Multiplication and Math Practice: Do Jo Boaler’s Math Theories Hold Water?

A recent New York Times commentary by American engineering professor Barbara Oakley has, once again, stirred up much public debate focused on the critical need for “Math practice” and why current “Discovery Math” methodologies are hurting students, and especially girls. “You and your daughter can have fun throwing eggs off a building and making paper-mache volcanoes, “ she wrote, “but the only way to create a full set of options for her in STEM is to ensure that she has a solid foundation in math.”  Mathematics is “the language of science, engineering and technology,” Oakley reminded us. And like any language, she claimed, it is “best acquired through lengthy, in-depth practice.”

That widely-circulated commentary was merely the latest in a series of academic articles, policy papers, and education blog posts to take issue with the prevailing ideology in North American Mathematics education, championed by Professor Jo Boaler of Stanford University’s School of Education and her disciples.  Teaching the basics, explicit instruction, and deliberate practice are all, in Boaler’s view, examples of “bad math education” that contribute to “hating Math” among children and “Math phobia” among the populace. Her theories, promulgated in books and on the “YouCubed” education website, make the case that teaching the times tables and practicing “multiplication” are detrimental, discovering math through experimentation is vital, and making mistakes is part of learning the subject.

Boaler has emerged in recent years as the leading edu-guru in Mathematics education with a wide following, especially among elementary math teachers. Under the former Ontario Kathleen Wynne government, Boaler served as a prominent, highly visible member of the Math Knowledge Network (MKN) Advisory Council charged with advancing the well-funded “Math Renewal Strategy.” Newsletters generated by the MKN as part of MRS Ontario featured inspirational passages from Jo Boaler exhorting teachers to adopt ‘fun’ strategies and to be sensitive to “student well-being.”

While Boaler was promoting her “Mathematics Mindset” theories, serious questions were being raised about the thoroughness of her research, the accuracy of her resources, and the legitimacy of her claims about what works in the Math classroom. Dr. Boaler had successfully weathered a significant challenge to her scholarly research by three Stanford mathematics professors who found fault with her “Railside School” study. Now she was facing scrutiny directed at YouCubed by cognitive science professor Yana Weinstein and New York Math teacher Michael Pershan.  Glaring errors were identified in YouCubed learning materials and the research basis for claims made in “Mistakes Grow Your Brain” seriously called into question. The underlying neuroscience research by Jason S Moser and his associates does not demonstrate the concept of “brain sparks” or that the “brain grows” from mistakes, but rather that people learn when made aware of their mistakes. 

Leading researchers and teachers associated with researchED are in the forefront of the current wave of evidence-based criticism of Boaler’s theories and contentions.  Australian teacher-researcher Greg Ashman, author of The Truth About Teaching (2018), was prompted by Jo Boaler’s response to the new UK math curriculum including “multiplication practice” to critically examine her claims. “Memorizing ‘times tables,’ “she told TES, was “terrible.” “I have never memorised my times tables,” she said. “I still have not memorised my times tables. It has never held me back, even though I work with maths every day.”  Then for clarification:” “It is not terrible to remember maths facts; what is terrible is sending kids away to memorise them and giving them tests on them which will set up this maths anxiety.”  

Ashman flatly rejected Boaler’s claims on the basis of the latest cognitive research. His response tapped into “cognitive load ” research and it bears repeating: “Knowing maths facts such as times tables is incredibly useful in mathematics. When we solve problems, we have to use our working memory which is extremely limited and can only cope with processing a few items at a time. If we know our tables then when can simply draw on these answers from our long term memory when required. If we do not then we have to use our limited working memory to figure them out when required, leaving less processing power for the rest of the problem and causing ‘cognitive overload’; an unpleasant feeling of frustration that is far from motivating.”

British teachers supportive of the new Math curriculum are now weighing-in and picking holes in Boaler’s theories. One outspoken Math educator, “The Quirky Teacher,” posted a detailed critique explaining why Boaler was “wrong about math facts and timed tests.” Delving deeply into the published research, she provided evidence from studies and her own experience to demonstrate that ‘learning maths facts off by heart and the use of timed tests are actually beneficial to every aspect of mathematical competency (not just procedural fluency).” “Children who don’t know their math facts end up confused,” she noted, while those who do are far more likely to become “better, and therefore more confident and happy, mathematicians.”

