Appetizers and Lessons for Mathematics and Reason  ( Français)  
www.whyslopes.com            Back ] Up ] Next ]
 Logic mastery is key to easing or avoiding learning difficulties in work & studies. 
What does it mean to use a formula forwards and backwards? 

Online Volumes (Book Orders)
1,  Elements of Reason. 1996
1A. Pattern Based Reason  1995
1B. Math Curriculum Notes 1996
2. Three Skills for Algebra  1995
3.
Why Slopes & More Math 1995

Links To Tutoring Services

Site  Folders for Instructors & Adults
A.  Public Policy Matters -  Essays
B.  Mathematics  Education Essays  2006-7
C -Logic & Applied Math Program  
    for education,  June 22, 2008 
D. Quebec English Math Ed -  1997-2005
E. Help your child or teen
How TOs/ Ref.-08- 2008
1. Arithmetic Reference
2. Algebra 
3. More Algebra 
4. Geometry  
5. More Geometry
6. Calculus
7. Logics in Maths
216 Nonsense or BullShit Back ] Area Intro ] Next ]
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..

 Area Intro ] Copy Right Matters ] Curriculum Cuts ] Intermediate Objectives ] MEQ Objectives ]

Up
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

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

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 chapter.   Correct me if I am wrong.

 

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]
y = k x. The element of truth arises since   k = y/x but that element still misses the mark.

 

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 of objective that secondary II mathematics introduce and develop algebra sense.

 

[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. It possible that chapters two and three should come after the fourth chapter on algebraic calculations. However, page 18 of the government objectives for secondary III mathematics in pdf file http://www.mels.gouv.qc.ca/dfgj/dp/programmes_etudes/secondaire/pdf/mata314.pdf 
states

 

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.


The use of function notation in secondary II is in accordance (?) with the secondary government objectives of describing transformations with variables,  but it is not in accordance with secondary III objectives.

 

[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.
The replacement set is a set of numbers such as N, Z or a set of numbers chosen for a particular situation.

 

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.

 

www.whyslopes.com   Back ] Up ] Next ] [Top of this Page]   

Road Safety Message  Do not walk on a road with your back to the traffic - rule of thumb
Please report by
email,  errors in mathematics or grammar or terminology to site author
If a mathematics topic you need is not covered in site pages,  report that as well. Topics in most demand
will be covered first in site growth.  

All trademarks and copyrights on this page are owned by their respective owners.
Copyright to comments & contributions are owned by the Poster. 
The Rest © 1995 onward by site author,   Alan Selby (
email form) All Rights Reserved.