Parallel Mathematics Instruction for Montreal Students:
Your son or daughter (given the pay) will work hard. Program details - |
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YOU are better than YOU think. Show yourself how: |
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Logic
Mastery Do not leave here without it - 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 linear2007 Equations ; or (b) see this calculus starter lesson and Volume 3, Why Slopes & More Math, chapters 2 to 6; 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. |
The following webpages support each course in the old MEQ program.
[ 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 ]
They shorten and paraphase) old MEQ objectives documentation for the sake of clarity. They derive course checklists from the intermediate objectives in the old MEQ course documentation. They give suggestions for each course. They review and criticise the MEQ approved books for each course. That being said, some webpages are better written than others - revision to follow.
Dismay in the format of Quebec Mathematics Education programs for secondary schools.
- The old MEQ objectives for secondary I to V mathematics consists of statements and assertions whose validity we do not want to dispute, but might, in a form which is incoherent and so full of generalities, the question of which skills and concepts are be taught and why is not clear. Only recently, have I realized that the intermediate objectives are islands of clarity in otherwise poorly written (confusing = poorly written) documents, full of vague terms and concepts or vague principles to guide instruction or to distract the reader of course objectives from the islands of clarity given the statement of intermediate objectives, clearer yet still not definitive. I looked at the objectives for clarity after reading English language versions of the MEQ approved textbooks.
- The textbooks used in English language instruction in
Quebec, poorly translated versions of Guy Breton books for secondary II to V
mathematics, are also full of mathematics statements and formulas, valid for
the most part, but lacking a logical development of skills and concepts.
Topics are out of sequence. For example, the approved book I and II texts
for mathematics 436 use the word define and definition repeatedly in Book I
in algebraic context while giving an explanation of concept of what is
a definition in Book I. That is out sequence for any logical development of
the subject. Similarly, Book I use logical notions of implication and
equivalent while the explanation of these notions appears in Book II.
The out of sequence appearance of skills and concepts is not limited to a
single year. Function notation is employed in secondary II textbooks while
it only briefly and perfunctorily explained in the mathematics 436 text.
- French language instruction is more fortunate than English
language instruction in Quebec because alternative approved text in French
provide a more logical development of skills and concepts. Yet, both French
and English language instruction in Quebec are still subject to the direct
influence of the old MEQ objectives in secondary III, IV and V while
secondary I and II which now follow the new Quebec high school mathematics
program is only subject indirectly to the old MEQ objectives for those
years. The new program calls for changes in delivery style and the
development of cross-curricular competencies or abilities while keeping the
old objectives for secondary I and II. Here the new program is subject to
criticism, the lack of supporting material, or a lack of
management-provided lesson plans easily understood and repeated by teachers,
to meet the new goals. And at the same time, in mathematics, the new
programs builds on early objectives for secondary I and II that are
obscurely put.
- In the past we use to joke about teachers being two pages
ahead of the students in course textbooks. With the passing of textbooks as
demanded by the new Quebec program, teachers not have authoritative guides
for lesson planning and delivery. That passing will lead to anarchy in
course delivery. Results will be ad hoc. Schools in the past have been
know to put teachers in a classroom, and say teach, here is the book.
What happens now when such a teacher has no authoritative program to follow,
and the teacher is not an authority in the subject and cross-curricula
abilities demanded. There are some foreseeable problems which the MEQ
should address before implementation of the new program or reform.
Where is the joke now? Text books for better or worse may help
instructors teach and give students able to read, an alternative viewpoint
to follow.
- The site entrance page www.whyslopes.com points to starter lessons and goals for mathematics education in Quebec and elsewhere that will most likely be effective in easing and avoiding difficulties, and be effective too refining and consolidating skills and concept development. Those pathways for clearer instruction compensate for difficulties in the old program and are not even considered in the new program. Quebec bureaucrats in charge of mathematics education need to wake-up.
For instructional materials, the English schools in Quebec are essentially orphans. The first material in French to be MEQ approved may be translated for better or worse, while later MEQ approved material, much improved, is not. Help from first nation school boards in Quebec may be needed to remedy the situation - to provide the funds for translation of the clear or better material available to the French sector, or approval to use material from other provinces or places in senior high school mathematics and science.
My example: In the MEQ approved textbooks written by Guy Breton with the aid of multiple authors for secondary II, III and IV mathematics 216, 314 and 436, Topics are out of sequence and incoherent and translation errors and poor English in the translations are present.
In particular, for the Guy Breton et al., Mathematics 436 textbooks, Books I and II, in particular shines in its incompleteness and incoherent composition, and so undermines the education of advanced mathematics students in Quebec English schools. Book I for instance uses the word define many, many times in instructions to students but what is a definition, and its role, is only explained in Book II. The level of diction, language, in the teacher guide for the Guy Breton books I and II is college level and even clear in contrast to the confusion and lack of clarity in Books I and II themselves.
