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Posts Tagged ‘Mathematics Education’

A model Grade 6 classroom in Sherwood Park, Alberta, now comes fully equipped with every imaginable solution to coping with fidgety kids, including spin bikes, exercise balls, rotating stools and stand-up desks. The latest classroom pacifiers, ‘Wiggle stools,’ are being hailed as a godsend by a harried Grade 2 classroom teacher in a Sackville, NB.

jumpyclassroomsherwoodparkSchools across Canada went to great lengths to re-engage fidgety students in what will likely always be known as the Year of Self-Regulation. Coping with today’s restless generation of kids now requires every conceivable pacifier, including spin bikes, exercise balls, wiggle stools and stand-up desks.

That is why in any Canadian survey of the top five K-12 education issues in 2016, coping with today’s antsy students would top the list.

Mindfulness and Self-Regulation

High anxiety educators have also embraced the latest panacea known as ‘mindfulness’ and are going whole hog into ‘self-regulation’ of their students.  It’s the brainchild of American advocate Jon Kabat-Zinn who transformed ‘Buddhist mindfulness’ into teaching practice and his Canadian apostle York University’s Stuart Shanker. That approach has emerged in 2016 as the latest wave in what has been characterized as a pseudoscience reform movement.

wobblechairsdallastx“It helps with their focus, helps with their creativity, helps promote problem-solving, gives them some way to self-regulate as they have a place to burn-off energy or to gain energy as they need it,” Alberta teacher Kurt Davison told Global TV News Edmonton. Eleven-year-old Connor Harrower heartily agreed: “In other classes, I’m sitting at desks and I’m bored.”

Teacher Misconduct and Discipline

A CBC-TV Marketplace investigation into ‘Teacher Discipline’ in Canada’s provincial school systems aired in April 2016 and immediately drew attention to glaring weaknesses in  professional evaluation, regulation, and discipline. It revealed that only two provinces, Ontario and British Columbia, provide public access to teacher discipline records, and most of the others continue to conceal information from parents and the public, including cases of serious misconduct, incompetence and sexual abuse

Fewer than 400 teaching certificates were revoked in Canada (outside Quebec) over a ten year period from 2005 to 2015, which represented one in every 5,780 teacher certificates each year. In the U.S., the revocation rate was about 30 per cent higher. According to the most recent data from the National Association of State Directors of Teacher Education and Certification, the American figure in 2015 was one certificate out of every 4,360.

The Marketplace investigation raised a fundamental question: If your child’s teacher was punished for a serious offence such as sexual, physical or verbal misconduct, would you be able to find out about it? Depending on where you live, the answer was ‘probably not.’

Chronic Student Math Woes

Ontario students, like those in most Canadian provinces, continued to struggle mightily in mathematics. Grade 4 Ontario students lagged behind their counterparts in Kazakhstan, Lithuania and 25 other jurisdictions in mathematics, landing them in the middle of the pack in the 2015 TIMSS assessment, a U.S.-based global study of math and science.

Those startling TIMSS results came on the heels of a dismal showing from Grade 3 and 6 students on the latest provincial test by the Education Quality and Accountability Office (EQAO), with scores dropping to the lowest levels in more than 15 years. Only 63 per cent of Grade 3s met the acceptable standard, dropping to half in Grade 6.

Math standards advocates such as Teresa Murray of @FixONTmath claimed that pumping $60-million more into a math strategy might not make much of a difference without a return to teaching the fundamentals in the early grades.

B.C. ‘Class Composition’ Court Ruling

The British Columbia Teachers’ Federation (BCTF) won a critical Supreme Court of Canada decision in November 2016 that ended a union legal battle that began in 2002. That ruling immediately restored clauses removed from the B.C. teachers’ contract by the Gordon Campbell Liberal Government dealing with class size, the number of special needs students in a class, and the number of specialist teachers required in schools.

The BCTF court victory was forecasted to have far-reaching ramifications for contact negotiations across Canada. Teachers in Nova Scotia embroiled in a contract dispute of their own took heart from the decision prohibiting the ‘stripping’ of ‘working conditions’ and denying teachers the right to bargain on those issues.

PISA 2015 Test Results Fallout

Crowing about the showing of Canadian students in the 2015 Programme for International Student Assessment (PISA) report was widespread and the current Chair of the Council of Ministers of Education (CMEC), P.E.I. Education Minister Doug Currie, was first-off-the mark on December 6, 2016 to hail the student results in the three subjects tested: science, reading and math.

The real devil was evident in the details and more clearly portrayed in the OECD’s own “Country Profile” for Canada. Yes, 15-year-olds in three Canadian provinces (Alberta, British Columbia, and Quebec) achieved some excellent results, but overall Mathematics scores were down, especially in Manitoba and Saskatchewan, and students in over half of our provinces trailed-off into mediocrity in terms of performance. Our real success was not in performance, but rather in reducing the achievement gap adversely affecting disadvantaged students.

Final Words of Wisdom

Looking ahead to 2017, we can find some solace in the April 2016 comments of Dr. Stan Kutcher, one of the world’s leading experts on teen mental health. “We are not facing a mental health crisis in schools,” he pointed out, but we do have to learn to distinguish between “the daily slings and arrows of outrageous fortune” and those “more serious conditions requiring treatment.”

Why and how did Canadian elementary schools become so enthralled with “mindfulness” and “self-regulation”?  What critical education issues were either obscured or ignored in pursuit of pseudo-scientific cures for today’s classroom challenges? What will be the legacy of turning the younger grades into therapeutic classroom environments? What does all of this portend for Canadian K-12 education in 2017 and beyond? 

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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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