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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