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Archive for the ‘Mathematics Education’ Category

With the release of the 2015 Program for International Student Assessment (PISA) on the horizon,  the Organization for Economic Cooperation and Development (OECD) Education Office has stoked-up the “Math Wars” with a new study. While the October 2016 report examines a number of key questions related to teaching Mathematics, OECD Education chose to highlight its findings on “memorization,” presumably to dispel perceptions about “classroom drill” and its use in various countries.

mathsubtractionboardThe OECD, which administers the PISA assessments every three years to 15-year-olds from around the globe, periodically publishes reports looking at slices of the data. It’s most October 2016 report,  Ten Questions for Mathematics Teachers and How PISA Can Help Answer Them, based upon the most recent 2012 results, tends to zero-in on “memorization” and attempts to show that high-performing territories, like Shanghai-China, Korea, and Chinese-Taipei, rely less on memory work than lower-performing places like Ireland, the UK, and Australia.

American Mathematics educator Jo Boaler, renowned for “Creative Math,” jumped upon the PISA Study to buttress her case  against “memorization” in elementary classrooms. In a highly contentious November 2016 Scientific American article, Boaler and co-author Pablo Zoido, contended that PISA findings confirmed that “memorizers turned out to be the lowest achievers, and countries with high numbers of them—the U.S. was in the top third—also had the highest proportion of teens doing poorly on the PISA math assessment.” Students who relied on memorization, they further argued, were “approximately half a year behind students who used relational and self-monitoring strategies” such as those in Japan and France. 

Australian education researcher Greg Ashman took a closer look at the PISA Study and called into question such hasty interpretations of the findings.  Figure 1.2: How teachers teach and students learn caught his eye and he went to work interrogating the survey responses on “memorization” and the axes used to present the data.  The PISA analysis, he discovered, also did not include an assessment of how teaching methods might be correlated with PISA scores in Mathematics.  Manitoba Mathematics professor Robert Craigen spotted a giant hole in the PISA analysis and noted that the “memorization” data related to “at-home strategies of students” not their instructional experiences and may wel;l indicate that students who are improperly instructed in class resort to memorization on their own.

mathpisateacherdirectedgraphWhat would it look like, Ashman wondered, if the PISA report had plotted how students performed in relation to the preferred methods used on the continuum from “more student-oriented instruction” to “more teacher-directed instruction.” Breaking down all the data, he generated a new graph that actually showed how teaching method correlated with higher math performance and found a “positive correlation” between teacher-directed instruction and higher Math scores. “Correlations,” he duly noted, “do not necessarily imply causal relationships but clearly a higher ratio of teacher-directed activity to student orientation.”

Jumping on the latest research to seek justification for her own “meta-beliefs” are normal practice for Boaler and her “Discovery Math” education disciples. After junking, once again, the ‘strawmen’ of traditional Mathematics — “rote memorization” and “drill,” Boaler and Zoido wax philosophical and poetic: “If American classrooms begin to present the subject as one of open, visual, creative inquiry, accompanied by growth-mindset messages, more students will engage with math’s real beauty. PISA scores would rise, and, more important, our society could better tap the unlimited mathematical potential of our children.” That’s definitely stretching the evidence far beyond the breaking point.

The “Math Wars” do generate what University of Virginia psychologist Daniel T. Willingham has aptly described as “a fair amount of caricature.” The recent Boaler-Zoido Scientific American article is a prime example of that tendency. Most serious scholars of cognition tend to support the common ground position that learning mathematics requires three distinct types of knowledge: factual, procedural and conceptual. “Factual knowledge,” Willingham points out, “includes having already in memory the answers to a small set of problems of addition, subtraction, multiplication, and division.” While some students can learn Mathematics through invented strategies, it cannot be relied upon for all children. On the other hand, knowledge of procedures is no guarantee of conceptual understanding, particularly when it comes to complexites such as dividing fractions. It’s clear to most sensible observers that knowing math facts, procedures and concepts is  what counts when it comes to mastering mathematics.

mathtimestableimageSimply ignoring research that contradicts your ‘meta-beliefs’ is common on the Math Education battlefield. Recent academic research on “memorization” that contradicts Boaler and her entourage, is simply ignored, even that emanating from her own university. Two years ago, Shaozheng Qin and Vinod Menon of Stanford University Medical School led a team that provided scientifically-validated evidence that “rote memorization” plays a critical role in building capacity to solve complex calculations.

Based upon a clinical study of 68 children, aged 7 to 9, studied over the course of one year, their 2014 Nature Neuroscience study, Qin, Menon et al. found that memorizing the answers to simple math problems, such as basic addition or multiplication, forms a key step in a child’s cognitive development, helping bridge the gap between counting on fingers and tackling more complex calculations. Memorizing the basics, they concluded, is the gateway to activating the “hippocampus,” a key brain structure for memory, which gradually expands in “overlapping waves” to accommodate the greater demands of more complex math.

