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Private Instruction in Montreal:
Monitoring and Tutoring for students, alone or in groups. .
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YOU are better than YOU think. Show
yourself how:
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Read logic
chapters 1 to 5 in online volume Three
Skills for Algebra for greater skills & confidence
in work
and study.
Learn to read notes and textbooks
like a lawyer, so that no nuance, no subtlety and no clause escapes
your attention. |
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Logic
chapters 1 to 5 re- appear not in sequence, as is or
longer, in Volume 1A, Pattern
Based Reason, Bon Appetite.
SVP, leave a tip
for the site author.
Thank you.
Logic
Mastery
Amazing, Amusing, Amorous, Delicious, Delightful,
Edifying, Strengthening Elixir.
It eases work & learning difficulties Makes the hard easier. Opens
eyes. Leads to greater precision.
in reading and
writing
Logic
mastery makes the hard, easier. Logic
mastery leads to better, stronger and richer comprehension.
Logic
mastery improves reading and writing. Logic
mastery ease learning difficulties. Logic
mastery gives a headstart. In sum, logic
mastery will develops critical thinking, improve reading and
writing, and give a firmer base for work and studies at many levels. Good
luck.
After logic,
(a) continue reading Three
Skills for Algebra, chapters 8 to 14 and do so alongside site
area on solving
liinear Equations ; or (b) see this calculus
starter lesson and Volume 3, Why
Slopes & More Math, chapters 2 to 6;
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Caution: Site advice is
approximately correct, for some circumstances, not all. That leaves
room for thought |
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What may be learnt and when depends on how
skills and concepts are developed. Making the hard easier and clearer will
allow earlier & richer development of skills and concepts.
Try the Twiddla
Whiteboard. In principle, it
allows to people to draw and chat together online on a copy of this
webpage or a clean sheet. The chat may be via text or audio. Visit www.twiddla.com
to set up whiteboards to work with the webpage of your choice.
For online automated help in senior high school maths & calculus,
visit quickmath.com For
Automatic Calculus and Algebra Help with derivatives, integrals, graphs,
linear equations, matrix algebra, visit calc101.com
With overlap, each site quickmath
& calc101offers a different range
of services, some free, some not, all based on webmathematica. Good luck.
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Area content attempts to decipher and explain
- Quebec government objectives
and
- Quebec government approved and required textbooks
prior to the current
reform. Some of those textbooks are still in use at the secondary IV and V level as
the reform is ongoing while the ongoing reform mentions the previous objective
as a base.
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Quebec Secondary Teacher Certification Farce:
The site author, a 1983 McGill Ph. D. in mathematics
failed a field experience, very last element of a 2003-5 McGill Faculty
of Education, teacher certification B. Ed., program. How follows.
Indecipherable Quebec course documentation and English language course
materials impeded rational lesson planning. There-in lies a farce which any
master of Mathematics in the employ of the Faculty would have duty to
recognize, correct, and even prevent. . However, McGill mathematics
teacher training makes no mention of the nonsense or indecipherability.
Teachers and field supervisors not screened for mathematics & classroom
management methods etc decide whether or not would be instructors are
certified? Finally, an appeal committee had no master of
mathematics on it to recognize the foregoing farce in mathematics teacher
preparation and evaluation. Failure solely due to classroom management
skills would not have been a surprise, but failure due to indecipherable
government document, indecipherable course materials, etc. was. Will McGill
recognize, correct and end the farce?
The rabbit-hole went straight on like a tunnel for some
way and then dipped suddenly down, so suddenly that Alice had not a moment
to think about stopping herself before she found herself falling down what
seemed to be a very deep well. (A quote from Alice in Wonderland by Lewis Carroll.)
Today, there is a reform in Quebec English schools in which
a decade of nonsense in course materials could appear again in material
written for the reform as people who coexisted with the nonsensical
framework for instruction, accept and employ elements of that framework in
course design and course materials development. There-in lies a vicious cycle.
The site author has pending request for the McGill Senate
Advisory Committee to investigate and confirm for the sake of correct, the
lack of adequacy, reliability and depth of the Faculty teacher certification
program for mathematics instruction. There is a farce to expose and
correct. Suspension of the Mathematics Teacher certification program might be
due until the correction is possible. The year 2005 is the end of decade
during which nonsense, gibberish and even
bullshit in course documentation and materials arose on the watch of the
Faculty in contradiction with its mission and DUTY to improve
education, doubly so, given its dominant or elephantine position in the formation of English
Quebec, secondary school instructors.
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Parents who did well in high school or college mathematics should not be embarrassed
by their inability to follow Quebec approved and required secondary II to V
textbooks in English language schools. The words gibberish and nonsense
applies to many elements of the textbooks despite their cloak of mathematical
symbolism and phrases.
