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Posts Tagged ‘Discovery Math’

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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Ontario Progressive Conservative leader Doug Ford swept into power at Queen’s Park  on June 7, 2018 with an explicitly populist agenda in K-12 education. Campaigning with the slogan “Ford for the People,” he pledged to reform the school curriculum, defend provincial testing,introduce a moratorium on school closures, and consult more with disaffected communities. Most of these planks in the Ontario PC education “promise package” were presented in plain and simple language that appropriated “back to the basics” philosophy and “common sense” reform.

Presenting these policies in such unvarnished “populist language” made it easy for the Ontario media to caricature “Ford Nation” and earned him the derision of the Ontario education establishment.   On what The Globe and Mail  aptly termed “the mourning after,” the core interests who dominated the 15-year-long Dalton McGuinty- Kathleen Wynne era sounded traumatized and completely disoriented.  Premier Doug Ford clearly scares the Ontario education “elites,” but such straight talk only endears him more to “Ford Nation” supporters committed to “taking back” the public schools.

Doug Ford’s PC Education promises, once dismissed as “bumper sticker” politics, will now get much closer scrutiny.  The fundamental challenge facing Ford and his new Education Minister will be to transform that reform philosophy and list of education promises into sound and defensible education policy.  It not only can be done, but will be done if Ford and his entourage seek proper advice and draw upon the weight of education research supporting the proposed new directions.

The overall Ontario PC education philosophy rests on a complete rejection of the Wynne Liberal Toronto-centric vision and education guru driven brand of “identity politics” in education.  “At one time, Ontario schools focused on teaching the skills that matter: reading, writing and math. This approach helped to prepare our kids for the challenges of work and life. Today, however, more and more of our schools have been turned into social laboratories and our kids into test subjects for whatever special interests and so-called experts that have captured Kathleen Wynne’s ear.”

Premier-elect Ford’s campaign captured well the groundswell of public dissent over top-down decision-making and the tendency to favour “inclusion” in theory but not in practice. It was expressed in this no-nonsense fashion: “By ignoring parents and focusing on narrow agendas or force-feeding our kids experimental curricula like ‘Discovery Math’ the Liberals are leaving our children woefully unprepared to compete with other students from across Canada and around the world. And instead of helping our kids pass their tests, the NDP want to cancel the tests altogether.”

The Ford Nation plan for education appealed to the “little guy” completely fed-up with the 15-year legacy of “progressive education” and its failure to deliver more literate, numerate, capable, and resilient students. Education reform was about ‘undoing the damage’ and getting back on track: “It’s time to get back to basics, respect parents, and work with our teachers to ensure our kids have the skills they need to succeed.”

The specific Ontario PC policy commitments in its 8-point-plan were:

  • Scrap discovery math and inquiry-based learning in our classrooms and restore proven methods of teaching.
  • Ban cell phones in all primary and secondary school classrooms, in order to maximize learning time.
  • Make mathematics mandatory in teachers’ college programs.
  • Fix the current EQAO testing regime that is failing our kids and implement a standardized testing program that works.
  • Restore Ontario’s previous sex-ed curriculum until we can produce one that is age appropriate and broadly supported.
  • Uphold the moratorium on school closures until the closure review process is reformed.
  • Mandate universities to uphold free speech on campuses and in classrooms.
  • Boost funding for children with autism, committing  $100-million more during the mandate.

Most of the Ford Nation proposals are not only sensible, but defensible on the basis of recent education research.  Ontario Liberal Education policy, driven by edu-gurus such as Michael Fullan and Andy Hargreaves and championed by People for Education was out-of-sync with not only public opinion but education research gaining credence though the emergence of researchED in Canada.   The Mathematics curriculum and teacher education reforms, for example, are consistent with research conducted by Anna Stokke, Graham Orpwood, and mathematics education specialists in Quebec.

Provincial testing, school closure reform and addressing autism education needs all enjoy wide public support. Former Ontario Deputy Minister of Education Charles Pascal, architect of EQAO, supports the recommendation to retain provincial testing, starting in Grade 3.  The Ontario Alliance Against School Closures, led by Susan Mackenzie, fully supports the Ontario PC position on fixing the Pupil Accommodation Review process.  Few Ontarians attuned to the enormous challenges of educating autistic children would question the pledge to invest more in support programs.

The Ontario PC proposal to reform sex-education curriculum is what has drawn most of the public criticism and it is a potential minefield. The Thorncliffe Park Public School parent uprising and the voices of dissenting parents cannot be ignored, but finding an acceptable compromise will not be easy.  Separating the sex-education component from the overall health and wellness curriculum may be the best course of action.  Tackling that issue is a likely a “no-win” proposition given the deep differences evident in family values. Forewarned is forearmed.

How will the Doug Ford Ontario PC Government transform its populist electoral nostrums into sound education policy?  How successful with the Ford govenment be in building a new coalition of education advisors and researchers equipped to turn the promises into specific policies? Where are the holes and traps facing Ford and his Education Minister?  Can Doug Ford and his government implement these changes without sparking a return to the “education wars” of the 1990s?  

 

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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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