Unusual mathematical proofs, pervasive edu-myths, teacher recruitment strategies and more.
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Are more strategies in problem solving better? Teacher and instructional coach Mark Chubb examines this question, explaining “It is the relationships between strategies that is the MOST important thing for us to consider.”
From maths writer Rob Eastaway, are some back-of-the-envelope (literally) puzzles to get you thinking.
Some mathematical definitions cause frequent disagreement and debate. Here are two to get you started:
From Richard Elwes, ‘How many sides does a circle have?’
From Ben Orlin, ‘Why isn’t 1 a prime number?’
The New York Times feature, ‘What’s Going on in this Graph’, is back. A great prompt for getting students to critically examine and hypothesise about data. This one shows women’s four annual Grand Slam tennis tournaments:
“What does ‘anyone can do math’ really mean?” Mathematician and curriculum designer, Dan Finkel, examines what the sentiment behind this phrase actually means.
The serious and the silly of mathematical proofs:
The latest issue of mathematics education research journal ZDM is focused on mathematical evidence and argument, with 11 papers dedicated to the topic.
Mathematician Nalini Joshi has broken open the world of proofs with this tweet. Also on the list are proof by: exhaustion, reference to inaccessible literature, appeal to intuition, circular referencing and more. (There’s also now a bot thanks to Joshi’s tweet.)
Early Childhood to Tertiary Education
Science teacher Dr Kate Bridge found herself frustrated with her teaching. In response, Bridge launched a study into the factors needed to create a proximal learning zone and desirable difficulties for students in her Physics class.
In another instance of self-reflection, maths educator Robert Kaplinsky has shared ten things about his work that he’s embarrassed to talk about. It’s refreshing to see that the people around us are just that.
“For teachers, I wonder how much it really matters whether or not they believe in right/left brain or learning styles… As long as teachers believe that these learning differences in no way limit student learning, then how much does it matter if they believe in right- or left-brained people?”
— Director of the Center for Research and Reform in Education, Robert Slavin on whether teachers’ beliefs in myths matters.
Growth mindset has taken the education world by storm. “But the question sparking serious debate in education circles is whether it can be taught — and if not, whether schools are investing valuable time in a pointless activity.”
The International Federation of Library Associations and Institutions has developed a toolkit for developing national literacy and reading strategies and identifying the role that libraries play.
MiniLit is an explicit and systematic early intervention reading program for Year 1 students:
A randomised control trial conducted by a team from the Melbourne Graduate School of Education and the Murdoch Children’s Research Institute has examined MiniLit’s efficacy, costs and implementation factors which influenced outcomes.
In response to the evaluation, the team behind MiniLit has expressed concerns regarding “serious shortcomings in the report.”
Given the role of Health and Physical Education in schooling, researchers Vaughan Cruickshank, Brendon Hyndman and Shane Pill propose ways that it can best serve students for the long-term.
Will AI replace university lecturers? Senior lecturer Mark Haw confesses, “I worry that many universities and academics, myself included, may be unintentionally colluding in our own downfall.”
“Rather than impressing on college students that they should commit to particular jobs and the direction of corporate executives, colleges and universities ought to enhance students’ ability to experiment and prepare them for an open future, even one in which automation may play a significant role.”
— Associate Professor Caitlin Zaloom on why the prominent focus on STEM is misguided and overrated.
Stories of Learners & Teachers
This month, here are two incredible young people getting the world to stop and listen…
From 12 year-old Dujuan Hoosan, is this appeal to members of the United Nations to help put an end to Australia’s jailing of children as young as ten.
At a U.N. climate change summit, 16 year-old climate activist Greta Thunberg admonished world leaders for not doing enough to protect the environment.
ICYMI Thunberg’s actions have sparked global action with school strikes for climate around the world.
Here’s how one school, Newington College in N.S.W., has responded: “We consider that climate change caused by humans is an urgent issue, particularly for young people. We understand the importance of student critical thinking and student voice in addressing this singularly important issue. We thus support the decision of our boys whose parents have given them permission to be absent to represent their views about climate change at the climate march.”
When Teru Clavel moved her children back to U.S. schools after a number of years of being educated in Japan, the level of culture shock was extreme.
What would happen if you built a school on the grounds of an aged care facility? Ask no more.
Education Policy & Politics
What’s wrong with the school mobile phone ban? Researcher Joanne Orlando argues a case that “we are making unqualified policies in the name of ‘protecting the children’”. Meanwhile, the Tasmanian state government is conducting a review of policies around mobile phone use in schools, ahead of a decision on whether or not to put in place a ban.
Writes CEO of Learning First, Ben Jensen, there is a paradox with professional development policy: “on the one hand, professional development expenditure is normally ineffective and on the other hand it’s very difficult to find a system that has improved significantly without professional development being a key driver of improvement.” With this in mind, Jensen describes four steps that policymakers can follow.
