Quebec students head the class when it comes to mathematics. On the Pan-Canadian Assessment Program (PCAP) tests of Grade 8 students, written in June 2016 and released in early May 2018, those from Quebec finished first in Mathematics (541), forty points above the Canadian mean score of 511 and a gain of 26 points over the past six years.

The latest national results solidified Quebec’s position as our national leader in mathematics achievement on every comparative test over the past thirty years. How and why Quebec students continue to dominate and, in effect, pull up Canada’s international math rankings deserves far more public discussion. Every time math results are announced, it generates a flurry of interest, but it does not appear to have encouraged other provinces to try to emulate that success.

Since the first International Assessment of Educational Progress (IEAP) assessment back in 1988 and in the next four national and international mathematics tests up to 2000, Quebec’s students generally outperformed students from other Canadian provinces at grades four, eight and eleven. That pattern has continued right up to the present and demonstrated impressively on the most recent Program of International Student Assessment (PISA 2015) where Quebec 15-year-olds scored 544, ranking among the world’s top education jurisdictions.

One enterprising venture, launched in 2000 by the B.C. Ministry of Education under Deputy Minister Charles Ungerleider, did tackle the question by comparing British Columbia’s and Quebec’s mathematics curricula. That comparative research project identified significant curricular differences between the two provinces, but the resulting B.C. reform initiative ran aground on what University of Victoria researchers Helen Raptis and Laurie Baxter aptly described as the “jagged shores of top-down educational reform.”

Over the past thirty years, the reasons for Quebec dominance in K-12 mathematics performance are coming into sharper relief. The B.C. Ministry of Education 2000 research project exposed and explained the curricular and pedagogical factors and subject specialists, including both university mathematics specialists and mathematics education professors, have gradually filled in the missing pieces. Mathematics education faculty with experience in Quebec and elsewhere help to complete the picture.

Five major factors can now be identified to explain why Quebec students continue to lead the pack in pan-Canadian mathematics achievement:

- Clearer Curriculum Philosophy and Sequence:

The scope and sequence of the math curriculum is clearer, demonstrating an acceptance of the need for integration and progression of skills. The 1980 Quebec Ministry of Education curriculum set the pattern. Much more emphasis in teacher education and in the classroom was placed upon building sound foundations before progressing to problem-solving. Curriculum guidelines were much more explicit about making connections with previously learned material.

Quebec’s Grade 4 curriculum made explicit reference to the ability to develop speed and accuracy in mental and written calculation and to multiply larger numbers as well as to perform reverse operations. By grade 11, students were required to summon “all their knowledge (algebra, geometry, statistics and the sciences) and all the means at their disposal…to solve problems.” “The way math is presented makes the difference,” says Genevieve Boulet, Mount St. Vincent University Mathematics education professor with prior experience preparing mathematics teachers at Université de Sherbrooke.

- Superior Math Curriculum

Fewer topics tend to be covered at each grade level, but in more depth than in B.C. and other Canadian provinces. In Grade 4, students are generally introduced, right away, to Numbers/Operations and the curriculum unit on measurement focuses on mastering three topics– length, area, and volume — instead of a smattering of six or seven topics. Concrete manipulations are more widely used to facilitate comprehension of more abstract math concepts. Much heavier emphasis is placed on Numbers/Operations as Grade 4 students are expected to perform addition, subtraction, and multiplication using fractions. Secondary school in Quebec begins in Grade 7 (Secondaire I) and ends in Grade 11 (Secondaire V) and, given the organizational model, that means students are more likely to be taught by mathematics subject specialists. Quebec’s Grade 11 graduation courses, Mathematics 536 (Advanced), Mathematics 526 (Transitional) and Mathematics 514 (Basic), were once quite different, offering the same range of topics but covered to a different depth. More recently, Quebec has revamped its mathematics program, and now offers three streamed courses, designated 565 Science Option, 564 Technical and Science Option, and 563 Cultural, Social, Technical and Science Option.

- More Extensive Teacher Training

Teacher preparation programs in Quebec universities are 4-years long, providing students with double the amount of time to master mathematics as part of their teaching repertoire, a particular advantage for elementary teachers. In Quebec faculties of education, elementary school math teachers must take as many as 225 hours of university courses in math education; in some provinces, the instructional time averages around 40 hours.

