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Quebec High School Mathematics Education (English Version of)
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116 Textbooks
116 Objectives
116 Check List
116 Suggestions
216 Objectives
216 Check List
216 Book Review
216 Nonsense or BullShit
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
436 Nonsense in
514 Objectives
514 Suggestions
514 Book Reviews
536 Objectives
536 Suggestions
536 Book Reviews
More Links:
D
What to do in School & Why
E.How to Study Mathematics
Area pages represent an effort to follow and understand the objectives of the
1997-2005, the prior reform, and the
text books required and used 1997-2005. In retrospect, the objectives and texts
in question
are too incoherent, too full of nonsense, for rational comprehension and for
service as a base for the current reform. A farce is a farce,
is a farce
| | Quebec Mathematics Education
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I, Alan Selby, a 1983
McGill Ph. D in mathematics, returned to the university to
enroll in a McGill University instructor certification
program 2003-5 that would have allowed me to teach at the
high school level. In spring 2005, I failed the program.
The failure was not due to classroom management - I would not have
been too surprised by that. But the failure was due to the
then, if not continuing, indecipherable nature of course material
(high school level) and to the employment of teaching practice
supervisors without training in mathematics and the use of host
teachers whose background in mathematics was not screened to make
pass-fail judgments. The university Faculty of
Education coexisted with nonsense in course materials for a
decade, and did nothing to address to forestall or lessen the
effect on youth education. It allowed that nonsense to serve as a
base for the evaluation of would-be mathematics teachers by host
teaches and teaching practice supervisor not screened for
competence in mathematics. I would like an apology from the
University and a correction or two of the foregoing
situation.
University members may forward the
foregoing allegations to their Senate Advisory Committee for
processing, and also determine why it did not process my fall 2007
statement of them. In fall 2008, the McGill University
admin wrote that my allegations were inappropriate, and so
worthy of further processing. In and outside of Quebec,
mathematics education has a reputation of being hard. But in
English Quebec schools, nonsense in course materials coupled with
teachers untrained in mathematics, who have learnt to give courses
couple with nonsense in course material did not help.
Anatomy of Quebec's Maths Education Disaster
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The Quebec documentation of its
secondary mathematics objectives for the 1990's reform,
implemented 1997 onward, and being replaced a decade later by
new reform, is incomplete and includes indecipherable
parts. The program consists of generalities and
objectives prescribe in an unclear or sphagetti like manner,
with no clear rhyme nor reason. With a 1983 doctorate in
mathematics from McGill University, I could not fully decipher
what the objectives said, nor I rewrite them to clarify them
to make them clear. The Faculty of Education of McGill and
school of Education at Bishop University, as the only two
places in Quebec for with secondary level mathematics teacher
certification programs should have seen the difficulties and
addressed them. Why not needs to explained.
-
Quebec current reform in
secondary mathematics says it continues the objectives of the
previous reform. That means the current reform is
standing on quicksand. It lacks a firm foundation. The blind
are leading the blind.
-
The Quebec government approved
and required Guy Breton textbooks, poorly translated from
French into stilted English in secondary II to V mathematics
in provincially funded secondary schools - that is, all
secondary school except for the truly independent ones. Those
textbooks are full of recognizable terms, symbols and
concepts, incoherently organized in a sequence that I as a
mathematician cannot always follow, and where understandable,
would not sanction. The textbooks provide a primitive,
backward account of mathematics that no English nor French
Professor of Mathematics or Mathematics Education worth their
salt would approve or support. Nonsense and bullshit in
the secondary II and IV textbooks is identified below.
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The design level of the
education pyramid in Quebec, the government documentation and
approved English texts were unclear, unreliable and full of
incomprehensible babble. But the delivery level has its
difficulties as well. Two-thirds of the math instructors in
Quebec schools do not have a mathematics or quantitative
background at all, and most - even the teachers of senior high
school mathematics - do not have a mastery of calculus.
