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Quebec High School Mathematics Education (English Version of)
his folder has a tree like structure. The child, same level and parent level webpages for this webpage follow.. More Links: 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 |
Secondary
II Deficiencies – math 216: ·
Mathematics Carrousel 2, Secondary II, Book 1, Guy Breton & al,
1996, ISBN-289127-362-1 ·
Mathematics Carrousel 2, Secondary II, Book 2, Guy Breton & al, 1996
ISBN-289127-363-X English
language instruction in the secondary II, mathematics 216 courses, uses a
two-volume textbook package Mathematical Carrousel 2, 1996, written by Guy
Breton. This is the English version of a 1994 book
The word package echoes the Quebec government wording. [A]
(First Case of Bullshit) The government
objectives for secondary II mathematics 586-216, appear in the pdf file 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.
The topic “various modes of representation”
by tables values, equations, graphs and formulas gives terminology in the
government objectives that I never met before as a mathematics student and
in[s]tructor. The topic appears as a
formal theme in government objectives for secondary mathematics and amazing[ly]
in the title of the first chapter of the Guy
Breton textbooks for secondary mathematics. When I first met it, I had to ask
myself what was it mathematical interpretation or significance of the chapter
tittle. In my opinion, various modes of representation is a theme to be met as a
practice or practices as students and teachers weave their way through skills
and concepts, and not as a topic by itself. [B] (Where is the Algebra) The second chapter introduces proportionality
with words and numerical examples. Where a first quantity y is proportional to a
second quantity x, the text does not write y = kx for some constant k. It avoids
and never uses this algebraic description of a proportionality relation.
Furthermore, Page 108, the summary
or destination page for chapter 2, says the following: Constant
of Proportionality: factor by
which a numerator must be multiplied to obtain the denominator. There is an element of truth
in this statement, but it misses the mark. In general in talking about
proportionality, a quantity y is proportional to a quantity x if there exists a
constant k such [that] Now pages 90 and 91 in the
second chapter in two boxes labeled a travel log and a conference room present a
so-called mathematical or algebraic perspective of proportions and their
properties in a fashion that most likely will appear as gibberish (nonsense) to
students gifted and ordinary reading this text, and to any teacher
without a quantitative background required to teach mathematics 586-216. There
may be well some explanation in a teacher guide of how to use these two pages,
but students will not have access to that guide and hence this chapter does not
encourage self-instruction for first time learning and/or review. Not writing y
= kx anywhere in the chapter to represent a proportionality relation is
inconsistent with the Government [C]
The third chapter on similarity transformations introduces without
explanation of meaning, the notation m
AB for the length of a line segment AB. The page introduces advanced function
notation h(A) for the image of point
A under a similarity transformation h. The concept of proportionality re-appears
without any algebraic description. Functional notation should not be used, because it is important that
students be able to observe and explore situations without being distracted by
overly complex symbolism.
[D] (Cameo Appearances) Page
171 travel log for the fourth chapter on algebraic calculations says A symbol used to replace a number is called a variable. There is a counterexample –
the letter p donotes a constant. Page 176-176. The description
of properties of operations, that is closure, commutativity, associative
properties does not mention the type of numbers. That is, a pre-modern style of
exposition. On page 188, with no prior
explanation or use of the concept of what is a set, the text proclaims: The set of values that replaces a variable is called the domain
of the variable. The domain of a variable is called the replacement set. There is also no prior explanation of the symbols N and Z - the denote the natural numbers and the integers, respectively. There is no further development of the concept of a domain. Essentially, it makes cameo appearance on one page and then disappears with no plot, ryhme or reason for the appearance or visit. Thank you. It is easy to imagine the foregoing making little or no sense to student ordinary to gifted, and to teachers without a quantitative background being required to teach mathematics 216.. [E] (More Function Notation) In secondary II mathematics, the Guy Breton Book 2, for 216 in the travel log page 10 introduces or drops-in with no prior development, more function notation for [similarity] transformation of the plane. The same chapter also introduces subscripted function notation for rotations, reflections and dilatations. Similarity transformations will reappear in secondary III mathematics 314
and secondary IV mathematics 416 and 436 in accordance with the government
objective to derive the assumptions of Euclidean geometry from properties of
geometry transformations. [F] (Faulty Use of Terms) In secondary II mathematics,
the Guy Breton Book
II for 216 in the travel log page 99 gives the following to explain the
word capital: amount of money loaned or borrowed
in return for an interest payment. The chapter should use the word principal instead. Here we
hope for repayment of the principal, with
many and not just one interest payment. Page
83 employs the word capital where it should be using principal as well. There
are many, many instance of poor or abnormal word usage in the Guy Breton
textbooks for secondary II to IV mathematics 216, 314 and 436. Remark:
Secondary II is suppose[d] to introduce students to the algebraic way of
writing and reasoning. That being
said, chapter development and the end of chapter destination or summary pages
[in the secondary II textbooks] appear to emphasise numbers and words, and avoid
or not use algebraic expressions. |
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