Quebec Mathematics Education

An Alice in Wonderland Experience for students in Quebec.

The phrase sample survey, a translation fault in  secondary IV Guy Breton textbooks, has become part of the official language of the current reform. Will that fault continue. 

Page Contents 

1. Introduction

2. How to Ease or Avoid and Alice in Wonderland Mathematics Education Experience for your kids

3. Education Malpractice in Quebec 1995-2007 Who should have prevented it? Is it ongoing?

4. Nonsense or Bullshit in Government Obectives and Government Approved and Required Texts

5. A Note for First Nations in Quebec

6. Why did  a 1983 McGill Ph. D. in mathematics,  fail 2003-5 the McGill B. Ed program?   Read about my  Alice in Wonderland Experience in the McGill University, Faculty of Education. 

1: Introduction

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. As a mathematician, I recognize the the symbolism in these textbooks as mathematical, but the logic there-in I do not follow.  

The Quebec approved and required  textbooks for secondary II to V in their English language emanation 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 their continued use appeared to be a formality that sabotaged English Mathematics Instruction in Quebec, and has set a poor model for the ongoing changes or reform of that instruction.  

In classroom management, teachers have to be firm to retain control. Likewise, 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 lacks critical path analysis to define its ends, values and means, and their feasibility. 

On more serious note, 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 becomes bureaucratic.  Given that 50% or so of high school teachers are doing so without a mastery of calculus,  most students will not what calculus demands from high school studies in mathematics and educational change, democratically led, may lead to preparation for calculus being part of the hidden or forgotten agenda for high school mathematics instruction.  Presently, there are no long-term ends and values in mathematics education except for final examination preparation, a bureaucratic and alienating goal for mathematics instruction.  Education reform in mathematics that mentions everything but preparation for calculus and what calculus demands is suspect or surreal. 

The French school system reports a 60% drop-out rate for  male secondary students. Is that the mirror image of the Alice Adventures in Wonderland experience on the English side.  Or, is it independent story Through the Looking Glass and What Alice Found There. I should read one or both stories to see which satire fits best.

2: How to ease or avoid an Alice in Wonderland 
Experience for your son or daughter 

1. Send your teen or child out of the province.
   
2. Send your teen or child  to an international school which does not follow the Quebec Mathematics Curriculum.
   
3. Have  your son or daughter in a parallel mathematics education program which emphasizes the full strength mastery of arithmetic, algebra and geometry to the strengths and standards implied by calculus. 
   
    Pay a undergraduate student strong in mathematics and science to cover and verify the skills and concepts in See How-TOs. everyone, one by one, for your teen alone or as part of a group.  Require you teen to keep a binder full of written work that demonstrates this mastery to yourself and others.. Also 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 most of mathematics,  the reluctant to the written work correctly points to difficulties that need to be identified and corrected. The pay will overcome objections.  
   
   This approach will not work for all students. I do not think such an approach exist. But the approach here sets values, means and an end for mathematics studies that is not being met in Quebec or North American English language high schools. If you did well in calculus yourself, or know what it requires, instead of paying an undergraduate students to do it, do it yourself with the aid of site  How-TOs.  I will be posting videos online focusing on  Arithmetic, Algebra and Geometric Skill and Concept Development methods for tutors and teachers to support those  How-TOs. and even refine them.  
   
   Note: In the Whyslopes-Virtual-Classroom, there is a tutor-teacher training session, (List 2A or 2B) which you might join as parent who wants to tutor your own child or teen. Sessions will be scheduled when numbers warrant. 

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 not clearly put. That is absurd.  The past may yet affect the future.

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 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 as I expect, no jduge, no philosopher, no  mathematician in Quebec is willing to sanction course content, past and present, or to say that  the government objectives pre-reform and reform were or are clear that would be progress in the sense it would expose and lead to recognition of a fundamental obstacles to comprehensions in course design and delivery.  Is education in Quebec school based on the concept player, say yes boss, to reforms ahead of their time. 

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. 

3: Education Malpractice in Quebec 1997-2005.
Who should have prevented this? Is it ongoing?

I read government approved, required and translated textbooks for English Schooling in Quebec, those by Guy Breton  for secondary II to V mathematics instruction, in the hope of finding a clear and rational development of secondary mathematics.  What I  found in between mathematical symbolism and concepts occasionally but not always clear,  with a mix of standard and substandard English, and a generally hard to follow, incomprehensible, development of key skills and concepts.  

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.  

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. 

How much student alienation in Quebec high schools, French and English, is due to five years of Mathematics Education with substandard materials and practices? Is a knowledge of calculus and beyond necessary to teach mathematics in Quebec? Is a knowledge of calculus and beyond appear required the training of high school mathematics instructors, in the composition and verification of Quebec course materials, and in the design or redesign of mathematics courses in Quebec?   Is the past an indication of the future.  

