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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
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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
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Book Reviews 436.
The MEQ has approved two instructional packages for use as texts in
Mathematics 436.
See too Secondary
IV - Functions to Trig & Statistics - support for maths 436
(1) Addison-Wesley Mathematics 10, Québec Edition ©1994
| Kelly, B. et al. |
Instructional Package |
| Addison-Wesley Publishers Ltd. |
Certificate emitted November 30, 1994 |
|
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| Approved components |
Pages |
Student's Textbook
Teacher's Guide |
482
120 |
Here is a professionally written textbook. The language in the textbook
is consists of standard English and employs mathematical correct definitions and
explanations. It begins with a logic It develops ideas in a
deductive manner. The treatment of spheres, cones and cylinders, a possible
exception, emphasizes some physical relations between their volumes. It
employ set notation and modern mathematics symbols in a consistent manner.
This work focuses on the mathematics. The exposition is self-contained. The
teacher guide has fewer pages than the text. Use of this textbook appears
to be rare. Students in Quebec given their current (2005) formation in
arithmetic, algebra and notation would find this text too hard. Site
lessons plans for secondary I, II and III might remedy that.
(2) Mathematical Reflections 436 ©1998
Breton, G. et al.
Instructional Package
Les Éditions CEC inc. , Wilson & Lafleur Ltée
| Approved components |
Pages |
Student's Textbooks (2)
Teacher's Guides (2) ©2000 |
849
??? |
Even if 95% or more of the mathematical statements and definitions in these
two books are correct or justified in one way or another, their
presentation is incoherent. Inconsistency and incoherency
in the editing or content of books I and II is indicated by the repeated use of
the two words define or definition in the algebraic developments of Book I while
the first chapter of Book II explains what a definition is or should be. The
first chapter of Book II also talks about and explain ideas in logic previously
met or used in Book I. The books themselves includes many key terms and
concepts in bold face type, but they fail to provide clear definitions and a
clear logical development of skills and concepts understandable to myself with a
1983 doctorate in mathematics from McGill University. The Quebec
government should provide or approve alternatives.
Mathematical Reflections 436 Book 1, Guy Breton et al. 1997, ISBN
2-89127-426-1
The diction or language quality in this work is
far below the level of Addison-Wesley Mathematics 10.
- Page 2 covers the difference between a relation and a
function.
- The Math Express page 19 reviews or summarizes single-variable function
notation. The page identifies a rule for a computing a function with
an equation or algebraic expression. That is view belongs to the 19th
Century. A set or free-hand drawn graph in the plane which
satisfies the vertical line rule gives a graphical method or rule for
computing a function apart in the first instance from an equation or
algebraic expression.
- The LexiMath page 86 says a model as a mathematical and schematic
idealization that embodies the characteristics of a situation over the
interval described. I do not see that statement as enlightening.
My Collin Dictionary of Mathematics suggest a model is a mathematical
description of some process. The process need not be a situation over an
interval. So this LexiMath view of what is a model is too restrictive.
- The LexiMath page 86 characterization of a function is very general.
Emphasis of the vertical line rule might be clearer.
- In the LexiMath page 86, a table of values may tabulate a few of the
ordered pairs in the graph of a function as indicated, but in some cases it
might tabulate all.
- In the LexiMath page 86, the characterization of domain and
range uses the word assigned. A better form might say a
Domain of a function is the set of values a variable may take, and that the
Range of a function is the set of values taken by the function.
A mix of Set notation for domain & range with words, might be more
appropriate.
- In the LexiMath page 86, the description of when a function is
increasing or decreasing employs words alone without giving an algebraic
perspective. For instance a function f(x) defined on an interval [a,
b] is increasing on the interval if whenever w < v are both
in the interval, we have f(w) < f(v).
- In the LexiMath page 86, the characterization of a negative function is
incomplete. A real-valued function f(x) is positive on an interval [a,b] if
and only if f(x) > 0 for all numbers x in the interval while is negative
on the interval if and only if f(x) < 0 for all numbers x in the
interval. But a function which is not positive everywhere on an interval is
not necessarily negative everywhere on the interval.
- In the Leximath page 116, I would write unlike in place of the
term non-like.
- 13 in the Leximath page 234 I might write product of simpler (or
lower-degree) polynomials instead of simpler product of polynomials.
- The Math Express page 306 uses square brackets to indicate the
inclusion or exclusion of end-points in an interval. That is
consistent with the Quebec admissible symbols and notation, but it
excludes many English text using a mix of round and square brackets for
interval notation.
- The Math Express page 306 involves notation, the author's have
switched from a word-only description of concepts to a more conventional mix
of words and symbol. That is good.
Mathematical Reflections 436 Book 2, Guy Breton et al. 1997, ISBN
2-89127-427-X
- Math Express 14, page 39, says a theorem is a conjecture that needs to
be proved before being accepted in use. I would replace the word
conjecture by the word statement. Most known theorems today are no
longer conjectures. They have been proven.
- The LexiMath page 112 characterization of definition better applies to
definitions in plural. The page's characterization of axiom is debatable.
The pages characterization of theorem employs a sentence that includes
axioms among items that are proven. The z-axis is characterize with respect
to "the plane".
- Math Express 18, page 212, uses a pair of vertical lines || to
indicate equality.
- The LexiMath on page 266 employs a less common word variation to explain
an more common word change in the explanation or review of the
meaning change in the coordinates.
- Math Express 24, page 412, explains that similarity transformations
define similar figures. I would say give or yield instead of
define. I learnt a definition of similarity apart from the
discussion of similarity transformation that two figures are similar when
corresponding angles equal and corresponding measure of length proportional.
That definition is enough to meet the needs of Trig in secondary IV.
If I were to rewrite the Quebec curriculum in secondary II to
IV, I would simplify matters by omitting the discussion of similar
figures or solids in three dimensions. The statement of general
quantitative relations between lengths, areas and volumes for similar solids
at this level can be implied by example, but it cannot proven before
students have taken a first course in calculus. The general discussion lends
itself more to rote learning (here are the formulas and do not ask why) than
to a reason-based account of mathematics. If I had to teach this topic, I
might start with formulas for areas and volumes of solids, and show how the
formulas suggest the quantitative relations between lengths, areas and
volumes for solid related by a scale factor or similarity
transformation.
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