The whole debate over memorization is suspect because of the imprecision in the use of the term. Practice, drilling, and memorization are not the same, even though they get conflated in Jo Boaler’s work and in much of the current Mathematics Education literature. Back in July 2012, D.T. Willingham made this crucial point and provided some valuable points of distinction. “Practice,” as defined by Anders Ericsson, involves performing tasks and feedback on that performance, executed for the purpose of improvement. “Drilling’ connotes repetition for the purpose of achieving automaticity, which – at its worst, amounts to mindless repetition or parroting. “Memorization,” on the other hand, relates to the goal of something ending up in long-term memory with ready access, but does not imply using any particular method to achieve that goal.

Memorization has become a dirty word in teaching and learning laden with so much baggage to the point where it conjures up mental pictures of “drill and kill” in the classroom. The 2016 PISA Study appears to perpetuate such stereotyping and, worst of all, completely misses the “positive correlation” between teacher-directed or explicit instruction and better performance in mathematics.

Why does the PISA Study tend to associate memorization in home-study settings with the drudgery of drill in the classroom?  To what extent does the PISA Study on Mathematics Teaching support the claims made by Jo Boaler and her ‘Discovery Math’ advocates? When it comes to assessing the most effective teaching methods, why did the PISA researchers essentially take a pass? 

 

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A lively national conversation is underway in the United States over stalled upward mobility and stark income inequality and it has a more genteel echo in Canada.  Many North American educators point to poverty as the explanation for American students’ mediocre test scores and it also serves as a favoured rationale for explaining away the wide variations in achievement levels among and within Canadian provinces. Only recently have policy analysts, boring down into the PISA 2012 Mathematics data, begun to look at the alarming achievement gap between states and provinces, the relationship between education expenditures and performance levels, and the bunching of students in the mid-range of achievement.

PISA2012CanadaGraphicThe socio-economic determinists offer a simple-minded, mono-causal explanation for chronic student under-performance. American education policy analyst Michael Petrilli and Brandon Wright of The Thomas B. Fordham Institute recently recapped the standard lines: If teachers in struggling U.S. schools taught in Finland, says Finnish educator Pasi Sahlberg, they would flourish—in part because of “support from homes unchallenged by poverty.” Michael Rebell and Jessica Wolff at Columbia University’s Teachers College argue that middling test scores reflect a “poverty crisis” in the United States, not an “education crisis.” Adding union muscle to the argument, American Federation of Teachers president Randi Weingarten calls poverty “the elephant in the room” that accounts for poor student performance.

The best data we have to tackle the critical questions comes from the OECD Program for International Student Assessment (PISA), which just released its annual Education at a Glance 2015 report.  For its own analyses, PISA uses an index of economic, social, and cultural status (ESCS) that considers parental occupation and education, family wealth, home educational resources, and family possessions related to “classical” culture. PISA analysts use the index to stratify each country’s student population into quartiles. That broadens the focus so it’s not just about addressing the under-performance of disadvantaged children.

MathScoresSES2012The PISA socio-economic analysis identifies the key variations among international educational jurisdictions. Countries like Belgium and France are relatively better at teaching their higher-status students, while other countries like Canada and Finland do relatively better at instructing students from lower-status families. Contrary to past assumptions, the United States falls almost exactly on the regression line. It does equally well (or equally poorly, if you prefer) at teaching the least well-off as those coming from families in the top quartile of the ESCS index.

A Fall 2014 Education Next report by Eric Hanushek, Paul Peterson and Ludger Woessmann pointed out the wide variations, country-to-country, in overall Mathematics proficiency.   Some 35 percent of the members of the U.S. class of 2015 (NAEP) reach or exceed the proficiency level in math. Based on their calculations, this percentage places the United States at the 27th rank among the 34 OECD countries. That ranking is somewhat lower for students from advantaged backgrounds (28th) than for those from disadvantaged ones (20th).

Overall assessments of Mathematics proficiency on PISA offer no real surprises. Compared to the U.S., the percentage of students who are math proficient is nearly twice as large in Korea (65%), Japan (59%), and Switzerland (57%). The United States also lags behind Finland (52%), Canada (51%), Germany (50%), Australia (45%), France (42%), and the United Kingdom (41%). Within the U.S., the range is phenomenal – from a high of 51% in Massachusetts to a low of 19 % in Mississippi.

Cross-national comparisons are misleading, because Canadian students have plateaued on the PISA tests over the past decade.  While Canada was still among the high-level achievers, performance of the country’s 15-year-olds in mathematics has declined, with a 14-point dip in the past nine years. While performance in reading has remained relatively stable, the decline in science performance was “statistically significant,” dipping from an average of 534 in 2006 and 529 in 2009.

