- Ten Commandments for
Mathematics Teachers
| US, UK and Canadian Mathematics Curriculums, Etc
The UK link below includes all subjects and not just mathematics.
Course or curriculum discussions in one location may and should
influence discussions elsewhere. UK efforts are well-written. The
Quebec English curriculum for mathematics identifies well the
geometric requirements of upper high school instruction.
UK Resources for Education
All Years, Most Subjects. The UK
1996-20000 National Curriculum gives a detailed view of
English, Mathematics, Science, Design and technology,
Information and communication technology, History, Geography, Modern
foreign languages, Art and design, Music, Physical education,
Citizenship, and ???
The material is online in html format and in pdf files. The html
format is well-well organized.
The details of the mathematics curriculum offer a checklist or
attainment levels for what should be covered and when from elementary
school to the last years of high school. This site should be explored
for completeness if you are teaching one of the subjects it mentions. Here
is a reference for standards or course design elsewhere. The treatment
of history is notable - British history no longer call Britain great.
The absence of that pretension is welcome. The UK experience in
mathematics is different from that of the US experience - how should
be determined if you are interested in mathematic course design. A
divergence was present in the 1960's. UK schools in then did not
emphasize the set theoretic, axiomatic development of modern
mathematics.
The UK mathematics curriculum for 1995 was very detailed and
mostly written in plain English with very few platitudes. The 1995
version mentions that the study of the infinite in mathematics gave
the subject a spiritual value. One could also say that mathematics
has a great spiritual value as it becomes a great mystery for most
high school and college graduates. Other than that I did not see the
spirituality.
US Resources for Education
The following links provide detailed checklists for skills and
ideas to be covered in mathematics and/or other subjects.
Identification of what should be covered is more important than when.
What is high school material in one location may be college material
in another.
1. The first 5 years. The Talbot
County Framework page in a two or three page, well-written
table, includes mathematics
framework for preschool to grade 5, one grade or year per column.
Each curriculum item is accompanied by an action to support or reach
it. The resulting path gives a very clear checklist for what should be
covered in Pre-School to Grade 5, and when. Read this first if
you teaching these grades, or preschool. This checklist is close to
providing a script for instruction.
2. Years 6 and 7. The Talbot
County Framework page also also offers a mathematics
framework for grades 6 & 7. This table provides another check
list as well, not yet as clear as the pre-school to grade 5 one. Read
this short item second if you teaching these grade 1 to 8.
3. All Years, Most Subjects. The Massachusetts Department of
Education offers frameworks
for many subjects including mathematics. The Massachusetts August 2000
mathematics framework, is comprehensive for grades 1 to 12.. Read it third if you are
interested in US elementary and high school instruction. It provides a
detailed, well-written checklist for mathematics instruction from
primary school to college. This checklist follows and improves on the
"Standards" of the National Council of
Teachers of Mathematics.
4. Offline, The Mathematical
Association of America, CUPM Panel on Teacher Training, in 1983
published Recommendations for on the Mathematical Preparation of
Teachers, ISBN 0-99385-052-4. The recommendations are still worth
reading. Here CUPM stands for Committee on Undergraduate
Program in Mathematics. Compare or contrast this
reference with more recent efforts.
5. For Better or Worse. The US
National Committee of Teachers of Mathematics has an Illuminations
Website to illustrate it principles
and standards, online from 1989 onward. American Mathematics
Society, Mathematical Association of America, and the Society for
Industrial and Applied Mathematics have all permitted or designated
the US National Council of Teachers of Mathematics to take the lead in
defining what should be taught at the US national level. But so far, I
have found the committee written material of the National Council of
Teachers of Mathematics too wordy, and for the most part, I find
exploration of its principles and standards, a chore and not a
pleasure. That should not be the case.
Postscript: I find the principles and standards rest on pychological hopes and direction
for instruction, and immaterial view of the knowledge. Instead of observable skill development, the principles and standards imply true knowledge (in mathematics)
is a private matter, a product of reflection, located in the mind, a place instructors may not see and judge, with performance on tests (skill testing)
not a reflection of student "true" knowledge uncertain because students minds may vary. However, in daily life the skill and know-how
view of education requires skills and know-how, and hence practical, material knowledge, a distinct from the NCTM true knowledge,
to be seen to be believed, that is to be confirmed or corrected. Contructivist immaterial view of knowledge
echoes the philosohpy of a spiritual retreat in which reflection, not practice, is the path to true enlightment.
Canadian Resources for Education.
1. Offline, The Ontario Curriculum Guideline for Mathematics,
Part 3, Intermediate and Senior Divisions, 1985, is well-written. It
describes well what could or should be mastered in grades 7 to 12.
Compare or contrast it with more recent efforts.
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Teachers & Tutors: Site pages offer better or best practices for providing skills -
simpler than expected & comprehensive but for exercises. For your charges, your duty is to study them alone or in
groups and develop skill building exercises & activities to share. Start now. The effort here is the best I can do.
Others are welcome to refine or exceed it. Please do.
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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