Modularized Rigour in Skill Development
Mathematics can be learnt and taught in a modular manner with a focus on
providing and fine-tuning mechanical rigour in a practice first, theory
second or optional manner. Given a students who can do arithmetic with
decimals and fractions efficiently, the secondary school algebra or
geometry teacher will accept that and have no reason to review arithmetic
that has been mastered in practice. When solutions, derivations or proofs
appear in further mathematics, the main concern is not what a students
thinks, but what a student can do in an observable and correctable manner
in accordance with the rules and methods. The latter provides observable
and verifiable performance standards which parents, students and teachers
may see as right or wrong.
In the principles and standards for school mathematics skill development
advocated here instructors have an obligition to show students how to do
and record work in visible steps for the sake of checking, and in that
try to offer enough explanations for students to be able to do work in a
visible, repeatable and reproducible manner.
Each year of instruction covers several skill development modules. At the
primary school level, learning to count, measure, and figure; learning
about time, date and calendars; learning about money; learning to use and
draw maps, plans and diagrams; learning about chance or likelihood;
learning to solve mechanical or logic puzzles; and learning to about the
domino effect of mistakes altogether covers skills and practices
which are or might be of practical value. Students who learn to figure
need to understand place value. That understanding may help mastery if
not comprehension in full of addition, subtraction, multiplication and
division with decimals. For each arithmetic operation, some students will
follow instructions without needing nor wanting detailed explanation of
how or why the operation works. Others will be uncomfortable without
greater comprehension. Thus arithmetic steps may be mastered by rote
learning, or with full but more likely partical comprehension. The task
of the teacher is to help students to learn to figure with explanation of
why full, partial or absent in accordance with their needs, modulo
the instructors training.
Students may learn mathematics and logic from arithmetic to calculus in a
modular manner. Some modules may be mastered by rote - with sufficient
demonstration and explanation for students to be able to do and record
work in steps that can be seen as done or later for confirmation or
correction. Other modules may be mastered with instructions that
emphasize giving and recording reasons for each step, so that not only
the steps but also their reasions or justification for them may be seen
and checked as well. Including the reasons may be seen as deductive
rigour. But in all arts and disciplines where work is to be done and
record in visible steps for checking, emphasise of doing and recording
provides rigour of the empirical kind for development of skills and
practices.
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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
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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