Next up was University of  Pennsylvania professor Paul L. Morgan, Research Director of his university’s Center for Educational Disabilities. Popular claims by Boaler and her followers that “math practice and drilling” stifle creativity and interfere with “understanding mathematical concepts” were, in his view, ill-founded. Routine practice and drilling through explicit instruction, Morgan contended in Psychology Today, would “help students do better in math, particularly those who are already struggling in elementary school.”  Based upon research into Grade 1 math achievement involving 13,000 U.S. students, his team found that, of all possible strategies, “only teacher-directed instruction consistently predicted greater first grade achievement in mathematics.”

Critiques of Jo Boaler’s theories and teaching resources spark immediate responses from the reigning Math guru and her legions of classroom teacher followers. One of her Stanford Graduate Education students, Emma Gargroetzi, a PhD candidate in education equity studies and curator of Soulscrutiny Blog, rallied to her defense following Barbara Oakley’s New York Times piece.  It did so by citing most of the “Discovery Math” research produced by Boaler and her research associates. She sounded stunned when Oakley used the space as an opportunity to present conflicting research and to further her graduate education.

Some of the impassioned response is actually sparked by Boaler’s own social media exhortations. In the wake of the firestorm, Boaler posted this rather revealing tweet: “If you are not getting pushback, you are probably not being disruptive enough.” It was vintage Boaler — a Mathematics educator whose favourite slogan is “Viva la Revolution.”  In the case of Canadian education, it is really more about defending the status quo against a new generation of more ‘research-informed’ teachers and parents.

Far too much Canadian public discourse on Mathematics curriculum and teaching simply perpetuates the competing stereotypes and narratives. Continued resistance to John Mighton and his JUMP Math program is indicative of the continuing influence wielded by Boaler and her camp. Doug Ford’s Progressive Conservative Government is out to restore “Math fundamentals” and determined to break the curriculum gridlock.  The recent debate over Ontario Math education reform on Steve Paikin’s TVOntario program The Agenda featured the usual competing claims, covered familiar ground, and suggested that evidence-based discussion has not yet arrived in Canada.

What explains Professor Jo Boaler’s success in promoting her Math theories and influencing Math curriculum renewal over the past decade? How much of it is related to YouCubed teaching resources and the alignment with Carol Dweck’s ‘growth mindset’ framework? Do Boaler’s theories on Math teaching work in the classroom? What impact, if any, have such approaches had on the decline of Math achievement in Ontario and elsewhere?  When will the latest research on cognitive learning find its way to Canada and begin to inform curriculum reform?

 

 

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The Ontario Hall-Dennis Report, Fifty Years On: What Remains of Its Legacy?

Fifty years after its appearance, the June 1968 Ontario Hall-Dennis Report lives on in the philosophy and pedagogy that it seeded in the schools of Ontario and right across Canada. In its ringing endorsement of child-centred learning, its imagery of playful school children, its spirit of experimentation, and its flirtation with gradeless education, the Report left its mark and defined the limits of so-called “progressive education” for a generation or more. It also ushered in a student-centred philosophy harkening back to days of the renowned American educational progressive educator John Dewey that remains deeply ingrained in elementary education.

The “progressive education” mantra bequeathed by Hall-Dennis exposed deep divisions over core philosophy and preferred teaching practice.  Education professor Ken Osborne perhaps put it best in his 1999 guide to the Canadian education debate:  In its day, the Report was revered as “the shining star of educational reform,” but two decades later it was considered passe — and “painted as at best wholly-minded idealism and, at worst, reckless irresponsibility.” 

Child-centred teaching, teacher as facilitator, and learning centres many not have originated with the Hall-Dennis Committee, but all were sanctified in the Report and became preferred methodologies associated with ‘good teaching.’ From that time forward, child-centred approaches did become like a “Holy Writ” among elementary school teachers, while high school educators considered it symptomatic of “dumbing down” subject teaching.  A few smaller elementary schools, even today, like the Halifax Independent School, are explicit in their adherence to Hall-Dennis inspired progressive ideals.

One Toronto elementary school, Alpha Alternative School, founded in 1971, continues to hold a candle for the educational philosophy and approach to education espoused in the Hall-Dennis Report.  It also provides a lens through which to examine and take stock of the Report’s key principles.  The first line of the 1968 report “The truth shall make you free” remains today as the essential mission of Alpha and its 2007 satellite site, Alpha II.

