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Archive for the ‘Mathematics Mindset’ Category

The Homework Debate never seems to go away.  Popular books and articles inspired initially by American education writer Alfie Kohn and his Canadian disciples continue to beat the drum for easing the homework burden on students or eliminating homework altogether before the secondary school level. That “No Homework” movement made significant inroads in the United States and Canada during the 2000’s. The Organization for Economic Cooperation and Development (OECD), responsible for the Program of International Assessment (PISA) test, confirmed that the amount of time students in North America spend on doing homework had declined, as of the 2014 assessment year.

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A critical question needs to be asked: Has the “No Homework” movement and the apparent push-back against homework had an adverse effect on student achievement? That’s difficult to answer because, despite the critical importance of the issue and the long history of homework research, few North American researchers have been inclined to study the role that homework plays in enhancing student achievement, even in mathematics.

One little-known researcher, Lake B. Yeworiew, an Ethiopian scholar, based at the University of Calgary, but recently-arrived in Canada, saw the hole in the research and recently tackled the whole question. His focus was on assessing the relationship between homework and Grade 8 Mathematics student achievement, comparing Canadian students with the top performing students in the world. While attending the AERA 2019 Congress (April 5-9) in Toronto, I got a sneak peak at his findings.  While his research study attracted little attention, it will be of considerable interest to all of those committed to maintaining and improving student performance standards.

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His University of Calgary study, co-authored with Man-Wai Chu and Yue Xu, laid out the essential facts: The average performance of Canadian students in Mathematics (PISA) has declined since 2006 (OECD, 2007, 2010, 2014, 2016)  Students from three top performing Asian countries, Singapore, Macau-China and Japan, continue to outperform our 15-year-old students by a significant margin.  Furthermore, OECD reports that students in Asian countries (Singapore, Japan, Macao- China and Hong Kong-China) spend more time doing homework and score much higher. It is estimated that they score 17 points or more per extra hour of homework.

Recent North American research seems more alert to the need to study the relationship between homework and academic achievement, particularly in mathematics. A literature review, conducted by Yeworiew, Chu and Xu, demonstrates that, while the findings cut in both directions, the weight of research favours homework. In fact, the Canadian Council of Ministers’ of Education (CMEC 2014) has come down in favour of homework. Based upon Canadian national test surveys (PCAP), CMEC confirms that math achievement of students who do not do homework is significantly lower than those doing regular homework.

Yeworiew and his research team provide further confirmation of this 2014 CMEC assessment. Utilizing the 2015 TIMSS study in Canada, involving 8,757 students and 276 schools in four provinces (Ontario, Quebec, Manitoba and Newfoundland/Labrador), the authors demonstrate the clear value of regular homework in modest amounts.

The research findings are effectively presented in a series of graphs mapping the study results, reprinted here directly from their AERA 2019 Toronto presentation:

 

 

The relationship between homework and achievement is becoming less of a mystery. Based upon the performance of Grade 8 students in the 2015 TIMSS study, short but frequent homework assignments contribute to improved student learning and achievement in mathematics. Frequent homework assignments, up to four times a week, have a positive effect on math achievement, but less sop when it is of longer duration. No discernable differences were detected for girls in relation to boys at the Grade 8 level in Canada.

Why do Canadian researchers produce so few studies like the University of Calgary project attempting to assess the impact of homework on achievement?  To what extent is it because Canadian homework studies tend to focus on psycho-social aspects such as the impact of homework on student attitudes and the opinions of parents?

Are we asking the right questions? “How much is enough?” is surely a sounder line of inquiry than “How do you feel when overburdened with homework? ” What is really accomplished by asking ‘Does homework ad to your anxieties?” Should we be more conscious of the inherent biases in such research questions? 

 

 

 

 

 

 

 

 

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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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