The modern mathematics curriculum reform in the 1960's
introduce a major change in course content and instruction which left parents
mystified, Textbooks developed skills and concepts in a hard to follow and new
manner that was still rational and logical while reflecting recent trends in
advance mathematics. Their introduction for the sake of progress (panic
driven by . negated the principle that textbooks in schools should be
understandable to educated parents. Since then changes have been fewer while
the modern mathematics changes of the 1960's have been diluted. That being
said, in the last decade 1996 on prior to the current reforms and associated
textbook changes in Quebec English schools, textbooks for secondary II
to V are difficult to follow not because of their logic, but the due to the
lack of it, due to an incomplete, incoherent or pre-modern development of
skills and concepts at the precalculus, high school mathematics
level.
Parents in Quebec may hope but should not trust that the high
school development of mathematics skills and concepts for their teenage son and
daughters, but past experience 1996-2005 points to the past use of substandard
texts and indecipherable government document that undermines learning and
teaching in Quebec, and may continue to do so at the senior high school where
and while previously approved texts are still in use, may do so in through
the current reform because of continuing influence of substandard textbook
exposition on math teachers and math consultants helping with the current
reform. Parents committees should give copies of course materials employed in
schools to experts in mathematics (Mathematicians, Engineers, Physicists and so
on) and ask for their evaluation. The aim is to avoid a second decade of
substandard course material in Quebec high schools.
This message comes from a 1983 McGill Ph. D. in mathematics
who failed in the McGill Faculty of Education B. Ed. program for teacher
certification in mathematics due to nonsense and gibberish in Quebec government
documentation of it secondary mathematics courses and due to nonsense and
gibberish in government approved and required textbooks for English, Secondary
school mathematics. Since 1990 offline and then online, the site author has
been exploring different paths for developing
skills and concepts (a) to ease or avoid common fears and difficulties - all
should like that; and (b) to provide a fuller explanations - those who
want to understand methods as well as use them will like that. These
site
reviews indicate the extent and scope of his work.
Education Malpractice in Quebec 1997-2005
I read government approved, required and translated textbooks for English Schooling in Quebec, those by Guy
Breton for secondary II to V mathematics instruction, in the hope of
finding a clear and rational development of secondary mathematics. What
I found in between mathematical symbolism and concepts occasionally but
not always clear, with a mix of standard and substandard English, and a
generally hard to follow or incomprehensible development of key skills and
concepts.
For example, the Guy Breton texts for mathematics 436 may be employed in
Quebec English high schools for another year or so. That course has a
been a pre-requisite for the mathematically more able students planning to enter Quebec junior colleges
(CEGEPs) and
study calculus. Yet that text represents incomplete and incoherent
mastery of high school level mathematics. The development of
skills and concepts is confused and confusing. But amazingly that text has
been in service for almost a decade in Quebec English language schools. Its
deployment and service point to a lack of judgment and ability in the
management, design and operation of the Quebec English school system.
The approval of the Guy Breton 436 text, English version, is shocking.
In sum, the government 1990 program for secondary mathematics
education, and the government approved and required textbooks
(English forms) for secondary II to
IV instruction in English Quebec schools 1997-2005 separately and together
provide an unclear, indecipherable, incoherent and nonsensical framework for
secondary mathematics education of all students in public and private English
language schools.
Parents should ask what bureaucratic division of labor between schools,
school commissions, universities and government departments allowed the
foregoing mess and disservice to student to happen in English and similarly
perhaps, in French schools in Quebec.
McGill Faculty of Education
The McGill Faculty of Education has a dominant role in in English Secondary
instruction through its certification of instructors and through its graduates
staffing its own university education positions at McGill, Concordia and Bishops
University. The McGill Faculty of Education should have been a shield
against the aforementioned nonsense in secondary mathematics education.
Students aiming for English, high school instruction in Quebec may
attend McGill or Bishop for teacher certification. McGill University has 1500
in teaching certification programs while Bishop University may have a tenth of
that number. So McGill Faculty of Education dominates English secondary
level teacher certification in Quebec. It website includes a mission
statement to that effect that it has a mission to improve instruction in and
out of Quebec.
The McGill Faculty of Education, if its mission of improving
instruction in Quebec English schools is not tongue in cheek, had a
public duty to explain how a deficient mathematics 436 text was employed
for nearly a decade, and to describe what measures, if any, it took to offset the
damage done by that employment. In the last decade, the education year after
year of high school graduates and high school drop-outs have been slowed or
damaged by the employment of substandard textbooks. Furthermore, teachers not
trained in mathematics but able to deliver mathematics courses with substandard
Guy Breton texts in English schools have been provided a very poor model for
mathematics education. Those teachers need to be retrained, or at least provided
course materials which compensate for the model seen in the last decade.
McGill University should be asked to encourage subject expects in and
OUTSIDE of its Faculty of Education to examine, review and write textbooks for
use in Quebec English, and/or Quebec English schools should be allowed to use
rational course materials and curricula in use in other schools systems -
whatever works. The advent of the CEGEP system in the mid- to late 1960s
and earlier 1970s separated University professors from any immediate observation
of high school graduates and high school programs. Implicit in that was
some quality control with university professors immediately objecting to the
effect of poor practices in secondary schools on their undergraduate students.
But today, university professors meet CEGEP graduates instead of high school
graduates while CEGEP professors lack the standing to review and criticize high
school practices. So subject expert, interaction with secondary and primary
school practices in mathematics, science and humanities has vanished.