The English language school network in Quebec in providing advice and directions for using Books I and II, may be in earnest, but it supporting the use of a poorly written textbook, one that teachers and parents with backgrounds in mathematics will found awful, worthy of condemnation. In contrast, texts in French, for instance Mathophile for 436, and possibly Scenario, are clear, sequentially and do not add gaps into the exposition of mathematics.
The best advice for students in mathematics 436, English version, is as follows. Buy the French text Mathophile for 436 for the course and read them alone or with help. You will find this French textbook clearer than the English ones. (It is possible that Scenario for Mathematics 436 will do as well, but I have not had time or made time to read it fully.) Similar advice may apply to students in secondary II to V in other mathematics courses - here again I have not had time to review the alternatives.
At this website, as time permits besides other duties, I will be posting lessons or problem sets to help students and teachers meet or the exceed the Mathematics 436 intermediates objectives.
The Minister of Education (leisure and sports) in endorsing inclusive education (apart from streaming according to language skills) is effectively turning large high school into a collection of classrooms, each one equivalent to a one room school house. That is being done besides calls for students to be given differentiated instruction (streaming did that a little) and for teachers to explain matters indirectly. That is for students in the youth sector. But for students in the adult sector, a different approach applies. Differentiated instruction is provided by a modular approach to course design and delivery. Each student has a workbook and/or text, with step by step questions or problems to do, one at a time and one after another, at their own pace, while the teacher helps and evaluates. The text and material for adult education are clearer and more self-contained, and often simpler than the confusing or ambitious texts and objectives employed in the youth sector. So the youth and adult sector are governed by different philosophies. The adult education material could be used or tried for self-instruction by youth, teenagers, with parental assistance, during the summer months. That being said, senior high school students, or younger and gifted students, may explore material online here and elsewhere. Good luck.
New (November-December 2006) :
Lesson plans for secondary I, II and IV mathematics, posted online fall 2006, offer ideas that worked and ideas that might. Secondary I and II lesson plans offer excellent preparation for mathematics 436 and further studies in mathematics.
- Secondary
I - fractions & allied concepts (decimals, percentages) -
support for maths 116.
In accordance with old MEQ intermediate objectives, secondary I should be the year of fraction consolidation with decimals and percentages regarded as different ways to represent fraction - proper, improper or mixed.
- Secondary
II - Algebra (arithmetic versus algebraic methods, backward use of
formulas and proportionality equations) - support for maths 216, easier
ways to learn and teach.
In accordance with MEQ objectives, secondary II should introduce and would be unified by the message that each formula met in high school and college in mathematics or other disciplines may be used directly and indirectly, that is forwards and backwards. And if one must keep the discussion of dilatations in the course, I would place that after the discussion of proportionality relations y = kx and how to use them backwards and forwards.
- Secondary III Mathematics - a
proposal that departs from the MEQ objectives. For student
engagement, I would like to see secondary III recast as the year of
applications of mathematics in consumer, business, construction
trades, navigation and even science. And then continue with the old
MEQ curriculum for Mathematics 436 minus the discussion of transformation
geometry - the discussion of the latter in the current MEQ courses or
textbooks for English language instruction in Quebec is unclear and
unnecessary - the curriculum should focus on less - the essentials - and do
that well.
- Secondary IV - Functions to Trig & Statistics - support for maths 436, that is, clarification and enrichment of course content - how to meet or exceed most course objectives (we hope). This a rough draft - a good starting point for some mathematics 436, but some elements properly put in a mathematically sense may have to be rewritten or identified as enriched material for the the mathematics 436 course. Given the quality of the approved textbook package for mathematics 436, the final examinations are mean and harsh, cruel and unusual summative tests. Composers of the final examination should look at the intermediate objectives for 436 and not at MEQ approved texts.
New (November 2006): Here are links (unsolicited) to Loyala High School Math Notes:
- Secondary I: - Math 116
- Secondary III - Math 314
- Secondary IV: Math 426 useful for 416 436 as well.
- Secondary V - Math 536
and here is another link (sylvain.lacroix/maths/526-536/526-536.htm) (euclidiennes.free.fr/536/) for mathematiques 536.
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Still more senior high school mathematiques: L'intégrale des maths for mathematics 536.
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Notes and Observations
a call for action
For the sake of students, note:
- The arithmetic skills called for in the MEQ objectives for mathematics 116
are not mastered or not maintained in secondary I to V by most
students. Students cannot do arithmetic efficiently on paper or with a
calculator in repeatable and reproducible manner.