MathPISA2012RangesMuch like the United States, Canada exhibits significant variations from one provincial school system to another.  A 2013 Canadian Council of Ministers of Education Canada (CMEC) review of the OECD PISA 2012 Mathematics performance levels revealed the stark achievement inequalities. Four Canadian provinces set the pace – Quebec, British Columbia, and Ontario – and the remaining six are a drag on our average scores. Fully 25% of Prince Edward Island students score Below Level 2, below the OECD average (23%), in Mathematics proficiency. The other provinces with the next highest levels of under-performers were: Manitoba (21%), Newfoundland/Labrador(21%), Nova Scotia (18%), and New Brunswick (16%).

There is no case for complacency in Canada, as pointed out, repeatedly, by Dr. Paul Cappon, former CEO of the Canadian Council on Learning (2005-2011) and our leading expert on comparative international standards. For a “high-achieving” country, Canada has a lower proportion of students who perform at the highest levels of Mathematics on recent PISA tests (CMEC 2013, Figure 1.3, p. 25).  Canada’s 15-year-olds are  increasingly bunched in the mid-range and, when it comes to scoring Level 4 and above on Mathematics,  most score at or below the OECD average of 31 %.  The proportion of high-achievers (Level 4 and above in 2012) was, as follows: PEI (22%); Newfoundland/Labrador (27%); Nova Scotia (28%); Manitoba (28%); Saskatchewan (33%); and Ontario (36%). Mathematics students from Quebec continue to be an exception because 48% of students continue to score Level 4 and above, 17 points above the OECD average score.

Students coming from families with high education levels also tend to do well on the PISA Mathematics tests. The top five OECD countries in this category are Korea (73%), Poland (71%), Japan (68%)Germany (64%) and Switzerland (65%), marginally ahead of the state of Massachusetts at 62%. Five other American states have high-achievement level proficiency rates of 58% or 59%, comparable to Czech Republic (58%) and higher than Canada (57%) and Finland (56%). Canada ranked 12th on this measure, well behind Korea, Poland, Japan, Switzerland and Germany.

Educators professing to be “progressive” in outlook tend to insist that we must cure poverty before we can raise the standards of student performance. More pragmatic educators tend to claim that Canadian schools are doing fine, except for the schools serving our disadvantaged populations, particularly Indigenous and Black children.  Taking a broad, international perspective, it appears that both assumptions are questionable. There are really two achievement gaps to be bridged – one between the affluent/advantaged and the poor/disadvantaged and the other one between Canadian high achievers and their counterparts in the top PISA performing countries.

Does low Socio-Economic Status (SES) marked by child and family poverty set the pattern for student achievement in a deterministic fashion?  To what extent can and do students break out of that mold? How critical are other factors such as better teacher quality, higher curriculum standards, and ingrained ethno-cultural attitudes? Do school systems like Canada and Finland tend to focus on reducing educational inequalities at the expense of challenging their high achievers?  Is this the real reason that many leading western G21 countries continue to lag behind those in Asia? 

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Today the Organization for Economic Development and Cooperation (OECD) has succeeded in establishing the Program of International Student Assessment (PISA) test and national rankings as the “gold standard” in international education. Once every three years since 2000, PISA provides us with a global benchmark of where students 15 years of age rank in three core competencies — reading, mathematics, and science. Since its inception, United States educators have never been enamoured with international testing, in large part because American students rarely fare very well.

PISATestVisualSo, when the infamous OECD PISA Letter was published in early May 2014 in The Guardian and later The Washington Post, the academics and activists listed among the initial signatory list contained the names of some familiar American anti-testing crusaders, such as Heintz-Deiter Meyer (SUNY, Albany), David Berliner (Arizona State University), Mark Naison (BAT, Fordham University), Noam Chomsky (MIT) and Alfie Kohn, the irrepressible education gadfly. That letter, addressed to Andreas Schleicher, OECD, Paris, registered serious concerns about “the negative consequences of the PISA rankings” and appealed for a one cycle (three-year) delay in the further implementation of the tests.

The global campaign to discredit PISA earned a stiff rebuke in Canada. On June 11 and June 18, 2014, the C.D. Howe Institute released two short commentaries demonstrating the significant value of PISA test results and effectively countering the appeal of the anti-PISA Letter. Written by Education Fellow John Richards the two-part report highlighted the “Bad News” in Canada’s PISA Results and then proceeded to identify What Works (specific lessons to be learned) based upon an in-depth analysis of the once every three-year tests. In clear, understandable language, Richards identified four key findings to guide policies formulated to “put Canadian students back on track.”