University subjects expects need not have the lead in school practices, but they
should have an influence along side that of recent or practicing teachers who
are familiar with students strengths and weaknesses.
The Quebec government needs to invite English and
French speaking experts, say professors of mathematics, physics,
chemistry, English, French, and geography to monitor secondary course
materials for content and diction, logical development and readability
included, and then to help in the content formation of primary and
secondary school teachers. The introduction of CEGEP after 1965
means university professors in their respective fields outside of
education only see above average CEGEP graduates and not ordinary
high school. graduates.
Teacher Formation
Finally, in the formation of students teachers, great care and consideration
should be taken in the supervision of do or die field experiences where student
teachers spend 20 weeks in primary and secondary schools working with host
teachers and university field experience supervisors. Host teachers should
be screened for classroom management abilities and for subject expertise. The
evaluation and training of student teachers by host teacher whose
classroom management abilities and subject expertise are unknown factors
introduces great risk into the evaluation.
Course material in the McGill fall 2005 teaching methodology course I
followed, in a preprint of a paper to be published, indicated that 65%
or so of secondary mathematics instructors in the US are not trained in
mathematics. [To do find the paper and reference it.]. Here in Quebec statistics may be similar. I remember
a Gazette article suggesting 60% of the mathematics teachers in Quebec come
from non-quantitative, non-mathematical disciplines.
Here in Quebec, about two thirds of the mathematics instructors have no
formal training in a mathematical subject, and hence may have poor mathematical
habits with which student teachers in mathematics, student teachers with a
command of calculus, must comply to pass. That is absurd. Similarly, here
in Quebec, the employment of unscreened host teachers without the appointment of
field experience supervisor with subject knowledge adds to the complexity and
absurdity of teacher certification in mathematics with unclear and unreadable
textbooks and incomprehensible government objectives.
Conclusions and Recommendation
Today, there is a reform ongoing in Quebec high schools. The reform is
gradually replacing Quebec high school texts for secondary II to V
mathematics. The quality of the replacements remains to be seen but in
mathematics it stands on or continue a very poor basis.
The Reform stands on a Poor Foundation
The Quebec documentation
for the reform claims to continue previous objectives, but in mathematics those
previous objectives and their implementation were indecipherable - confused in
many parts.
School board consultants are most likely experienced teachers
with good classroom practices, but without a
knowledge of calculus and the standards it sets for high school instruction.
School board consults are most likely experienced teachers who have seen and taught mathematics in a ritualistic manner
- Nothing more is possible given the Quebec course objectives and
approved textbooks of the last decade. The school consultants who
writing the new material are not mathematicians.
School boards should engage for the sake of quality
control and rational course development, senior or retired Professors of
Mathematics with a knowledge of the great variation in mathematics course design
and delivery over time in Quebec and between school systems in and out of
Quebec. The last decade of indicipherable government objectives for secondary
mathematics and substandard texts should not be the model for school board
consultants and further producers of course texts and material in the current
reform.
A Note to First Nations in Quebec
First nations
(aboriginal communities) in Quebec who attempt to follow the Quebec
curriculum as is in a first language form are compounding difficulties, not
replacing them. First nations in Quebec should seek an alternative - look for
an educational system elsewhere that has successful tackled similar
problems. First nations in Quebec should ask University subject experts
outside of Quebec (University of Toronto may suffice) to evaluate the Quebec
curricula and its materials and to say whether or not, the skills and
concepts are developed in a clear and sensible manner for youth, first nation
or not. There-in lies a great urgency. If Quebec curriculum and course
materials is inappropriate for students who are not first nation, the
curriculum and course materials are also inappropriate for first nation
students.
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www.whyslopes.com
Notes on Qc Math Education
Road
Safety Message (Online here in 1995, a decade before the Quebec Government
advocated in its)
Area Intro and Entrance
Old Site Entrance
Copy Right Matters
Curriculum Cuts
Intermediate Objectives
Links
MEQ Objectives
Objectives, Check lists, Suggestions and Book Reviews
for Quebec Sec I to V Mathematics. (out of date)
Area Intro and Entrance
116 Objectives
116 Check List
116 Suggestions
216 Objectives
216 Check List
216 Suggestions
314 Objectives
314 Check List
314 Suggestions
416 Objectives
416 Check List
416 Suggestions
436 Objectives
436 Checklist
436 Suggestions
436 Book Reviews
514 Objectives
514 Suggestions
514 Book Reviews
536 Objectives
536 Suggestions
536 Book Reviews
Seeing the past may help us with the present and future
BBC Link: Teacher
Conference to Give Worst Examples of Edu-Babble.
Lesson Plans for Secondary mathematics
Secondary
I - fractions & allied concepts (decimals, percentages) -
support for maths 116
Secondary
II - Algebra (arithmetic versus algebraic methods, backward use of
formulas and proportionality equations) - support
for maths 216
Secondary
IV - Functions to Trig & Statistics - support for maths 436
[Algebra
Lesson Notes - All levels]
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