Student-directed education inspired by Hall-Dennis springs from Article 26 of the Universal Declaration of Human Rights of the United Nations enshrined in the 1968 report. Based upon that Declaration, the Report proposed fundamental principles for Ontario school education:

1. the right of every individual to have equal access to the learning experience best suited to his needs, and
2. the responsibility of every school authority to provide a child-centered learning continuum that invites learning by individual discovery and inquiry.

While the principles conveyed a spirit of openness, it was firmly committed to “progressive education” and surprisingly prescriptive about “how child-centred learning should take place.” The key tenets of the Hall-Dennis Report convey a sense of certitude that implies imparting a “new wisdom” in education:

The Child-Centred Curriculum

“The curriculum of the future must be child-oriented and must provide opportunities for choice within broadly defined limits. Teachers at every level, supported by qualified counselors, will be required to guide each child along his own critically determined path, far more flexible than a computer guide, but critical in the sense that the learning programs initiated and developed will best meet the needs of each child at the time best suited to his development. ” (H-D R, p. 52)

The Open and Flexible Learning Environment

“There is increasing evidence that children are often better taught in groups centered around interests, and as individuals, than in classes consisting of 30 or 40 pupils. Group teaching and individual learning programs break down the old formal class organization. But despite advocacy of clustering children around interests, supported by appropriate resource teachers, children, particularly young children, seem more relaxed and at ease when identified with at least one home teacher…., so that she may be aware of the child’s changing moods and responses. “(H-D R, p. 56)

The Student- Attuned Curriculum for Young People

“A good curriculum must meet the needs and expressed desires of pupils. It creates in the school a pleasant and friendly environment in which young children know that they are appreciated and accepted; in which maturing young people will find that they and their ideas are respected; and in which all pupils find interest and satisfaction in learning. It gives a realistic and objective exposition of society and its institutions. It encourages pupils to ask questions, to contribute further information, and to express their opinions freely, and it encourages teachers to answer pupils’ questions truthfully as often and as fully as possible. At the same time, such a curriculum provides for studies related to institutions of higher or further education or which are needed to obtain specific qualifications.” ((H-D R, p. 56)

Eliminate Grade Promotion and Curtail Examinations

“The curriculum must provide for the individual progress of pupils. To make this possible, two major innovations are indicated: complete abolition of the graded system throughout the school; and the use of individual timetables at the senior level. The introduction of graded textbooks and the placing of pupils in ‘books’ or grades undoubtedly improved education in Ryerson’s day…. But during the last fifty years, as it has become increasingly difficult to retard and eliminate pupils at an early age by failure, the graded system has become an anomaly…. [Formal examinations are] “arbitrary measures of achievement” and “concepts of promotion and failure” should be “removed from the schools not to reduce standards, but to improve the quality of learning. The evaluation of pupils’ progress should be a continuous part of the learning process, not a separate periodic exercise….” (H-D R, p. 72)

Page 93—Developing a Sense of Responsibility in Students

“Teachers can take definite steps to develop a sense of responsibility in children, such as: Have pupils plan and manage their own routines of study; Encourage pupils to suggest ventures in learning which they would like to undertake;Encourage joint or group undertakings; Reduce assigned homework in favor of pupil-planned study or practice; Apply only those rules that are necessary for the maintenance of a healthy, invigorating and pleasant learning atmosphere; Give pupils practice in making decisions of a personal and social nature. ” (H-D R, p. 93)

The Teacher as Guide at the Side

“The modern professional teacher is a person who guides the learning process. He places the pupil in the center of the learning activity and encourages and assists him in learning how to inquire, organize, and discuss, and to discover answers to problems of interest to him. The emphasis is on the process of inquiry as well as on the concepts discovered.” (H-D R, p. 93)

Innovative Learning Environments – Cooperative Learning, Study Centres, Learn Through Doing

“In the future a school will contain various kinds and sizes of learning areas, including classrooms, small study centers, and large open areas. In a well-organized schoolroom efficient, flexible use is made of available resources, and routines proceed with a minimum of confusion and interference….. The organization of schoolroom routines should be regarded as a co-operative activity of teachers and pupils, operating within the general organization of the school. The establishment of routines should be an exercise in democracy in which pupils establish and maintain as many as possible of their own ‘rules,’ evaluating and revising them as conditions demand. This exercise provides for the development of self-discipline and responsibility….