Teacher-guided or didactic instruction has been one of the Quebec teaching program’s strengths. Annie Savard, a McGill University education professor, points out that Quebec teachers have a clearer understanding of ‘didactic’ instruction, a concept championed in France and French-speaking countries. They are taught to differentiate between teaching and learning. “Knowing the content of the course isn’t enough, “ Savard says. “You need what we call didactic [teaching]. You need to unpack the content to make it accessible to students.”

Teacher pedagogy in mathematics makes a difference. Outside of Quebec, the dominant pedagogy is child-centred and heavily influenced by Jean Piaget and behaviorist theories of learning. Prospective teachers are encouraged to use ‘discovery learning’ and to respond to stimuli by applying the appropriate operations. In Quebec, problem-solving is integrated throughout the curriculum rather than treated as a separate topic. Shorter teacher training programs, according to Boulet, shortchange teacher candidates and can adversely affect their preparedness for the classroom. Four-year programs afford education professors more time to expose teacher candidates to the latest research on cognitive psychology which challenges the efficacy of child-centred approaches to the subject.

- Secondary School Examinations

Students in Quebec still write provincial examinations and achieving a pass in mathematics is a requirement to secure a graduation (Secondaire V) diploma. Back in 1992, Quebec mathematics examinations were a core component of a very extensive set of ministry examinations, numbering two dozen, and administered in Grades 9 (Sec III), Grade 10 (Sec IV), and Grade 11 (Sec V). Since 2011-12, most Canadian provinces, except Quebec, have moved, province by province, to either eliminate Grade 12 graduation examinations, reduce their weighting, or make them optional. In the case of B.C., the Grade 12 provincial was cancelled in 2012-13 and in Alberta the equivalent examination now carries a much reduced weighting in final grades. In June of 2018, Quebec continues to have final provincial exams, albeit fewer and more limited to Mathematics and the two languages. Retaining exams has a way of keeping students focused to the end of the year; removing them has been linked to both grade inflation and the lowering of standards.

- Preparedness Philosophy and Graduation Rates

Academic achievement in mathematics has remained a system-wide priority and there is much less emphasis in Quebec on pushing every student through to high school graduation. From 1980 to the early 2000s, the Quebec mathematics curricula was explicitly designed to prepare students for mastery of the subject, either to “prepare for further study” or to instill a “mathematical way of thinking” – reflecting the focus on subject matter. The comparable B.C. curriculum for 1987, for example, stated that mathematics was aimed at enabling students to “function in the workplace.” Already, by the 1980s, the teaching of B.C. mathematics was seen to encompass sound reasoning, problem-solving ability, communications skills, and the use of technology. Curriculum fragmentation, driven by educators’ desires to meet individual student needs, never really came to dominate the Quebec secondary mathematics program.

Quebec’s education system remains that of ‘a province unlike the others.’ While the province sets the pace in mathematics achievement, a February 2018 report demonstrated that it lags significantly behind the others in graduation rates. Comparing Quebec’s education system with that of Ontario, Education Minister Sebastien Proulx points out, is “like comparing apples to oranges.” The passing grade in Quebec courses is 60 per cent compared to 50 per cent in Ontario and the requirements for a graduation diploma are more demanding because of the final examinations. When the passing grade was raised in 1986-87, ministry official Robert Maheu noted, the decision was made to firm up school standards. Student achievement indicators, particularly in mathematics, drove education policy and, until recently, unlike other provinces, student preparedness remained a higher priority than raising graduation rates.

Quebec Math and the Rest – *Vive le Difference*

School systems are, after all, not always interchangeable, and context is critical in assessing student outcomes. As David F. Robitaille and Robert A. Garden’s 1989 IEA Study reminded us, systems are “in part a product of the histories, national psyches, and societal aspirations” of the societies in which they develop and reside. While British Columbia and the other English-speaking provinces have all been greatly influenced by American educational theorists, most notably John Dewey and the progressives, Quebec is markedly different. Immersed in a French educational milieu, the Quebec mathematics curriculum has been, and continues to be, more driven by mastery of subject knowledge, didactic pedagogy, and a more focused, less fragmented approach to student intellectual development.