Thus classroom delivery was based on an incomplete mastery of
mathematics combined with incomplete textbooks and unclear
course designs. That may be coupled with great variation
in final examinations in mathematics from too easy to too
hard. Prior to the current reform, mathematics education
design, delivery and testing was flawed. But final
examination practices, even though greatly variable, implied
course content and implied to both teachers and students what
to include in course delivery and studies for them. Incoming
instructors from afar, well-trained in mathematics, cannot
rely on government documentation past and present to determine
course content. Preparation for finals provide the only guide
even though that be against the nominal principles of past and
current reform.
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The current program in Quebec
mathematics is flying by the seat of its pants. New
textbooks clearer and far better written are being introduced
- I have seen only the secondary III texts. But the new course
material despite better diction and greater clarity still
suffer from the lack of clarity, an effective vacuum, in
Government course definitions and guidelines - the
intermingling of present and past reforms. The
course materials also suffer from the continuation of recent
traditions and practices, those engendered by the previous
reform, minus I hope some of the obvious nonsense (cul de
sacs) in the previous course materials. It should be a
simple matter for English language school boards in Quebec,
given their large budgets, to engage a professor of
mathematics or two, to review all elements of the primary and
secondary mathematics program for logical consistency,
completeness and clear ends, and in their
absence provide
them.
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The past and current reform are
based on a subjective theory of knowledge in which testing is
considered to be an unreliable part of skills and concept
development, and in which anything goes as the minds of
students are not readable. But subjective theories of
knowledge are inconsistent with arts and disciplines -
mathematics and science at the youth and college level, and
law at the college level - which strive for objectivity based
on the study and mastery of methods and conventions for for
arriving at results in a repeatable and reproducible
manner, visible and correctable if need-be. Where modern
mathematics and science were proud of their progress to
objectivity, subjective theories of education in fashion
since the 1990s walk in the opposite direction. There-in lies
an inconsistency which further undermines mathematics
education while explaining in part the state of government
course design directions. Critical path analysis of
course design and delivery practices, material included,
for a subject expert in mathematics or science while
subjective theories of learning and cognition prohibit
objectivity or striving for it in education. Oops.
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Page Contents
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How
to Help your child/teen in Quebec English Schools
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Guiding
or Shaping the Current Reforms
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Nonsense
in Government Objectives and Government Approved and Required Texts (Pre-reform)
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Advice for
First Nations in Quebec -
The previous mathematics educations reforms in the 1990s signed
by led to course objectives for Quebec secondary
mathematics in general and English versions of mathematics textbooks for
secondary II to V which I would classify as incomprehensible or nonsensical in
large part. The current reform claims to be continuous with the previous
practices, the definition of which unclear. The lack of clearity appears
to be point of continuity. While the replacement texts are likely to be better written and
clearer, there are fundamental flaws in Quebec English school
mathematics course design and delivery likely to continue.
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The Quebec mathematics education program is flawed, and not
subject to critical review or critical path analysis by content experts, namely Professors of mathematics
in universities here in Quebec and elsewhere.
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Standards for for mathematics education in English
Quebec High schools was set 1997-2005 by indecipherable government
course objectives (both languages) and incoherent or indecipherable
mathematics textbooks, the use of which is being phased out in English
schools. Did the McGill Faculty of Education see and reacted to the
foregoing problems 1997 onward? I
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Teacher Certification practices in Quebec are unreliable
if the practice of using unscreened teachers etc is common. In North
American universities, there are is no guarantee that a professor of
mathematics education has an advanced knowledge of mathematics - a knowledge
of what is required to learn and teach calculus or the senior high school
mathematics it requires. So there is no guarantee that teacher
certification programs in mathematics education will provide student
teachers with models for instruction better than just seen in their high
school days. Professors in charge of math teacher
formation need to clearly and deliberate provide examples and models of best
practices., and beyond that identify flaws in existing practices and
materials. The transcripts of Quebec Professors of Mathematics
education to show what level have they mastered mathematics, need to
be put in the public domain.