- Secondary II to V textbooks translated from French periodically include
English language sentences difficult or impossible to understand or
explain. The description of some concepts is nonsense due to poor
writing or poor translation (I cannot tell which, see for example the
exposition of the difference between quadratic and exponential
functions).
- A simpler, more effective high school program with less alienation of
students might follow from focusing on preparation for calculus and consumer
mathematics. Presently, the curriculum in covering too many topics,
mathematically pleasing or not, is too complicated for students and teachers
to follow, and becomes a source of alienation. Reducing the number of topics
and covering them well over secondary I to V is advised.
- Reforms should be tried and tested before being implemented. Mathematics
reforms should be tested for logical completeness, necessity and feasibility
by asking mathematicians if they understand each and every step of the high
school mathematics programs, purpose included, and whether or not the ends
require the step.
- Mastery of site lessons and lesson plans for secondary I and II mathematics would give primary and secondary school teachers tools and a firm base for mathematics instruction ina repeatable and reproducible way. See site lesson plans for Secondary I - fractions & allied concepts (decimals, percentages) - and for Secondary II - Algebra (arithmetic versus algebraic methods, backward use of formulas and proportionality equations)
A farce is a farce is a farce - action required.Mathematics is a greater cause of student failure than need-be due to delivery and content issues. Most students in not mastering fractions in secondary I have difficulty in further courses.
For the past decade, say 1997 onward, the Quebec high school mathematics program in approving poorly written textbooks for secondary II to IV, if not V, has set a low standard for clarity and completeness in the in exposition of the discipline the course objectives and the course textbooks. Today, we have new teachers entering mathematics instruction for which the old mathematics program low standard is their model for clarity and completeness in the discipline, a vicious cycle has been begun.
The combined lack of clarity of the MEQ documentation and these approved textbooks, the only ones allowed, has undermined or sabotaged mathematics instruction in secondary II to IV.
Education reform in mathematics needs to go beyond introducing new delivery styles for an old curriculum, and look at the content or curriculum changes as well. Style changes alone cannot make the old curriculum engaging and appealing. Style changes cannot fill gaps in the systematic development of algebraic skills and concepts - gaps made self-evident by recent advances for instruction - see site content. The adult education program in Quebec (SOFAD) provides manuals for self-instruction. are deliberately clear and deliberately accessible - step-by-step. There-in lies a model for differentiated instruction, a practical one when students may start a course anytime, or a practical one for the rational or irrational return to the one-room school house espoused by calls for inclusion in education reform where students at many levels are kept in the same classroom with a single a teacher. Except for the social environment, I would recommend adult adult education asap for students in difficulty in mathematics. For secondary school youth, course documentation and textbooks written in nominal accordance with great principles for instruction aimed at the students discovering how, each in their own fashion, need to forget the deliberate introduction of vagueness for the sake of authentic individually constructed comprehension not imposed by the instructor or course text. The MEQ documentation needs to provide a clear, feasible, self-contained route or foundation for instruction. MEQ course descriptions and approved textbooks need to be clear, well-ordered and self-contained - forget the deliberate introduction of cognitive tension or dissonance - if learning and teaching with repeatable, reproducible and thus verifiable results are wanted. MEQ course descriptions and approved textbooks need to provide lean, fat-free authentic authoritative path sufficient for self-instruction by the gifted and sufficient for instruction by teachers. Ease of comprehension and accessibility need to be emphasized. The intermediate objectives in the old MEQ documentation in mathematics provide essentially clear, minimal directions for teachers - they identify skills and concepts in the courses. In contrast the old MEQ documentation as originally written for high school mathematics in calls for activities and delivery styles is too general and too inaccessible for domain experts and ordinary to understand after one or two readings. There-in lies a vacuum which is filled by the MEQ final examinations and the MEQ approved textbooks. Here English language textbooks (and the original French versions) lin putting key terms and concepts in bold face without defining them clearly nr present concepts out of sequence and a garble manner do not help.
That being said, I am slowly collecting the MEQ French language textbooks, those not available in English, to see which if any improve upon the English language situation. Those that do would be better for bilingual students or students able to read mathematics in French. |
www.whyslopes.com
English Quebec Math Education NonsenseRoad Safety Message (Online here in 1995, a decade before the Quebec Government advocated in its)
Area Intro Old Site Entrance Copy Right Matters Curriculum Cuts Intermediate Objectives Links MEQ Objectives Math Ph. D. fails McGill B. Ed. program Objectives, Check lists, Suggestions and Book Reviews for Quebec Sec I to V Mathematics. (out of date)
Area Intro 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 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 116Secondary 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