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Posts Tagged ‘Quebec Math’

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:

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

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