The call for a pause in the PISA tests was clearly an attempt to derail the whole international movement to establish benchmarks of student performance and some standard of accountability for student achievement levels in over 60 countries around the world. It was mainly driven by American anti-testers, but the two Canadian-based signatories were radical, anti-colonialist academics, Henry Giroux (English and Cultural Studies, McMaster University) and Arlo Kempf ( Visiting Professor, Program Coordinator, School and Society, OISE).

Leading Canadian educationists like Dr. Paul Cappon (former CEO, Council on Learning) and even School Change guru Michael Fullan remain supporters of comparative international student assessments. That explains why no one of any real standing or clout from Canada was among the initial group, and, by late June, only 32 Canadian educationists could be found among the 1988 signatories from all over the globe. Most of the home-grown signatories were well known educators in what might be termed the “accountability-free” camp, many like E. Wayne Ross (UBC) and Marc Spooner (U Regina), fierce opponents of “neo-liberalism” and its supposed handmaiden, student testing.

John Richards’ recent C.D.Howe commentaries should, at least temporarily, silence the vocal band of Canadian anti-testers.  His first commentary made very effective use of PISA student results to bore deeply into our key strengths and issues of concern, province-by-province, focusing particularly on student competencies in mathematics. That comparative analysis is fair, judicious, and research-based in sharp contrast to the honey-coated PISA studies regularly offered up by the Council of Ministers of Education (Canada).

The PISA results tell the story. While he finds Canadian students overall “doing reasonably well,”  the main concern is statistical declines in all provinces in at least one subject, usually either mathematics or reading.  Quebec leads in Mathematics, but in no other subject.  Two provinces (PEI and Manitoba) experienced significant declines in all three subject areas. Performance levels have sharply declined ) over 30 points) in mathematics in both Manitoba and Canada’s former leader, Alberta. Such results are not a ringing endorsement of the Mathematics curriculum based upon the Western and Northern Canada Protocol (WNCP). 

The warning signs are, by now, well known, but the real value in Richards’ PISA Results analysis lies in his very precise explanation of the actual lessons to be learned by educators.  What really matters, based upon PISA results, are public access to early learning programs, posting of school-level student achievement results, paying professional level teacher salaries, and the competition provided by achievement-oriented private and  independent (not for profit) schools. Most significantly, his analysis confirms that smaller class sizes (below 20 pupils per class) and increasing mathematics teaching time have a negligible effect on student performance results.

The C.D. Howe PISA Results analysis hit home with The Globe and Mail, drawing a favourable editorial, but was predictably ignored by the established gatekeepers of Canada’s provincial education systems. Why the reluctance to confront such research-based, common sense findings?  “Outing” the chronic under-performance of students from certain provinces ( PEI, Manitoba, New Brunswick, and Nova Scotia) is taboo, particularly inside the tight CMEC community and within the self-referenced Canadian Education Association (CEA) circles.  For the current Chair of CMEC, Alberta Education Minister Jeff Johnson any public talk of Alberta’s precipitous decline in Mathematics is an anathema.

Stung by the PISA warning shots, Canada’s provincial education gatekeepers tend to be less receptive to sound, research-based, practical policy correctives. That is a shame because the John Richards reports demonstrate that both “sides” in the ongoing  Education War are half-right and by mixing and matching we could fashion a much more viable, sustainable, effective policy agenda. Let’s tear up the existing and tiresome Neo-Con vs. Anti-Testing formulas — and re-frame education reform around what works – broader access to early learning, open accountability for student performance levels, paying respectable, professional-level teacher salaries, and welcoming useful competition from performance-driven private and independent schools.

What’s the  recent American Public Noise over “PISAfication” all about anyway?  Why do so many North American educators still tend to dismiss the PISA Test and the sound, research-based studies stemming from the international testing movement?  To what extent do John Richards’ recent C.D. Howe Institute studies suggest the need for a total realignment of provincial education reform initiatives?

 

 

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Teaching all children Mathematics may well be possible. That’s the inspiring lesson delivered by Dr. John Mighton at an April 24 Public Lecture, sponsored by the Mount Saint Vincent Faculty of Education, and attended by 150 curious educators and concerned parents.  He is the founder of JUMP (Junior Undiscovered Math Prodigies), a Toronto-based charitable organization that seeks to “multiply the potential in children” and to instill in them the joy of truly mastering mathematics.

MightonJUMPMathMighton is an incredibly talented mathematician on a mission.  Founded as a kitchen-table tutoring group in 1998, JUMP Math is presently challenging  the prevailing math education “discovery math”  ideology  embraced by North American curriculum consultants and reinforced in textbooks and online resources published by giant learning industry multinationals, Pearson and Oxford/Nelson. Since June of 2013, JUMP Math is breaking out with new adoptions in Manitoba, Calgary, and Vancouver where teachers are looking to significantly improve elementary level student math performance.