Socio-historical and cultural factors weigh heavily in explaining why Quebec continues to set the pace in Mathematics achievement. Challenging curricula and final examinations produces higher math scores, but it also contributes to lower graduation rates.

* A revised version of this post was published October 22, 2018 by the IRPP magazine, Policy Options.

on October 25, 2018 at 9:44 pm |John MyersThe thread begins with “Quebec students head the class when it comes to mathematics. On the Pan-Canadian Assessment Program (PCAP) tests of Grade 8 students, written in June 2016 and released in early May 2018, those from Quebec finished first in Mathematics (541), forty points above the Canadian mean score of 511 and a gain of 26 points over the past six years.”

541-511= THIRTY points or a bit above 5%. This + the fact that all governments, regardless of political party, seem to get the numbers wrong when figuring out policy indicates that MAYBE this issue is more complex than suggested.

on October 29, 2018 at 10:19 am |TeresaIt may be more complex, but these factors seem to be a good baseline for improvement. I would also wonder if Quebec parents need to take their elem aged children to tutors/spend hours teaching them to compensate for perceived failures in curric./resources and pedagogy. Despite unprecedented spending on math ed., thousands of Ontario families have found they have to take charge of their child’s math education.

on October 29, 2018 at 3:33 pm |John MyersIt would be nice to have some numbers on tutoring like -how many do tutoring? characteristics of tutored population? score gains? long-term achievement effects? decisions based on “need” or “perceived need”? Moreover, do we KNOW what the goals of math ed are: e.g., what math understandings, other than EQAO scores, do students need at the end of elementary, secondary, post-secondary, workplace, citizenship role, “life”? If my claim regarding “political math” is valid…? What is the connection, if any, of students teachers passing some math qualifying test and their ability to teach math effectively? Lots of questions but answers…?

on October 30, 2018 at 12:26 amTeresaWe dont have numbers. I have my own theories as to why this is not well studied, but I will leave that aside. There have been thousands of stories from 9 out of 10 provinces. For about 12 or so years, basics disappeared in many areas of the province. And I mean children simply did not learn how to do subtraction with regrouping, division and other very simple arithmetic. When I tutored at this time, no child had learned to divide and none knew times tables. That was a given. Serious pressure has brought about some improvements and I hear and see far fewer stories of basics being absent. Much more progress is needed. I have tutored many students over the last 6 years. Four boards, numerous private schools, across the SES spectrum. Always see exact same issues. It has gone from critical to a re appearance of fundamentals of arithmetic, but sporadic and topics not learned well and spotty across province. Most of the children I have tutored should not have needed a tutor, but parents were desperate.

The recent survey by OISE did ask a question abt tutoring and came up with 1 in 4 I believe, but there are many others who teach their own children after achool and have not used a tutor. The pain and financial burden on parents has been huge and of course many have been left behind.

My position is that by the end of grade 8 all students should have had a very robust opportunity to learn arithmetic. This is what opens doors, provides opportunity. Fractional arithmetic is crucial, but weak in curric. I have no difficulty with careful use of inquiry, interesting math, puzzles that stretch, some ambiguous problems, but I would say we remain quite far from a solution.

Many new teachers are graduates of current curriculum and require support and education, however, teachers have been routinely blamed by ed establishment for 20 yrs now and I would say that most of the answers lie above teacher level. ( Blame might be too strong a word, but I fear testing teachers could be a bit of a red herring) And here I would mention ResearchEd. They provide a large tent and are asking many important questions.

Was the worst ed crisis I saw in 32 years. My petition Ontario Math Petition has many comments.

on October 29, 2018 at 3:51 pm |DougIt seems Ontario has a net negative score of 1. This does not seem to constitute an emergency. Ontario became the poverty capital of Canada during the McGuinty Wynne government 2003-2018. Poor kids always do badly. More poor kids = lower scores.

Want to pump up math scores notwithstanding the above?

1) Phase in only math university majors (or engineering…) to teach elementary math on an itinerant basis the way French is taught.