Send your teen or child to a school which does not follow
the Quebec Mathematics Curriculum if you can afford it. Less
expensive options follow below.
Be a Skeptic -
Defend your Child/Teen's Education - Monitor it. Talk
to other parents about what standards you should set for your child's
education in primary school in mathematics, reading and writing.
Two heads or several may be better than one.
In primary and secondary mathematics education, there is no
certainty that basic skills in arithmetic onward will be develop in
schools. So parents have to hope for that development, but also position
themselves to take charge of their child or teen's mathematics education
if schools do not deliver, or if there is confusion in course design and
delivery. If a mathematics course includes topics not seen before,
ask a neighbor or a family member, near or far, with a knowledge of
mathematics or a family doctor to view and judge the qualify of
mathematics texts and notes your child or teen meets or gets in school.
If an individual with advanced education in medicine, accounting,
engineering or science (the list could go on) does not understand what is
being taught in school, be alarmed and raise your concerns with other
parents, and if possible with university experts (Professors outside of
education) in mathematics or another discipline at hand.
Skeptism is a must. The writers of textbooks and course
materials for primary and secondary courses may put theories of style in
skill and concept development and verification, styles that may exclude
verification, before content matters and knowledge. Whence dated
or misleading or incoherent views of a subject may appear in textbooks.
Be a skeptic to guard against and to be on watch for the latter, so that
it can corrected.
Adopt a Subject or Discipline Viewpoint of Education
If a art or discipline is worth meeting year after year in school,
then respect for the methods and values of that art or discipline are
also required. Anything less pay lip service to education in that
discipline.
Where the student of carpentry cuts, carves and binds wood to show
skill, the mathematics student writes to show skill in
an observable hands-on manner. Respect for and use of the
phrase "show me your work, what you have written" is key to
proof of progress and correction. Otherwise, student progress
will be invisible and unchecked.
In the martial arts, students expect to practice basic moves and then
more complicated ones, one at a time and one after another. Just as
students understand that the alphabet need to met and mastered for the
sake of spelling, reading and writing, they need to understand that
arithmetic, algebra and geometry need to be mastered to face and solve
routine problems in daily life at home and at work. Before we ask
students to think out of the box, to invent new methods for solving
problems, we should teach them the routine methods for working with
routine or common problems in a way that develop the self-discipline need
to learn and follow steps carefully and precisely. Focus on the basics.
Focus on what is feasible. There most students and most instructors in
primary school and junior high school, mathematics should be kept simple
and consist of figuring skills with numbers and geometry that are easily
mastered and repeated with verifiable results.
Binders and Documentation of Learning
Encourage or require your son or daughter to keep a mathematics note
and work binders in each year of school, and collect them at them at each
year to document his or her level of comprehension, and if you have
younger kids, to have an aid and a reference for them and yourself to
consult.
If you have knowledge of high school mathematics, look through the
binder and protest whenever its content does not make sense to you or when
the work is not neatly done. Tell your child or teen that the
binders have to include neat copies of each type of question, example and
problem met in their mathematics classes with answers written clearly and
full, so that you can observe their progress. The binders may
include work marked by teachers or tutors with corrections.
Give your child or teen the job of keeping notes, of
documenting what they meet in mathematics in a manner that proves mastery
to you or another you have asked to help in the monitoring of his or her
education. Students 6 to 14 should show progress in arithmetic and
geometry. Students 13 to 17 should show progress in algebra as well.
Tell your child or teen that skills met one year must be kept and
maintained. The child or teen who says "I Learnt
fractions last year, I do not need them this year" is more trouble
than he or she knows.