The founder of JUMP Math shot to prominence in 2003 with the publication of his book, The Myth of Ability.  Leading mathematicians like Dr. Robert Dawson, Editor of the Canadian Mathematical Society Notes, sat up and took notice.  In the Newsletter, he compared Mighton to the classroom teacher Jaime Escalante in the inspiring feature film, Stand and Deliver.  Both educators, he noted, embraced the idea that mathematics was “something that everybody can learn to do.”  His book, he added, “may be a big step in that direction.”

The Mathematics Education Wars are fought on contested pedagogical terrain and Mighton’s JUMP Math is emerging as a logical and welcome middle ground. In his recent lectures, he makes a persuasive case for a “balanced’ approach, starting with fundamentals and then empowering students to engage in creative problem-solving activities. He’s clear in explaining the limitations of both “drill and fill” traditional teaching and “fuzzy Math” promoted by romantic progressives.

“Students must be empowered to succeed” is his consistent message.  Beginning math instruction is broken down into tiny and carefully-structured chunks, that any student, working with any teacher, can learn thoroughly.  It’s teacher-guided but also exploratory and provides elementary students with the scaffolding needed to possess the knowledge and skills to eventually tackle creative problem-solving.  “Teachers are my heroes,” he says, because they are the ones who have driven the spread of JUMP Math, not the math consultants.

Canadians tend to be slow to embrace their own heroes and seek validation of their talents elsewhere. Mighton holds a Ph.D. in mathematics from the University of Toronto, completed NSERC  postdoctoral research in knot and graph theory, teaches Mathematics at U of T, and in 2010 was appointed an Officer of the Order of Canada. He’s also a playwright and script writer, known in Hollywood for his star turn in the feature film Good Will Hunting.

Mighton’s JUMP Math has evolved significantly over the past decade and now boasts supportive classroom effectiveness research, including studies at Toronto Sick Kids Hospital. in Lambeth, UK, and at the Mabin School.  While he was once “the nation’s math conscience,” Manitoba Education Minister James Allum now sees his approach as giving that province an edge over provinces like Alberta, wedded to the standard Western and Northern Canada Protocol (WNCAP) curriculum and continuing with “less successful methods”.

What’s standing in the way of Mathematics education reform?  Two key factors jump out as the obvious explanation – the established “Discovery Learning” ideology and the preponderant influence of its proponents, the late Richard Dunne (1944-2012), creator of Maths Makes Sense, and his Canadian counterpart, Dr. Marian Small, purveyor of Nelson mathematics problem-solving books.  They are a formidable force backed by the Pearson and Oxford/Nelson publishing conglomerates and a small army of textbook author replicators here in Canada.

Richard Dunne and his Canadian camp followers talk about mathematics but their real agenda is to promote a “whole school approach” to discovery learning.   His distinctive teaching style,  initiated at Reading Boys’ Grammar School in the late 1960s, uses concrete “manipulatives” to help kids understand math concepts.  Based upon his theories rather than research, Dunne cut a plastic cup into 10 pieces to demonstrate the meaning of decimals and then developed other dramatic demonstration techniques to introduce children to abstract ideas.

Dunne was a teacher and math consultant rather than a mathematician.  His earlier version of Maths Makes Sense published in the 1980s proved popular with teachers who were non-specialists, but was resisted by many university based mathematicians and then rejected by the British Government in 1989 with the introduction of a more rigorous National Curriculum. Panned in the U.K., his teaching methods enjoyed greater popularity in North America and his version of “Discovery Math”  made a comeback in 2007 with the re-publication of Maths Makes Sense.

Dunne’s “whole school approach” was embraced by North American math consultants education schools seeking to promote “discovery learning” in all subject areas.  Secondary school mathematics specialists remained skeptical and most stayed true to traditional methods, but Discovery Math made deep inroads among regular elementary teachers, often with little or no mathematics training.  It achieved the height of its influence in Canada when the WNCP Math curriculum spread across the provinces, supported by the Pearson Canada Math Makes Sense series of books and online resources.

Declining Mathematics achievement levels from 2003 to 2012, on PISA and Canadian national tests, began to raise red flags.  A WISE Math movement, sparked by Winnipeg math professors Anna Stokke and Robert Craigen, demonstrated the direct relationship between declining scores and the spread of  Dunne-inspired WNCP curricula.  In September 2013, Manitoba re-introduced Math fundamentals and approved JUMP Math for use in the schools.  Over the past year, the number of students studying JUMP Math has jumped from 90,000 to 110,000 as more and more schools are breaking with the entrenched Discovery Math methods and adopting a more systematic, teacher-guided, step-by-step progression in their teaching of early mathematics.