2) Dedicate more curriculum time to math.

3) Blend Discovery/Inquiry math with traditional math. Insist multiplication tables are learned one way or another.

Many charters and vouchers in USA believed very strongly that a strong dose of traditional math only would fix the math problem. The results show that public schools using blended or more Inquiry math approaches consistently posted higher NAEP scores than charters or vouchers.

The Public School Advantage : Why Public Schools Outperform Private Schools

Lubinski & Lubienski University of Chicago Press 2013

on October 29, 2018 at 11:51 pm |TeresaDoug, multiple other international tests and standardized tests have shown a greater decline than a single point. Poverty not withstanding we have had complaints from across the spectrum from parents (and many teachers) about the curric pedagogy and resources. My own bd after constant complaints simply banned the approved text. Not sure of current situation. I cant tell you how many times I nearly flung it through the window. Many who can simply flee to tutors for even young typical children.

I certainly do not simply advocate a trad approach, ( the devil is in the details though) however, it is not acceptable for parents to see no option, but to go to a tutor or have to teach their own child at night.I am speaking about children as young as grade 1 or 2. I have also heard far too many sad stories from far too many teachers, who feel they have no where to turn.

on October 30, 2018 at 1:10 amDougMath is down in many places. I believe when the research is it it will show very little relationship to curriculum or pedagogy. Far more to do with poverty.

on October 30, 2018 at 1:51 am |TeresaPerhaps, but that does not address the other points I made

re parents, no division, gr.2 tutoring, concerns across the SES spectrum are unimportant) I realize you like the big picture, but that does not mean the finer details and costs to individual families are unimportant.

on October 30, 2018 at 10:13 am |John MyersAs Doug might point out, poor kids cannot afford tutoring. My parents certainly could not afford it.

So we are left with good teaching, as we have always been.

on October 30, 2018 at 11:44 am |TeresaJohn did you read my posts?

on October 30, 2018 at 2:13 pm |John MyersOf course, hence my questions

on October 30, 2018 at 1:45 pm |TeresaFor the last 10 yrs I taught teachers were forced to teach according to prescribed methods/weak curric. My bd was particularly strict, but much teacher autonony completely vanished. There were numerous ways of ensuring compliance, I won’t go into them all here. There is only so much a teacher can/or should do to try and circumvent the intense pressure to conform. This intense pressure from above .forced compliance and has damaged math education in Ontario and recovery takes much longer than destruction. Younger teachers were much more susceptible than older ones.

Everything was about high scores, not teaching. I believe it has relaxed a little, but damage done.

Younger teachers are also graduates of this particularly bad time in math education and may well have had their

own math ed. very damaged.

Education is far more complex than ‘good teaching’. Time to look at the entire system, the quality of research, teacher ed and accountability above teacher level. S

on October 30, 2018 at 2:18 pm |DougOECD PISA keeps telling us we have very little to worry about.

on October 30, 2018 at 2:30 pm |DougI dont consider Hong Kong, Macao, or Singapore, Taipei or Shanghai, to be real countries. Totally artificial, However Japan, Korea, are.

PISA math real countries

1) Japan

2) Korea

3) Switzerland

4) Estonia

5) Canada

60 other nations

Sccience -real countries

1) Japan

2) Estonia

3) Finland

4) Canada

5-65 Other countries

https://www.businessinsider.com/pisa-worldwide-ranking-of-math-science-reading-skills-2016-12

on October 30, 2018 at 2:59 pm |DougThis article and the TDSB research behind it, demonstrates that we are dealing with a rich-poor problem much more than an an Inquiry-traditional problem.

https://www.huffingtonpost.ca/ian-cooper/ontario-math-education-problem_a_23408209/

on October 30, 2018 at 3:47 pm |John MyersWe can always improve but best to encourage than to scare.

And I still await a clear statement as to the goal of mathematics in society since we are more able to reach a target when we know what the end goal is. Grade eight is NOT an end goal though it is a checkpoint.