Hope but verify the quality of education of your son or daughter
If your son or daughter attends a school, in which math teachers and
guidance counselors do not know and hence do not emphasize the full
strength mastery of arithmetic, algebra and geometry to the strengths and
standards implied by calculus, take charge of the education of your
son or daughter. Pay a undergraduate student strong in
mathematics and science to cover and verify the skills and concepts in
mathematics, one at a time, one after another. Require
you teen to keep a binder full of written work that demonstrates this
mastery to yourself and others.. Also instruct or reward ( pay) your
son or daughter to cooperate with the tutor, and to produce the
written work necessary and well-formatted in accordance with calculus
implied standards. The work required is dry and boring, but the pay
will be necessary if your son or daughter would otherwise lack the initial
motivation to do the necessary work in a written manner that demonstrate
progress or reveals weakness. In mathematics education, the
reluctant to do written work correctly points to difficulties that need to
be identified and corrected. The pay will overcome objections.
Remember, its is quality first and speed second
Have your tutor and your student keep a binder full of student
work and tutor notes/explanations, so that your child or teens work is
observable. Your child or teen, not knowing better, may want to do
less. This quality first kind of tutoring in which work and progress is
recorded will initially require more time and be slower than tutoring
done quickly, but it will set or raise standards and show your child or
teen how to learn and what is expected. Rewards or pay for learning (or
parental firmness) may provide the student with the will to sit down and
do the work in an readable and observable manner.
The people who shaped the last decade 1997-2005 of secondary
mathematics education in English Schools in Quebec should be closely monitored
or replaced.
I have not seen the course materials for the ongoing reform in mathematics
education.. But the government reform emphasizes continuity with previously
state objectives, those objectives are unclear and the implementation in the
decade 1997-2005 was incompetent.
A Shadows of the pass: The redundant phrase sample survey represents a decade old translation
error in a government approved and required secondary IV textbooks. That error
continues in the English version of the government outline of the current
reform in Quebec high schools. The reform focuses on style matters, but
the continuation of the error raises the question of whether or not Alice
in Wonderland nature of pre-reform course material will influence future
instruction. The reform material itself emphasizes that the reform
continues earlier government objectives. Yet those government objectives
for secondary mathematics are less than clear.
Parents committees should give copies of past and forthcoming course materials employed in
schools to experts in mathematics (Mathematicians at the Ph. D level in
University and Quebec CEGEPs, 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. I would like a general
inquiry by the Quebec Government (or an independent parents committee in defense
of the quality of education of their teens and younger children) into the state of English and/or French course
materials and course designs, an inquiry in which content experts confront past
and present course materials and/or the clarity of course designs.
If the future is like the past,
there will no clear documentation of course content and objectives, and course
delivery will be driven in undocumented ways by preparation for final
examinations. The selection and organization of material will be spaghetti-like,
with no critical path analysis, so that some topics will be included due to
past traditions and not due to any future need for them that students may
have. Indeed, there will no needs analysis and such needs analysis will be
offensive to the spirit of the reform. (If needs analysis is not done, the
question of why learn will be left unanswered, and students will be left to
bring their own motivations and reasons for study instead of being offered
ones that are described not as a absolute, but as a approximately correct.
August 29th, 2008. Textbooks for Grade 10 have
arrived. They have been subject so we are told to review of mathematical
content and diction. However, who did the review is a mystery. So
only the Sec V textbooks from the era 1997-2005 are continuing in use.
Secondary mathematics represents one fifth of each
school day on average, and its mastery is promoted as being important. However,
if in practice, the long term benefits of its mastery are mysterious to teachers
and hence many students, studying mathematics for the sake of passing a final
examination will remain the guide to mathematics learning and teaching in
Quebec.
My Opinion: In mathematics education, course design has to be firm in
support of the full strength skill and concept development of the key skills
and concepts that calculus requires, and beyond that to weave the coverage of
supplementary topics into that support. For students heading for
calculus or not, there is a need to provide routine problem solving skills or
methods in an observable, repeatable and reproducible manner.
Mathematics education in Quebec could not (1997-2005) support clearly and
fully the preparation for calculus and college mathematics, given the
substandard nature of texts for secondary II to V in the period. .
Lessons From the Past - Decade of Nonsense
Experts in mathematics and science
(people with doctorates with a knowledge of content matters, not pedagogy)
should check the mathematics and science course materials being written for
the reform to see
if they are readable, to see if they are logically self-contained and
coherent, and to see whether they are lean or fat in the skill and concept
development.
