4 Ways to Improve Education Reform
- Respect inductive
principles for course design and delivery.
- Test ideas for reform in optimal and sub-optimal conditions first -
reform in haste, repent at leisure. Reforms like drugs should be tested
before widespread use.
- Provide materials and methods simple to understand and follow as a
lower bound or safety net for teachers parachuted into unfamiliar topics.
Do not assume that teachers are providing instruction within their area
of comfort - an ideal situation, but one is too often absent in
mathematics where two-thirds of instructors in North America, if not
elsewhere, do not regard themselves as skilled and confident in
mathematics.
- For instruction not streamed by ability, for instruction to be
inclusive and for instruction of students with poor attendance, develop
multi-term or multiyear, multilevel modules to favour self-paced
instruction skill and concept mastery. Include enrich material to
slow the more gifted students while everyone else catches.
For instruction, teachers and mathematics education committees need to
proactively collect and review ideas for not wait for
others. Course design and delivery, and approval of materials
or textbooks in secondary and even primary school mathematics
should include university professors of mathematics, so that content gaps,
inconsistencies and material that is not essential, your standard
curriculum pitfalls, are flagged. Good intentions should defer to or
combine with discipline knowledge.
The invention or collection of appetizers and lessons easily
understood and followed in class BY TEACHERS is one way to
make learning and teaching more effective. Some adjustment or
variation will be needed for different cultures, different learning
styles, in which students may be passive to active, cooperative to
resistance, to instruction, voluntary to compelled. Modular course design
may allow instruction to cope with multi-level classrooms and
intermittent attendance. And where instructors may be given teaching
assignments outside their zone of comfort or expertise, textbooks
and modules easily understood and followed by students and teachers could
provide a lower bound for education, and in place of complete confusion
may allow first-time instructors in a discipline to be two pages
ahead of students.
The question of how to develop skills and concepts, so the study of
mathematics and logic seems purposeful and not endless remains
open. Primary school and junior high school mathematics could
provide practical drill and practice on geometric and quantitative
figuring and measuring skills and concepts needed daily life at work, in
the home and in buying and selling, while offering or providing a
thought-based development. But skills and confidence may come from the
mastery through rote or comprehensions of methods which give repeatable,
reproducible and hence verifiable results. The direct and simple
use of formulas, given if not derived, could be part of this wide
ranging, preliminary and practical education. Saying and showing how to
use measurement and mathematical methods in a repeatable and
reproducible, and hence verifiable manner may be designed to help
students who end their studies early while providing an invitation and a
context for further studies. Ease of exposition and mastery would be the
guide. Details how need to be determined.
Hope for benefits, but look for the limitations first in any reform,
and then provide alternatives.
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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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