The spotlight in the school is shifting from methods of teaching to experiences for learning, and the truly professional teacher now employs in each situation the methods that will enhance the quality of the learning experience of the pupils in his care….In establishing the atmosphere for learning the professional teacher remains sensitive to the interests and problems of pupils, and allows the direction or pace of the lesson to change as the situation demands. He realizes that for an individual child the sequence of steps in the lesson may be less important than a word of praise or kindness, or a sign of recognition or reassurance; indeed, such actions are themselves part of teaching ‘method.’ A teacher may actually be teaching very well when he is apparently doing little more than observing pupils at work; he does not believe that effective teaching demands constant activity on his part.” (H-D R, pp. 139-40)

Student Evaluation – and Assessment for Learning

“With the introduction of a child-centered program, evaluation is changing in both function and form: its function is to determine the effectiveness of the program in the pupil’s development; it takes the form of day-by-day observations of the pupil’s interests and activities, difficulties and achievements. Evaluation is part of the learning program, is often planned jointly by the pupils and the teacher, and provides for self-evaluation as well as for diagnosis. The process may involve a discussion of the effectiveness of a learning situation, of the degree of participation of the pupils, and of suggestions for improvement of study habits, research and discussion procedures, and use of reference materials.”(H-D R, pp. 142)

Democratic Schools and Teacher Autonomy

“The structure of the system and of the school itself should be a democratic one-one where the teacher has freedom, not one that is so rigidly bound by rules and regulations that he feels his freedom is being questioned. The teacher’s loyalty to the system will be conditional upon the degree to which the system and the individual school serve to make it possible for him to do his best work. The system that meets the professional needs of its teachers will usually have the highest teacher morale. “(H-D R, p. 157)

The Principal as Curriculum Leader

“The principal who sees himself as the curriculum leader of the school acts as a consultant, adviser, and co-ordinator, and spends most of his time with children and teachers in psychological, sociological, and curricula activities. He subscribes to the theory that the aims of education are determined philosophically, and he realizes that striving for uniformity through standardized tests, external examinations, and other devices and controls has little to do with the attainment of objectives in education. Subjectivity is his accepted mode for educational endeavor; objectivity is desirable only in specific instances, subordinate to the major purposes of education. “(H-D R, p. 170)

Looking back, it is striking to see how much of the so-called “progressive orthodoxy” was articulated and extolled in a document that is all-too-often forgotten, especially among teachers born after its appearance. Few who lived through the Hall-Dennis era would miss the connective tissue linking contemporary “innovations” with concepts and ideas espoused in that Report.

What contemporary educational principles, concepts and pedagogical approaches find earlier justification in the Hall-Dennis Report?  Which of the Hall-Dennis reform proposals proved the most successful?  Which of the proposals simply fizzled and went nowhere?  Will there ever come a time when the vision is fully realized in K-12 education? 

Third and Final commentary in the Series.

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Flipping the System: Where Should Ground Up Education Reform Start?

Two Dutch classroom teachers, Jelmer Evers, and René Kneyber, have teamed up with Education International to produce a stimulating book with a great title, Flip the System: Changing Education from the Ground Up. It originated as a project inspired by a genuine classroom teacher-driven movement in the Netherlands where Jelmer, an education “progressive,” and  René, a self-declared “traditionalist,” joined forces to “reclaim our beloved teaching profession ourselves.”  So far, so good.

A funny thing seems to have happened to that grassroots project on its way to publication. The teacher initiators decided that “neoliberalism” was the source of “top-down” education managerialism and turned to its sworn enemy, Education International, the global coordinating organization for teachers’ unions. While classroom teachers like Evers, Kneyber and Brit Tom Bennett ignited the movement, they turned to EI for funding and the ‘usual suspects’ for added credibility in an attempt to go global.

With a little help from EI’s Fred van Leeuven, a few familiar professional education change promoters began to surface, including Finnish “Fourth Wave” proponents Andy Hargreaves, Dennis Shirley and Pasi Salhberg. .Professor Gert Biesta, editor-in-chief of Studies in Philosophy and Education, 1999-2014, also joined the cause. It’s a real credit to the two editors that they actually found a place for the founder of ResearchED, Tom Bennett, a refreshingly forthright, independent voice for today’s teachers. His chapter on “The Polite Revolution in Research and Education” explains the origins of ResearchED and testifies to his commitment to put teachers “back in the drivers seat’ of the system. 

