Help for Home-Tutoring and Home-Schooling
At the elementary school level, parents may choose amony many approaches
to providing basic skills. Some parents may buy exercise booklets to
provide a path for to check and develop skills on weekends and school
vacations. With or without such booklets, some parents may continuously
watch for teachable moments and activities that provide an opportunity in
context to build figuring and reasoning skills of value for adult and
daily life. In general, a parent with a good base in primary and high
school mathematics may be informal and formal lessons monitor and provide
a good mastery basic logic and quantitative skills and practices. At
home, unlike in large classrooms, one to one attention from a parent or
tutor may provide a quicker and more efficient command of skills and
concepts in many subjects. Indeed, three hours of home tutoring or
instruction may be the equal of six hours in school because at home the
needs of the one, the child, is not lost among the needs of the many.
Before the centralization of educational authority, different schools or
school district may choose or design their own courses and textbooks. The
absence of central standards implied great freedom and great variability.
In that, the local professional judgement of schools and teachers had a
chance to thrive and/or be throttled. Today, centralization of school
authorities leads to common curricula and common textbooks. The latter
may be designed and choosen by committee in accordance to commond
standards or common objectives, those provided by education committees.
At the primary and secondary school level, too many cooks spoil the
broth. Committees decide what is correct or not. With this, the
professional duty of schools and teachers is to follow the party-line,
the committee line, be that with or contrary to their own judgment. And
committees today may be composed of young or long-serving instructors who
have not seen practices outside their own school system.
For example, in Quebec mathematics education, mathematics mastery by
rote is so well-established that school teachers on becoming
mathematics committe members or school mathematics consultants will not
have seen anything else. In Quebec mathematics education, I would be
extremely surprised if rote learning of mathematics endured for another
two to four decades.
With centralization, educational theories of what to cover, how and why
need only influence a few in order to become dominant and then permanent.
Presently, educational pyschology of the constructivist form say "true
knowledge" is a product of personal experience and reflection, located in
the mind and beyond the reach or testing and correction of others,
teacher included. Educational pyschology further holds that mastery of
given skills and practices is a form of rote learning. There many be an
element of truth in the latter. Many skills and practices in daily and
adult life are useful without our full comprehension of how and why they
work. The operation of electrical and mechanical appliance is often
hidden out of sight behind walls and inside boxes, so the inner
mechanisms of how and why they work is not seen. Only minimal skill and
comprehension is needed for their operation. That being said, in material
arts and disciplines such as cooking, cloth-making, carpentry, metalwork,
electrical work, car-driving at one level, and such as mathematics and
science at another level, mastery of skill and practices have to be seen
to be believed. And what can be seen can be observed and judged. The
notion that true knowledge is a located in the mind, a private matter,
apart from the correction of others, echoes the notion that religion and
spiritual matters are private matters. However, in this material world,
education needs to provide observable and verifiable mastery of skills
and practices, concepts exposition included, for that mastery to be seen,
shared and defined. Site material may provide food for reflection or
thought, but site material also provides or offers steps, ends and values
for observable and verifiable skill and concept development in
mathematics and logic.
The Site Five-Phase Framework
The site, December 2011, five-phased framework for mathematics and
logic-skill development is unique and original, not in all, but in many
of its elements. It is written in plain language that a parent or adult
may follow with a basic command of primary and secondary mathematics. By
fall 2007, I had addressed all the technical issues or barriers that
faced mathematics skill development in the best possible way that I could
see. Better skill development practices amy exist elsewhere. If you find
them, please share them. That being said, the issue of why provide or
develop skills and concepts remained. The site five-phase framework
provides an answer. It attempts to serve multiple ends and values,
consistently, in order to provide context and motivation. Primary or
basic school level mathematic education today generally leaves a good
impression on adults and students. Basic skills and practice mastery
serve common needs of daily and adult life. The first three phases
attempt to provide and leave a good impression of mathematics and logic
by collecting and putting first those skills and practices in arithmetic,
logic, geometry and algebra - algebra upto formula use - that have clear
take-home value for adult or daily life, or some potential value worth
mentioning without exxagerating too much.
The main aim is to leave a good impression. The secondary aim is to
prepare students for further more technical studies in mathematics and/or
logic with less take-home value for adult or daily life, but still
required by to trades and professions not needing calculus; or still
needed by calculus and/or calculus-based or calculus-requiring college
programs.
Site technical steps and framework may be useful for home-tutoring and home-schooling
because the technical steps hope to represent best practices for skill devevelopment,
preparation for calculus being the aim, while the framework provides a larger
context. In composing the steps and the framework, I was concerned about
departing from the existing logical structure of modern mathematics programs
in secondary schools. However, with half the mathematics teachers in Canada
and North America not being versed in mathematics nor a quantitative discipline,
the steps and framework together do not imply any loss of rigour. Indeed,
they may imply a gain, both empirically in terms of skill mastery and theorectically
in terms of a unified and more accessible development of skills and concepts.
Ideally, earlier users or adopters will have a mastery of
calculus or mathematics enough to recognize any flaws and enough to fill
in any gaps.
Framework completion signals a solution to the question of how to
provide context and motivation. But writing is an iterative matter.
The polishing of site methods for skill and concept development was put on hold or at least delayed by
reflection about ends and values. With the ends and values provided by the framework,
polishing and further completion of site steps will begin.
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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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