We need numbers to help explain the world but numbers while necessary are not sufficient.

on October 30, 2018 at 4:33 pm |TeresaI have no numbers. Retired in 2012 with many increasingly serious questions. Had never heard of ResearchEd, but all my questions were their questions. Very broad agreement with rheir approach, not every detail. But they have helped me answer a few of them. I won t rehash all of that or the math detail rn.

on October 30, 2018 at 7:01 pm |John MyersGiven that this thread is about math. number count.

on October 30, 2018 at 9:27 pm |TeresaI am not able to do such a count.

on October 30, 2018 at 10:04 pm |TeresaI can only say abt 2012 or so there was a change to a balanced curric. Principals got the message that students must learn basics. A number of math computer programmes were widely circulated and they have a more systematic approach to fundamentals.A line appeared on an offficial website stating that Min had always intended that basics be taught. I cannot remember location of this site although I have looked since. There has been a shift in language used in publications etc. I also had a reasonably sympathetic conversation with a math ed prof re this topic. I won’t go into details, but felt some genuine concern for parents. . These changes folliowed declining scores and much media pressure. However, they have not been consistent across the province or so I have heard. I have noticed an improvement as I have tutored, but think that there is still much work to be done. Family anecdotes and reports from 2000 to 2012 will remain anecdotes unless research is done.

on October 31, 2018 at 9:58 am |John MyersAgree that

– more needs to be done

– the quality in the “field” varies

– anecdotes are far from sufficient which is why we have EQAO in Ontario

– EQAO is better than nothing but we need more- and NOT more testing

– quality pd and follow-up costs $$$

– the current provincial govt is highly unlikely to invest in better education

on October 31, 2018 at 11:07 amDougObama was looking at a proposal before he was finished. It involved identifying excellent math teachers and paying them a bonus to work in schools which are underperforming in math. They would do full time math on a rotary basis. The incentive would be high, say $20 000 /yr. With an application, interview process.

on October 31, 2018 at 11:55 am |John MyersI would be careful about too many links to what happens in the US since

– what happens is often not good

– what they do too often gets pushed into Canada

We are NOT the same in some key ways, though in other ways we are.

I see this in my family and in my work on both sides of the border.

on October 31, 2018 at 12:46 pm |TeresaI agree somewhat John. Except I have seen no shortage of money. All those anecdotes could easily be researched, but won’t be. Research simply moves on to all the next initiatives. I guess I naively believe that researchers have an interest in checking and rechecking their own work.

I have watched this pattern for 32 years and that is why I support ResearchEd. Much more light must be shed on ed research, how it is used and misused and its quality. This is a very long term project, but finally the genie is out of the bottle.

The days of simply focusing on the teacher and what he or she is doing correctly or incorrectly must end. I have been appalled at some of the research/PD I have seen and endured

and have witnessed the considerable damage.

on October 31, 2018 at 12:57 pm |TeresaI realize such topics will always remain anecdotal. Important issues are frequently and deliberately ignored every day.

on October 31, 2018 at 1:31 pm |John Myersthe human condition too often

on October 31, 2018 at 7:07 pm |TeresaSo yes it is more complex than the data suggests as you originally stated. And I will continue to always mention the pain individual families went through (and still go through) knowing full well it is anecdotal.

on October 31, 2018 at 8:02 pm |John MyersOK so what do we do with the individual bad cases?

on October 31, 2018 at 11:41 pm |TeresaWell there are 1000s of them.My petition was signed by 4000 and I have heard from countless others. I suspect I have only scratched the surface. We continue working towards ensuring this is fixed and I hope that going forward many of the questions raised by ResearchEd start to be answered. There are always casualities in anything that is done, but we make conscious atttempts to minimize that number. The math issue has been just been a particularly egregious example.

Rdg instruction is a second one and perhaps a littke simpler to solve as the details have been worked out over time. The research used by the Ministry is incomplete. Many problems are flowing from this and impact is greater on more vulnerable.

The short answer is we need to look at ed research.

on November 1, 2018 at 2:11 am |DougCanada is currently number 1 on the planet in reading for real countries, tied with HK which is not representative of China and behind only Singapore which is a totally artificial creation. They send their poor back across the bridges to Malaysia at night where the poor kids go to school.

Doesn’t seem like much of a reading problem to me. We are ahead of the other 64 nations in the OECD.