Bennett’s 2013 book, Teacher Proof, was a direct hit on educational orthodoxy supported by flimsy explanations resting only on questionable social science theories. After a decade of teaching in East London, he knew something was amiss because a succession of pedagogical panaceas such as Neuro-Linguistic Programming (NLP), Brain Gym, learning styles, and ‘soft persuasion techniques’  simply did not work in the classroom.

His teacher training and PD programs promoted the latest methods of educating children and directing their behaviour as if they were holy scripture. “It took me years, “Bennett now says, ” to realize that the thing I smelled was a bunch of rats in lab coats.”  Defenders of such pedagogical science justified such initiatives with little more than the common phrase ” the research shows.”  Digging into the research behind such schemes, he discovered that whole movements like “Learning Styles” were “built on quicksand.”  Freeing regular teachers from the “intellectual bondage” and “Cargo Cult Science” sustaining these orthodoxies became the whole raison d’etre of what became the British teacher-led movement for reform.

The ResearchED founder is notably more independent in outlook than many of the contributors to Flip the System. Co-editor Evers, in particular, sees neo-liberalism not only behind accountability testing but concealed in a whole range of initiatives threatening teacher autonomy. Judging from the introduction and his writings, he’s a committed education progressive viewing education though a very explicit ideological lens. Collected works sometimes make for strange bedfellows. In this case, Evers  writings exhibit the same “bias confirmation” difficulties that so trouble Bennett and the key members of ResearchED.

Two very independently minded teachers, Andrew Old and Greg Ashman , are conspicuous in their absence from the collection. British secondary school teacher Andrew Old, creator of Scenes from the Battleground Blog, is a ResearchED supporter who is vigilant in exposing “fakery” in British schools and a staunch defender of tried-and-true teaching methods. For his part, Australian teacher-researcher Greg Ashman, host of Filling the pail Blog, is an effective voice for teachers ‘sick-and-tired’ of  teacher forums that sound like a “share this idea” educational echo chamber.

In two recent commentaries, “The Trendiest Arguments for Progressive Education,” Old skillfully deconstructs four of the hollow claims currently made by ‘romantic’ progressives: 1) firm discipline and setting exams adversely affects children’s mental health;  2) “traditional” vs. “progressive” debates are stale, irrelevant and meaningless; 3) defenders of higher academic standards and knowledge-based curriculum perpetuate “white privilege” in schools; and 4) every new ‘reform’ initiative is an example of the “free market conspiracy” enveloping the system. Like Bennett, he decries the absence of plausible evidence supporting some of these outlandish claims.

Ashman specializes in exposing fallacies perpetuated by educationists and bureaucrats that complicate and frustrate the lives of working teachers. He’s a serious educational researcher pursuing his PhD at UNSW and his posts draw upon some of the best recent research findings. In his July 31, 2015 commentary, “Nothing to prove (but I will, anyway…),” he zeroes in on research that demonstrates “explicit instruction” is superior to “constructivist” methods such as “discovery learning’ and ‘maker-space’ activities. He really digs into the research, citing twelve different studies from 1988 to 2012, ranging from Project Follow Through to Barak Rosenshine’s  2012 “Principles of Instruction” study. Where, he asks, is the hard evidence supporting the current constructivist approaches to teaching and learning?

One of the studies unearthed by Ashman is an October 2011 research report, “All students fall behind,” providing a critical independent assessment of the Quebec Ministry of Education progressive reform, Project-Based Learning initiative from 2000 to 2009. The Reform was implemented top-down and right across the board in all grade levels with little or no input from classroom teachers. Comparing Quebec student performance in Mathematics from Grades 1 to 11, before and after the “constructivist” Reform initiative, Catherine Haeck, Pierre Lefebvre, and Philip Merrigan document a steady decline in scores, compromising that province’s status as the leader in Mathematics performance. “We find,” they concluded,” strong evidence of negative effects of the reform on the development of students’ mathematical abilities.”

Reinventing education from the ground up will, of necessity, involve engaging and listening to teachers.  The education domain is littered with failed initiatives driven by totally unproven pedagogical theories. Following research where it leads instead of riding ideological hobby-horses would be a much sounder basis for education policy initiatives. In that regard, the researchED pilistines have much more to offer than many of the contributors to the hottest new book in education reform.

Turning the education upside down has its appeal, especially if you are a working teacher in today’s school system. Why do educational orthodoxies like traditional teaching and constructivism have such staying power? Why are teachers too often on the outside looking in when the latest education panacea comes down the pipe?  If teachers were truly engaged and empowered, would explicit instruction again rule the school day?

