PISA Mathematics Lessons: Why Zero-In on “Memorization” and Minimize Teacher-Directed Instruction?

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.

The 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.

What 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.

Simply 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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Local Education Democracy: What’s Killing Elected School Boards?

Regional school boards in Atlantic Canada like the Quebec English language boards are slowly dying of natural causes. The province of New Brunswick abolished elected school boards in March 1996, and they were eventually replaced by greatly weakened elected District Education Councils. More recently, Newfoundland/Labrador and Prince Edward Island (PEI) sacked elected boards and reverted to two provincial authorities, one each for English language and French language schools. In November 2015, PEI eliminated the one remaining English-language board and replaced it with an alternative parent consultation process.

Eight elected regional school boards are still standing in Nova Scotia, but their days may be numbered.  With the October 15 2015 municipal election on the horizon, the election of regional school board members has dropped completely off the public radar. That’s mostly because of the virulent spread of a potentially terminal democratic condition – acclamation disease.

Since 2012, when less than 40 per cent of eligible voters cast ballots for school board members, it’s much further advanced, especially outside Halifax. Surveying Nova Scotia’s eight school boards, 61 out of 97 school trustee positions (62.7%) will be uncontested and settled by “acclamation.”  Without the Halifax Regional School Board, some two out of every three (65.9%) of the seats failed to attract more than one candidate.

The Nova Scotia School Boards Association (NSSBA) 2016 campaign to drum up interest in school board elections has been a complete bust. A recent round of School Board candidate sessions, run by NSSBA independent of N.S. Municipal Affairs, for some reason, has netted fewer candidates than the last time. That glitzy website, School Board Elections.ca, intended to showcase democratic vitality, merely advertises the extent of the acclamation disease from board to board.

The drying-up of interest in running for school board seats could not have come at a worse time for those, like me, who still believe in local education democracy and legitimate public accountability.

Sparked by the November 2015 P.E.I. decision to completely eliminate the English language board, a 2016 N.S. Liberal Party AGM resolution on abolishing boards, presented by Halifax Region Liberals, not only passed, but attracted notable media attention. The official party policy calls upon the McNeil government to take immediate action to “eliminate our English Language Boards and replace them with a single provincial board with responsibility to advise government on matters related to public schools and education of importance to parents and the people of Nova Scotia.” It also upholds democratic principles in urging the Liberal cabinet to “study and implement other mechanisms to ensure that parents find avenues to have their voices heard within the management of their local school.”

Education Minister Karen Casey, clearly caught off-guard by the party uprising, was quick to comment that such resolutions were not binding upon the government. When the Legislature’s Public Accounts Committee reviewed serious concerns raised by the Provincial Auditor General over board accountability, the Liberal majority on that committee made no mention of the life expectancy of the boards themselves.

The NSSBA is proving utterly incapable of making the case for local democratic control over what goes on in our P-12 public schools. The NSSBA’s School Board Candidate training kit contained a Q and A resource sheet that did not include the most important question of all – “Why do we need Elected School Boards?”  Nor is anyone prepared to provide a clear, coherent answer.

Consolidating school board administration would produce significant savings, if it focused on reducing the regional board  bureaucracy which costs more than $36-million (2006-07) and employs 8 superintendents and 195 district administrators and consultants. Cutting all 97 elected trustees would only net about $1-million in savings, roughly equivalent to the cost of six senior administrators.

Public school electors tend to lump regional school administrators and elected trustees together when advocating for the abolition of school boards. Outside of Halifax, they also seem to have given up on “elected school board members” who no longer act like “trustees” accountable to the public.
Closing schools as a “school board member” does not win you many friends and, in rural and small town Nova Scotia, can land you in purgatory. Prospective candidates considering a run at office are simply driven-off by long serving incumbents, quietly derided as “board members for life.” Those unsinkable veterans are the strongest argument for “term limits.”

Saving local democratic control in education is worth fighting for, in spite of the example set by the current remote and largely unaccountable regional boards.  The current model has outlived its usefulness and needs to be completely reformed, root and branch.

It might help if the Education Minister and the NSSBA took the time to read and digest Dr. David McKinnon’s May 2016 study of School District Governance. His 92-page report identifies the real crux of the structural problem – the “role ambiguity” that plagues elected board members and renders them completely ineffective. He likens the existing elected regional board to a “rudderless ship” that “still floats, but wherever the winds and currents take it.”

Who represents the public in the K-12 school system is as clear as mud.  Constrained by the current School Board Governance model, elected members occupy ‘no person’s land’ and have been completely muzzled when it comes to speaking up for parents and local taxpayers.

Is it any wonder that fewer and fewer want to run for school board office? Elected school board members who dare to propose needed policy reforms or break ranks are sanctioned or disciplined for doing so.  For a measly stipend of $10,000 or so a year, you spend most of your time approving staff reports and implementing school reviews for closure. If elected boards are scrapped, the foreclosure sign will read “School Board Elections cancelled for lack of interest.”

Why are elected school boards imperiled in Nova Scotia and extinct in most of Atlantic Canada ? Is local democratic control worth preserving and rebuilding in the provincial school systems? Would turning the governance system upside down and investing in elected school-community councils improve the situation?  If so, where might we look for viable models of local democratic education governance? 

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