What’s standing in the way of Math correction in North American elementary schools?  Why has the “total school approach” made such inroads in the teaching of Mathematics in the early grades?  Can all or the vast majority of students be taught Mathematics? Will Dr. John Mighton eventually be vindicated for promoting fundamental building blocks?  Which of the Canadian provinces will be next in abandoning the core philosophy of the Discovery Math/WNCP curriculum?

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The ‘Big Test’ has hit us and rocked our education world. The sliding math scores of Canadian 15 year-olds outside Quebec have just captured all the headlines and a series of PISA news stories and commentaries identified the “discovery learning” approach to teaching mathematics as the source of the recent, and continuing decline. Columnist Konrad Yakabuski , a close observer of the American education wars, saw the declining math scores as a “damaging legacy” of discovery learning. We are falling backward, he claimed, in both excellence and equity raising the fundamental question – “Has the education elite learned its lesson?”

PISAMathKidsIn the OECD’s 2012 Programme for International Assessment (PISA) rankings released December 3, 2013, , Canada  dropped out of the top 10 in student mathematics scores, a decline that raised alarms about the country’s future prosperity. Canadian students placed 13th overall in mathematics, down three spots from 2009 and six spots from 2006, in the highly anticipated test conducted every three years and which measures how 15-year-olds around the world are doing in math, reading and science. Canada ranked behind many Asian economies, including Shanghai (China), Singapore, Korea and Japan, while the United States lagged far behind and 36th out of 65 participating countries.

PISA12RankingsThe PISA test jolt comes on the heels of declining math scores nationally and a surprisingly poor showing from youth on a recent OECD literacy and numeracy test. The Canadian math curriculum, ushered in over the past decade, catching the blame for lower scores for good reason.  Curricula like the Western and Northern Canada Protocol (WNCP) is out-of-sync with high performing Asian countries because it  places far more emphasis on real-world concepts  than on abstract thinking, standard algorithms, and practice. The accompanying OECD report, in fact,  noted that the top performers had more exposure to formal mathematics than word problems. That may explain why Shanghai students topped the rankings and performed three grade levels above those of most other nations.

Topping the PISA student performance rankings attracts international acclaim, school system imitators, and increasingly scarce public education dollars. Once reviled by Canadian anti-testing advocates, the PISA test results are –oddly enough –what provides the ammunition for much of what now passes for informed debate over quality, equity, and accountability in Canada’s provincial school systems. They also bred a certain Canadian complacency until the recent release of the 2012 student results.

National and provincial reputations now ride on the PISA results. From 2000 to 2006, the PISA test results catapulted Finland’s education system to star status, and that ‘Finnish infatuation,’ essentially swept the Canadian educational establishment off its feet, blinding us to the Quebec’s success in mathematics and Ontario’s progress in improving reading and closing the socio-economic education gap.

Between 2000 and 2009, Canada plateaued in overall student performance and Canadian students posted a 10 per cent decline in reading scores. This week’s PISA results confirm that 15-year-old Canadian students, with the execution of those in Quebec, are losing ground, particularly in mathematics.

The rise and fall of Alberta, Canada’s former top performing province, contains a few valuable lessons. Two decades ago, Alberta was the first province to really confront the global learning gap, forecasting that, if trends continued, Albertan and Canadian students were going to be left behind.  

Dr. Joe Freedman, a Red Deer radiologist, and Andrew Nikiforuk, a Calgary-based Globe and Mail columnist, raised the first alarm bells and founded Albertans for Quality Education.  In 1991, they convinced the Alberta Chamber of Resources (ACR) and the Conference Board of Canada to produce a truly ground-breaking study,  International Comparisons in Education, comparing Alberta math and science curriculum with that in Japan, Germany and Hungary.

Alberta’s mathematics and science curriculum was then virtually re-written and bench-marked against that of the top performing nations. Under Education Minister Jim Dinning, the province built its rock solid reputation on raising standards, student testing, school choice and charter schools.

While Alberta ranked first on the PISA tests and topped the Pan-Canadian Assessment Programme (PCAP) tests in literacy and science for most of two decades, it has slipped precipitously since 2006. Adopting the WNCP math curriculum with its “discovery learning” focus and the Finnish infatuation have been key factors in the decline.

The ‘Finnish solution’ began to lose its lustre after the 2009 PISA test when Finland saw its reading scores drop by 11 per cent. Outside of Canada, education policy analysts have now become far more enamoured with Asian school systems like Shanghai and Korea.

None of this seems to matter to Canadian ‘progressives,’ sponsoring a Canadian tour for Finnish education expert Pasi Sahlberg, promoting Finland as the “Global Fourth Way,” and seeking to curtail standardized testing. They are bent on turning back the dreaded “GERM,” the Global Education Reform Movement, supposedly carrying the plague of “neo-liberalism” and its principal strains — higher standards, school choice, and competition in public education.