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The Private Tutoring Explosion: Why are Parents Turning to Tutors After School?

The McTutor World is on the rise. Private tutoring is growing by leaps and bounds and it’s now the fastest growing segment of Canadian K-12 education. Since the financial meltdown of 2008, the tutoring business has rebounded, particularly in major Canadian cities and the burgeoning suburbs. From 2010 to 2013, Kumon Math centre enrollment in Canada rose by 23% and is now averaging 5 % growth a year. It’s estimated that one in three city parents in Toronto, Montreal, Vancouver and Calgary now hire private tutors for their kids.

My recent radio interviews on CBC Radio Drive Home shows (September 4-5, 2014) focused on the trend and tackled the bigger question of why today’s parents are turning increasingly to after-school tutors to supplement the regular school program. That’s a question that begs for a more thorough, in-depth explanation.

The expansion of private tutoring is driven by a combination of factors. The world is changing and, for good or ill, we now inhabit an increasingly competitive global world. International student testing is one symptom and so are provincial testing programs — and parents are better informed than ever before on where students and schools rank in terms of student achievement.  While high school graduation rates are rising, student performance indicators are either flat-lined or declining, especially in Atlantic Canada. In most Canadian provinces, university educated parents also have higher expectations for their children and the entire public education system is geared more to university preparation than to employability skills.

System issues play a critical role in convincing parents to turn to tutors. Promoting “Success for All” has come to signify a decline in standards and the entrenchment of “social promotion” reflected in student reports overflowing with edu-babble about “learning outcomes” but saying little about the pupils themselves.  When parents see their kids struggling to read and unable to perform simple calculations, reassurances that “everything is fine” raises more red flags.

New elementary school curricula in Literacy and Mathematics only compound the problem —and both “Discovery Math” and “Whole Language” reading approaches now face a groundswell of parental dissent, especially in Manitoba, Alberta, British Columbia, and Ontario.  It’s no accident that the private tutors provide early reading instruction utilizing systematic phonics and most teach Math using traditional numbers based methods.

The tutoring business is definitely market-driven and more sensitive to public demand and expectations. Canadian academic researchers Scott Davies and Janice Aurini have shown the dramatic shift, starting in the mid-1990s, toward the franchising of private tutoring. Up until then, tutoring was mostly a “cottage industry” run in homes and local libraries, mainly serving high schoolers, and focusing on homework completion and test/exam preparation. With the entry of franchises like Sylvan Learning, Oxford Learning, and Kumon, tutoring evolved into private “learning centres” in cities and the affluent suburbs.  The new tutoring centres, typically compact 1,200 sq. ft spaces in shopping plazas, offered initial learning level assessments, study skills programs, Math skills instruction, career planning, and even high school and university admissions testing preparation.

Hiring private tutors can be costly, but parents today are determined to come to the rescue of their struggling kids or to give the motivated child an extra edge.  Today it’s gone far beyond introducing your child to reading with “Fun with Phonics” and some Walmart stores even stock John Mighton’s tutoring books for the JUMP Math program. An initial assessment costs $99 to $125 and can be irresistable after reading those jargon-filled, mark-less reports. For a full tutoring program, two nights a week, the costs can easily reach $2,o00 to $3,000 a school year.  Once enrolled, parents are far more likely to look to private independent schools, a more expensive option, but one that can make after-school family life a lot simpler and less hectic.

The tutoring explosion is putting real pressure on today’s public schools. Operating from 8:30 am until 3:00 pm, with “bankers’ hours,” regular schools are doing their best to cope with the new demands and competition, in the form of virtual learning and after-hours tutoring programs.  Parents are expecting more and, like Netflicks, on demand!  That  is likely to be at the centre of a much larger public conversation about the future of traditional, bricks and mortar, limited hours schooling.

What explains the phenomenal growth of private tutoring?  With public schools closing at 3:00 pm, will today’s parents turn increasingly to online, virtual education to plug the holes and address the skills deficit?  How will we insure that access to private tutors does not further deepen the educational inequities already present in Canada and the United States? Will the “Shadow Education” system expand to the point that public schools are forced to respond to the competition?  

 

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Correcting Math Education: What Gives Students the Best JUMP Start?

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.

Mighton 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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Discovery Learning and Fuzzy Math: Will the PISA 2012 Results Signal the Beginning of the End?

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?”

In 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.

The 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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