Quebec French schools in contrast 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.  Can English Quebec Schooling match that?

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. 

 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.  For example, the previous decade saw 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.  In computer programming, spaghetti code is distinguished by subprograms that have inputs but not output. Such subprograms are not necessary.  That being said, some critical path analysis should be performed to see what is critical and what is expendable.  In particular, there should be a return on investment critical path analysis of all topics or  subprograms or complications in the Quebec math and science programs. Garbage in, Garbage out. 

With a Ph. D. in mathematics from McGill University, I abandoned my effort to fully decipher or follow Quebec course design and its materials in the last decade. The courses in question are being phased.  Albeit, 

5. Conclusions and Recommendation

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. Change in education is like a drug.  Yes, penicillin and insulin had life-saving effects that more than compensated for their immediate application, but in general drugs are supposed subject to field tests before implementation. 

 Today, there is a reform ongoing in Quebec high schools. 

 The reform is gradually replacing Quebec high school texts for secondary II to V mathematics.  The quality of the replacements remains to be seen but in mathematics it stands on or continue a very poor basis.  

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.  

Safety first should be motto to limit  the adventures course designers and textbook writers that impose on students and teachers.  If there  not enough qualified mathematics teachers,  there should be team teaching with master teachers supervising others. That assumes and requires course design and materials not of the "Alice in Wonderland" family. Bullshit and nonsense in education is a sign of rot. The Titanic has sailed and hit an iceberg. Ouch. 

5: A Note to First Nations in Quebec

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.  Reform in haste. Worry at Leisure.

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. If 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. 

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. 

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.    

6:  For the public record of the McGill University, Faculty of Education:

Why did a 1983 McGill Ph. D. in mathematics fail a 2003-5 McGill B. Ed program. 
It represents the site author's Alice in Wonderland experience.

 This site author, Alan Selby, a 1983 McGill Ph. D. in mathematics failed the very last element of a 2003-5 B. Ed program due to the inability to prepare lesson plans from government objectives, from government approved and required textbooks, without more assistance from host teachers that the Faculty of Education employs in the supervision and evaluation of student teachers in highs school practice teaching assignments.  That being said, The McGill Faculty of Education employed host teachers whose mathematics background and classroom management abilities are not screened, and it employs as teaching practice supervisors,  school principals and former teachers who do not have the mathematics background necessary to recognize how nonsense or lack of clarity  in government approved textbooks and government objective can leave  me, a Ph. D. in mathematics with decade of college instruction, at loss in identifying what should be taught and how.  Well-documented garbage-in, garbage-out results followed in spring 2005.  An appeal followed within the Faculty of Education, but no one on the appeal committee committee had the mathematics background needed to recognize the garbage-in aspect of the teaching practices.  

A complaint to McGill University alleging lack of due support and process was not processed, and judge insufficient (September 18, 2008) its in form to support a grievance process, or the formal consideration of the McGill Senate Advisory Committee. In that complaint, I objected to the Faculty of Education coexistence with nonsense or lack of clarity  in Quebec government objective - the lack of mention of the latter in its formation and evaluation of student-teachers;  its employment of host teachers and field experience supervisors without screening them for mathematical competence nor an awareness of the aforementioned lack of clarity,  etc.  It seemed that that the evaluation and assessment of students was a random affair in contradiction with the Faculty of Education and McGill University calls or regulations for due process and objectivity in student assessment.

 It is beyond the mandate of the McGill Senate Advisory Committee to consider fundamental criticisms of a McGill sanctioned and approve program of study.  Whence the McGill Senate Advisory Committee would not investigate my complaint, nor submit a summary of it to the McGill University Senate.  There-in lies a continuation, if not end, of my "Alice in Wonderland" Experience with the Faculty of Education.

If the program for the certification of secondary mathematics  is not for changing on the basis of academic independence and autonomy, it should be should be shut down.  Quebec itself should have a Etat General Commission of Inquiry.

Remark: With respect to my failure, the Faculty of Education offered a chance to re-enter and retake its program if I kept lesson plans for a year.  However, in 2005-6 I worked for only 3 months in education. Then in 2006-7, I worked for a full year in a high school, but duties changed often, and I was out of my depth.  Next in 2007-8, the Quebec government did not want unqualified teachers in the classroom. So the condition that I teach for a year and keep lesson for it became unattainable. 

www.whyslopes.com
English Quebec Math  Education Nonsense

Road Safety Message (Online here in 1995, a decade before the Quebec Government advocated in its) 

Area Intro
Copy Right Matters
Curriculum Cuts
Intermediate Objectives
MEQ Objectives

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 116

Secondary 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

[Algebra Lesson Notes - All levels]

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