in secondary school and the first years of college, mathematics
courses mostly cover skills and concepts required for college programs
in business, commerce, banking, insurance, science, engineering and
technology. Each requires mathematics, some more than others. High
school and college mathematics topics apart from the in above
application areas has long-term value for the practice and theory in
college programs, or for student or employer selection by college
programs. With regrets, most mathematics coursed after primary school
does not have take-home value. They are college oriented with courses
that are not being reserved for weaker students not heading for
college.
Site content may help secondary and college course designers recognize
and include (i) skill which serves actual or potential common needs;
and (ii) skills and concepts which are needed by college programs. Then
the full coverage of (i) by age 14 may provide motivation, context and
even an end for mathematics instruction while preparing for and
overlapping (ii). Food for thought: all students should meet (i)
with observable and verifiable skill mastery vital apart from full
comprehension, because of actual or likely take-home value. After that,
the college oriented mathematics in (ii) is optional.
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For home-tutoring or -schooling, or for schools or colleges
with course content control: Secondary
Mathematics for Ages 11+, A Practical Approach.
May 2012, Composition Starting:
Pre-School and Primary Mathematics - Quantitative Skills, An
Intellectual View, Feedback Welcome:
The 8 Most Popular Site Inlinks
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
Geometry
- maps plans trigonometry vectors
More
Algebra
70
Calculus Starter Lessons
Calculus Lessons Elsewhere:
-
How to Ace Calculus: Street Wise Guide - Mostly
Text.
-
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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