The Alberta Teachers Association (ATA), armed with a 2012 report written by Sahlberg’s North American ally, Andy Hargreaves, now talks of “transforming Alberta education” with “The Fourth Way, “ and is out to dismantle provincial testing, curtail expanded classroom learning time, and block teacher assessment tied to student performance. More recently, the Finnish wave of “personalized learning” has reached British Columbia.

Finland, like Canada, got a jolt from the 2012 PISA test results. That will finally prompt education observers to acknowledge that Finnish education is fuzzy on standards.  It is, after all,  light on standardized testing, soft on homework, and promotes a “culture of trust” instead of accountability.

Looking deeper, Finland is also a “one provider” system with little or no choice for parents, delays the start of school until age 7, and streams students after Grade 9  into two tracks, academic and vocational, based upon arbitrary average-mark cut-offs.

The Canadian attraction to “discovery learning” and the rush to abandon standardized testing have both hit a significant bump in the road. In the wake of the 2012 PISA results, Canadians are awakening to the dangers of turning back the clock to the days of ‘accountability-free’ public education. Without PISA and the OECD follow-up research studies we are left almost completely in the dark on critical educational quality issues that matter for students and our public schools.

What are the powerful lessons of Canada’s recent decline in PISA test scores?  When will Canadian mathematics educators face reality and come to accept the need to develop a more rigorous, soundly-based curriculum providing a solid grounding in the fundamental skills?  Will Canada come to accept the need to stop being what Paul Cappon aptly termed “a school that never issues report cards”?  And finally, is the real message sinking in?

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The earth moved in Canadian Mathematics education in late June of 2013.  On June 17, 2013, Manitoba Education Minister Nancy Allen introduced a significant change in Elementary Mathematics education and stated: “Let’s face it: Doing Math in your head is important.”  Just eight days later, Nova Scotia Education announced a joint public-private partnership project aimed at motivating Grade 7 Math students at Halifax’s Oxford Elementary School by providing them with tablet computers and access to online mathematics resources, including lessons from Khan Academy.  In heralding the pilot project, private donor Jim Spatz of Southwest Properties claimed that it was “a huge opportunity to bootstrap our whole public education system.”

TeachingMathWhat did the two different Mathematics teaching initiatives in Manitoba and Nova Scotia have in common?  Each new project, in its own way, acknowledged that so-called “discovery-based learning” was falling short and helping kids to make sense of Math.  The unmistakable signal sent out by the two initiatives was that providing the fundamentals is making a definite comeback in Canada’s elementary mathematics classrooms.

Discovery-based learning in elementary Math classes is now under considerable attack. A feature article written by The Globe and Mail Education Reporter Caroline Alphonso (September 20, 2013) clearly explained why.  Parent concerns voiced by KItchener, Ontario parent Angus Gale were now being heard in many Canadian schools. ” The schools have such a broad concept of what they want to teach without nailing down the fundamentals of arithmetic., ” Gale says. ” They’re trying to create mathematicians, but you can’t teach that without teaching arithmetic.”

Student confusion and parent frustration with elementary Math curriculum and pedagogy have reached what Alphonso aptly described as “a tipping point.”  Ontario’s Minister of Education Liz Sandals has expressed concern about lagging student Math performance levels. Kumon Math reports a 23 per cent increase in enrolment over the past three years.  Spending untold hours teaching children the Math basics at home or paying rising fees for Kumon after school tutorial classes has got to stop.

A growing body of cognitive research, as well as a determined group of Mathematics professors, are now challenging the current status quo in elementary Mathematics education.  Without teaching foundational skills and basic algorithms for addition, subtraction and division, discovery-based learning is simply not benefiting most young learners. National math student scores are lagging.   On the 2009 OECD report of results, math performance decreased in Manitoba, New Brunswick, PEI, Newfoundland, Alberta and British Columbia.  Nova Scotia math performance has stagnated and Ontario’s most recent Grade 3 and 6 provincial test scores dipped for the fifth year in a row.

The Math teaching reform movement was initiated by two Manitoba mathematics professors, Anna Stokke and Robert Craigen. Since September 2011, the two professors have mounted a determined campaign to restore the basics and formed WISE Math – the Western Initiative for Strengthening Math Education.  They are strongly supported by John Mighton, a mathematician and founder of the JUMP Math program based upon similar methods.  “Kids need to know basic number facts,” Mighton says, “so they can work conceptually.”