In the decade 1997-2005 in the past and in continuing and ending employment
of Guy Breton textbooks for secondary II to V mathematics in English Quebec
schools, and in the statement of government course objectives, there has been a
lack of transparency and great confusion. The textbooks with their stilted
English and often incomprehensible development of skill and concepts implied a
garbage-in situation for mathematics learning and teaching.
The Quebec approved and required textbooks for
secondary II to V in their English language version appear to have the
dictionary-like quality of providing several explanations or developments of a
skill or concept in the hope that the reader, a student or teacher, will pick
one to serve his or her needs.
The approval of these textbooks and the use sabotaged English Mathematics Instruction in Quebec, and has set
a poor model for the ongoing changes or reform of that instruction. The
following observations point to concerns, present or possible, that need to
remedied or avoided.
- Teachers and school consultants who became accustomed to and proficient in
the use of substandard texts 1997-2005 in course delivery and did so without aversion
to the substandard texts need retraining and should have no say in future
course design.
- New Mathematics teachers who studied mathematics in English Quebec high
schools in the past decade with Guy Breton texts for secondary II to V
1997-2005, formaly doing well in their mathematics studies with these
text, have been given or exposed to a poor model to follow as
mathematics teachers. Given the teacher training program at McGill, these
teachers accept what they have seen asas a
standard for accepting and judging texts, now and in the future.
- The McGill Faculty of Education in contributing to and coexisting with
substandards textbooks for a decade has not shown the leadership necessary
to compensate for the use of substandard textbooks in English school and the
bureaucratic language in education reform.
For example, the Guy Breton texts for mathematics 436 may be employed in
Quebec English high schools for another year or so. The English version
was developed with help from the McGill Faculty of Education. 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. But amazingly that text has
been in service for almost a decade in Quebec English language schools.
The approval of the Guy Breton 436 text, English version, is shocking.
If the Faculty of Education at McGill is to remain the foremost supplier and
"leader" for mathematics teachers in Quebec English schools,
should it explain its coexistence with a decade of nonsense in Quebec
English language textbooks in secondary II to V mathematics, and besides
that its association with the development of the English version of the Guy
Breton, 436 texts.
Quebec French schools unlike Quebec English schools have a 436 mathematics text Mathophilie
which was reviewed for content (scientific validity) and diction by 17 different
mathematics instructors, Ph. Ds in mathematics and mathematics education
included.
The past provides a base for education reform in Quebec English Schools, and
it is a very poor base which will haunt education for decades to come.
It is spaghetti. In spaghetti software, the program code is not clearly
structured. Code and subprograms are added and kept with one individual
or group to provide clear directions and goals. Over time, subprograms
that have input (consume cpu time) but no output may appear and be preserved
in the absence of a code cleaning. And the documentation for all aspects
of the code and its objectives is never written, or grows piecemeal and
incoherent. The result may be monster, required but hard to change and
hard to improve, beyond the comprehension of all who participated its growth
and maintenance.
In computer
programming, spaghetti code is distinguished by subprograms that have inputs
but not output and by logic too complicated for anyone to understand.
- In 1997-2005 Quebec secondary mathematics program, see the treatment
of dilatations. Dilatations in the
plane introduced to provide a base for similarity, but the exposition of that
point was unclear and became a mathematical ritual for students and teachers
to follow essentially by rote due to the lack of clarity. The topic, a
small subprogram, appeared in secondary II, secondary III and secondary
IV in a confusing manner that did not aid student comprehension of similarity.
The topic was not required in any further studies.
- The secondary mathematics program 514 further consists of a collection of
topics in mathematics and statistics not linked to the future studies or
needs of the students in it, save as a credit for secondary school
graduation. Why was this course invented? It cover topics beyond
the need of its students.
Some critical path analysis should have been performed to see what is critical and
what is expendable in the spaghetti like Quebec secondary mathematics
program 1997-2005.