Master teachers who “advise on classroom behaviour, specialist subjects, and teaching techniques” as well as more hands-on experience for trainee teachers are part of federal government reforms being put forward for primary and secondary schooling.
Interest in becoming a school principal is on the decline. Little extra pay and much greater responsibilities are among the reasons why.
Drawing on a Grattan Institute report: why comparing Australia’s teacher salaries to other countries isn’t the best way to measure and understand teachers’ pay.
From the Centre for Independent Studies’ Blaise Joseph and Glenn Fahey, increased teacher pay is not what’s needed to improve Australia’s educational performance.
There is growing concern being expressed by the N.S.W. government about a ‘cultural bias’ towards university and away from the vocational education sector. Joanne McCarthy argues, however, that the bias is people’s responses to government ‘reforms’, including the introduction of private colleges, closure of regional TAFEs and more.
In a move against the ATAR, Adelaide University is changing its entry requirements to admit students based on their results in specific subjects, rather than their final score. The chair of the federal government’s new Review of Senior Secondary Pathways, Professor Peter Shergold, agrees that its time for the ATAR to go.
Over in Victoria:
From 2021, all Year 11 and 12 students will be required to sit a literacy and numeracy test, regardless of whether they are completed scored or unscored VCE or Victorian Certificate of Applied Learning. The test comes in response to complaints from industry groups about the skill-levels of students finishing school.
Schools in regional and rural Victoria struggle to attract teachers. To address this, a new state government package will provide funding to support school leaders and attract and retain teachers at these schools.
Recruiting maths teachers across the country into regional areas is a particular challenge. Former vice-chancellor of the University of New England, Annabelle Duncan, explains what approach to addressing the issue is needed.
More generally, what are the best ways to attract and retain new teachers? Researchers Michele Simons, Anna Sullivan and Bruce Johnson argue that part of the solution could be to have fewer casual positions and less out out-of-work hours.
School staffing concerns are not just about principals and teachers, but teacher librarians as well. Qualified teacher librarians are increasingly being replaced by ‘library officers’ and ‘library assistants’, who often have no qualifications or educational training.
Education Around the World
China: New guidelines aimed at reducing academics burdens on students have been released by the Shanghai Education Commission. They include a ban on assessing teachers’ performance by using students’ test scores and on mid-term tests for primary school students.
Developing nations: A research review from the Australian Council for Educational Research has examined the question of “What effective interventions have been implemented recently in economically developing countries to improve children’s learning in the years before school?”
Germany: A new report has shown that the nation’s primary school teacher shortage is worse than government had previously understood.
South Korea: Starting from 2020, a new AI-based personal learning service will be introduced by the government for students in grades three to eight in public schools.
Switzerland: The Swiss High Court has ruled against homeschooling, reinforcing decisions made by “cantons to establish very restrictive rules, even bans on homeschooling.”
Evaluation & Research Practices
Incentive structures that reward scientists “for pumping out research papers encourages them to cut corners and creates a market for criminals to exploit scholars.” How to fix this? Australia’s Chief Scientist Alan Finkel is calling for reforms, including a ‘rule of five’ that would see a researcher’s performance judged based on their best publications over a five-year period.
The Alliance for Useful Evidence “champion[s] the smarter use of evidence in social policy and practice”. In this report, they examine how professional organisations in health, education and policing are better using and advocating for the use of research
Maths, Science & Tech
Never fear, Captain Math is here.
And some incredible mathematical breakthroughs:
Topological data analysis is a new approach conceived of by Italian mathematicians, Mattia Bergomi and colleagues, that enables artificial systems to “learn to recognise complex images even more quickly than they do now”.
The infinite lottery: “The winning collection of numbers is infinitely long, and each ticket can have an infinite number of rows, with each row containing an infinite number of numbers.” Is it possible to create a ticket that always wins? Thanks to mathematicians David Schrittesser and Asger Törnquist, this 50 year-old problem has now been solved.
Can each of the natural numbers below 100 be expressed as the sum of three cubes? Up until this year, this 65 year-old problem had two numbers remaining: 33 and 42. Thanks to mathematicians Andrew Booker and Andrew Sutherland and over a million hours of computing time, we now have solutions.
Central Victoria is experiencing a ‘meterorite renaissance’. As Senior curator of geosciences at Museums Victoria Dr Stuart Mills explains, the region is “punching above its weight for helping us understand what’s been happening in the universe”.
Biologist Michael Rampino and a team of scientists have identified a sixth severe mass-extinction event, from about 260 million years ago. Rampino explains, “Notably, all six major mass extinctions are correlated with devastating environmental upheavals”.
There’s black and then there’s black. A team of MIT researchers have developed a material that “captures at least 99.995 percent of any incoming light …[and is] 10 times blacker than anything previously reported.”