Nova Scotia’s new Grade 7 Math Boosters pilot project is motivated by similar concerns.  After attending a Harvard Management Seminar, Jim Spatz became a passionate supporter of Khan Academy. and its founder’s methods of teaching mathematics and sciences.  Created in 2006 by business entrepreneur Salman Khan, the website provides more than 3,000 free instructional videos, including some very popular ones for teaching early mathematics.  The Math instructional lessons, as Manitoba teacher Michael Zwaagstra recently pointed out, demonstrate time-tested methods and all of the standard algorithms, the exact opposite of the approach favoured by curriculum consultants and taught to beginning teachers in today’s faculties of education.

So far, Manitoba is the only province that has fully restored teaching of the math basics. Starting this September, the revised Math curriculum specifies that, before the end of Grade 4 all students will be expected to know the conventional ways of doing math, to be skilled at mental computation, and to master basic equations without a calculator.

Why have Canadian Mathematics educators been so slow to respond to the mounting evidence that discovery-based methods simply do not work in the early grades?  What’s the real cause of lagging student performance in elementary level Mathematics — dumbed-down curriculum, flawed teaching methods, the shortage of subject specialists, or some combination of all of these factors?  To what extent is the Manitoba curriculum and pedogogical reform the harbinger of changes in other provinces?

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High school Mathematics exam results still make the headlines.  On June 30, 2010, The Halifax Chronicle Herald featured a front page news story headed “55% failed Grade 12 Math Exam.” The electronic version of the story (http://thechronicleherald.ca/Search/1189774.html) attracted over 90 comments, the vast majority of which were  critical of Mathematics teaching and learning in Nova Scotia.

Mathematics standards had taken another hit.  The stark facts:  Only 45% of all Grade 12 students writing the Grade 12 Regular 2009 provincial Mathematics Examination managed to pass, down from 51% in 2008. Most of the failing students still passed, because the exam only counted for 30% of the final grade.  Even more remarkably, with or without passing the Math Exam, some 83% of Nova Scotia’s Grade 12’s secured a graduation diploma.

Struggling to pass Mathematics is certainly nothing new, especially in Nova Scotia.  While researching The Grammar School book, I  discovered that fifty years ago, in July of 1959, the province was in an uproar over the abysmal Provincial Examination results, particularly in Mathematics.  Halifax’s two dailies, The Mail Star and The Chronicle Herald were full of stories and letters expressing outrage and dismay over the latest results.  Reading last week’s paper, was like deja vu.

Student performance in Mathematics has long been fraught with controversy.  In July 1992, the Mattel Company’s statuesque doll, Teen Talk Barbie, was caught saying that “Math class is tough!.”  When the story broke, the American Association of University Women went ballistic over the aspersion cast on all young women.  The beleaguered company scrambled to change the voice recording and managed to escape a public relations disaster.  It was the age of Reviving Ophelia and the story then was the plight of girls and their poor performance in Mathematics.

What has really changed?  Today, girls tend to outperform boys in Mathematics and in most other subjects.  Indeed, high school boys now lag significantly behind girls on provincial examination results in Quebec and Nova Scotia.  Standardized assessments of math and literacy skills in Ontario and elsewhere testify to this new “gender gap” in education.

Whatever the gender differences, both girls and boys still find mastering Mathematics a challenge.  The June 2009 Mathematics Examination results in Nova Scotia are only the most recent demonstration of the chronic problem. It is also abundantly clear that education officials and mathematics consultants have tried a variety of remedies and now appear to be completely stymied by student under-performance in Mathematics.

The official Nova Scotia response to the Grade 12 Math exam debacle was typical. Education Minister Marilyn More admitted to being troubled by the math exam scores, but offered little in the way of remediation. Yet another “new elementary math curriculum” was promised, beginning in 2011, that would be “more focused” and aim for “deeper understanding.”  One brave Department official, Dan Harrison, conceded that “too many math concepts” were presented to Grade 12 students in “the time available during the school year.”

The Mathematics results created a real furor. Halifax Herald columnist Marilla Stephenson blamed the results on the lack of academic rigour, the absence of homework, and the laissez  faire attitude of both parents and students. (http://thechronicleherald.ca/Opinion/1190181.html)  Rather surprisingly, no one mentioned that the 2008-09 school year was the worst ever in terms of school days lost through cancellations. My AIMS Research Study, “School’s Out , Again,” released in May 2010 (www.aims.ca) was completely ignored, even though it offered the first detailed analysis of the impact of lost days on actual student performance. In a year when Nova Scotia students lost between 8 and 15 teaching days because of cancellations, it was definitely a contributing factor.

Today’s students still can’t do Math! What’s the root of the problem — the academic demands of Mathematics curricula, the quality of Math teaching, the decline in student work ethic, the laissez faire attitude of many parents, or some combination of these factors?  Why, after wave after wave of curriculum reform, do students still struggle to master Mathematics?

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