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. Bureaucrats and universities in
Quebec should be held to account for their lack of professionalism (the lack
of discipline knowledge in particular) that led to nonsensical or incoherent
textbooks to be employed in in Quebec English language mathematics
instruction.
Overlooked Expertise in the Province: In practice, the minimal requirement for employment as an
instructor in an English Quebec CEGEP is a master degree in mathematics.
Many instructors have doctorates as well or instead. University or CEGEP
Ph. D.s in mathematics need to be employed in review of content and diction
but to do so they would need job security and in that the license and
authority to speak freely and effectively in private or public. The
interjection of CEGEPs between high school and university implies senior
university professors in mathematics, science, English, Arts and History
are exposed to Quebec CEGEP graduates but not English Quebec
high school graduates. So senior professors interact with the CEGEP
system but not the high school system. Yet their exposure to high school
graduates and subsequent inquiry into high school practices might have led to
recognition of nonsense in course materials, and a stand against
it. That being said, senior mathematics instructors in English CEGEP
(Ph. Ds especially) may have the knowledge and seniority needed to speak about
high school mathematics and science, etc. (My comment about overlooked
expertise only applies to CEGEP teachers who completed their high school
mathematics before 1997 and the influence of Guy Breton texts, translated from
French, on English high schools.
Example
1:
The
government objectives for secondary II mathematics 586-216, appear in the
pdf file
http://www.mels.gouv.qc.ca/dfgj/dp/programmes_etudes/secondaire/pdf/math216a.pdf
There-in Terminal objectives 1.1, To translate one representation of
a situation into another, includes the following three intermediate
objectives. 1.1 for students
- To give a comprehensive description of a situation represented by a
table of values.
- To give a comprehensive description of a situation represented by a
graph.
- To represent a situation comprehensively, using a graph.
However the meaning of the word comprehensive is not evident in these
objectives nor implied in the text. That being said destination or
checklist on page 48 of the first chapter “Various Modes of
Representation” Guy Breton texts, Book 1, for mathematics 216 proclaims
the following skills should have been mastered by its readers:
- Giving a comprehensive description
of a situation represented
by a table of values.
Representing a situation comprehensively using a graph.
Giving a comprehensive description of a situation represented
by a graph.
But there is no clear explanation of what comprehensive means in the
previous pages, nor in the government objectives. |
Example
2:
The government objectives in pdf file
http://www.mels.gouv.qc.ca/dfgj/dp/programmes_etudes/secondaire/pdf/mata436.pdf
page
3, says the following.
Mathematics 436 differs from Mathematics 416 in two
ways.First, it covers more material in greater detail and deals with
more complex situations, problems and applications. Secondly, the
students must use advanced terminology and formal notation, always be
rigorous and precise, and justify every step in their solutions. In
addition to preparing the students for science instruction,
mathematics education should provide fertile ground for the
development of skills that will be useful to them in the future: As
Resnick and Klopfer have noted, "Graduates must not only be
literate; they must also be competent thinkers.”
The Guy Breton 436 texts,
Book 1 and 2, in my view do not supports the latter. These textbooks
for mathematics 436, provide a standard to avoid. The exposition of skills
and concepts in them is incomplete and incoherent. Very little is
self-contained. Yet
as a mathematics instructor and writer, I tell students to learn to read
like a lawyer, so that the nuances, subtlety or quirk in course notes or
texts can be understood. That assumes the texts given to students is
coherent and written in a lawyer like manner with attention to detail and
fine points. That attention to detail and fine point is not seen in
Books 1 and 2. Books 1 and 2 are in the large are incomprehensible to
this Ph. D. in mathematics.
There is mathematical symbols, words and diagrams in
Books 1 and 2. . While providing and pointing to alternate meanings
and paths for comprehension may be appropriate for a dictionary, the
coverage of logic and proofs in Book 2 if not Book 1 had a cut and paste
feeling. In the latter, common and old-fashioned statements about logic and proofs appeared, but
with no clear chain of reason or connection that I could follow.
Books 1 and 2 were too incoherent to follow in a literal manner.
If McGill
University had not been associated with the 436 text, see the front
matter, the mission
statement of the McGill Faculty of Education would have obliged the
Faculty of Education or the University at least to criticized the
English language translation of Guy Breton work for secondary II to V
mathematics, the 436 text included, AND call for their
replacement.
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In an engineering, business or software development project, hopes and
ideas provide motivation for planning and a critical path analysis of what has
worked in the past and what is likely to work today. But to start
on development or implementation of a project before critical path analysis is
complete or considered is folly. It puts hope and wishful thinking before
reason. Advocates of direct and indirect instruction in any art or discipline,
or in cross-curricular principles may state their principles and standards for
delivery and hopefully content matters first, but before those principles are
accepted as self-evident, courses of action or teaching and tutoring how-TOs
should be development and be documented in a clear fashion that teachers
trained or not (and most not in the case of mathematics) may follow with
results that will be observable, repeatable and reproducible.
Let be it known. 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 or Ph. Ds
with a solidh 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 indecipherable government objectives for secondary
mathematics and substandard texts should not be the model that school
board consultants and further producers of course texts and material follow
alone in the current reform. Where are the content experts? I suspect they
are out of town, or out of province. Their reaction to what is done in Quebec
may be bitter medicine for some to digest, but it is needed. Otherwise,
delivery style experts will be instructing teachers to engage students with
substandard and even incoherent materials and rituals without deep rhyme nor
reason. You can see a skeptic is writing this. I suggest hope that I am
wrong, and the course material is sufficient, but there should an authoritative
check by well qualified peers.
The reform is gradually replacing Quebec high school texts for
secondary II to V mathematics. There may be room for hope in the use of
Nelson texts from Ontario, as is or modified, in Quebec secondary mathematics
education. Yet that hope needs to be verified.
There is no answer here for the difficulties you are facing. But following
the Quebec Education program is folly for you when the program does not work
and is not proven in the rest of Quebec. Following the Quebec school program
in mathematics prior to the current reform and perhaps during it, may enlarge
difficulties and alienation instead of lessening them.
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 due the "Alice in Wonderland" characteristics of
course design and mathematics education materials in the last decade 1997
onward. 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 or not) 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. Where Quebec curriculum and course
materials is inappropriate or absurd for students who are not first nation, the
curriculum and course materials are also inappropriate and absurd for first nation
students. That has been the case for the last decade.
Most high school mathematics represents preparation for calculus, or can be
presented as such. That preparation is delicate. Despite the availability
of calculators, primary school students still need to have drill and practice in
arithmetic with whole numbers and fractions. Weakness there will compound
in the high school development of algebra and geometry, and undermine senior
high school studies. There is a problem in first nation communities due to the
colonial heritage and perspective of compulsory education, that was imposed and
disruptive (children kidnapped for instructional and assimilation ends). But
if compulsory education is continued under the management of first nation
leaders, there is a question of why it should be continued. For better or
worse, do first nation communities and opinion makers want education. In
first nations and out, there is problem of commitment to sit down and studies.
Education that is not compulsory or education that has become a formality calls
upon students to bring their own drive and commitment. Education that is not
compulsory needs to engage students. In present day high school mathematics,
there are many many topics, all present as preparation for college mathematics.
In and out of first nation education, I suspect mathematics education in
primary school and beyond needs to
describe the foreground and background use of mathematics in terms of saying
where is the mathematics in scenes from daily
life in terms of trading and shopping, in terms of banking and bank services,
and more money matters, and in terms of building trades and accounting and
so on. Geometry could be present in the use of maps and route
planning for hunt and fishing, and in the use of maps for farming and so
on. The problems are clear. But addressing them leave room for thought and
for decision making. All decisions will be compromises since old ways are
disappearing (if you live in or want a home with plumbing and electricity, that
is proof) and new ways need to be faced.
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