Mathematical memories, pedagogical perspectives, inspiring schools designs and more.
What's your earliest mathematical memory?
Here's mine: I knew $0.25 + $0.25 was $0.50, so I proudly inferred that $0.24 + $0.24 was $0.49. My teacher told me it was $0.48, and explained why. "Huh," I thought. "This math stuff is subtler than I thought."
— Ben Orlin (@benorlin) June 19, 2018
What’s your earliest mathematical memory? Ben Orlin posed the question to the twitter-sphere and got a plethora of responses about: the endlessness of numbers and other areas of content, discovery and insight, conflict with a teacher, visions of things to come, sorting and arranging, memorable tricks and drills, technology, learning through games, and falling in love with maths. Amazing.
What does fluency without conceptual understanding look like in maths? And what do fluency and understanding actually mean? Dan Myer dives into these questions, pointing out that in macro conversations about maths “nobody knows what anybody means by ‘conceptual understanding’.”
Building conceptual understanding about operating with positive and negative numbers can be tricky. The charge model is one way to represent what’s going on and overcomes problems that alternatives such as number-lines, thermometers and base ten blocks face.
Excitingly, the NY Times’ monthly What’s Going On in This Graph? feature is now weekly. Here’s one from September. What do you notice? What do you wonder? What might be going on in this graph?
New research by Bethany Rittle-Johnson, Erica Zippert and Katherine Boice at Vanderbilt University has found preschool children’s repeating patterning and spatial skills to be related, with these skills predicting broader mathematical knowledge. The research and its implications are discussed here.
Early Childhood to Tertiary Education
“[I]f we aren’t purposeful about understanding the risks of new technologies, we are likely to allow these technologies to be used in ways that perpetuate and exacerbate the systemic flaws and biases that have created today’s inequalities” — Jay Allnutt, CEO of Teach First NZ, on a digital future for education
- Not all questions are the same. Tom Sherrington explains the importance of questioning and presents a repertoire of questioning strategies that teachers can use.
- Supporting students to effectively work in teams is no easy task. The After-Action Review protocol provides teams with a structured process for learning from their experience. Teacher Zachary Herrmann explains how it works in practice.
- “What is our responsibility when a teacher delivers a lesson with outcomes that are detrimental to the development of students? How do we have those conversations in a way that leads to positive growth for all involved (and isn’t reduced to the teacher feeling attacked)?” Chase Orton poses this dilemma, and asks for your help.
New in education research:
- The September 2018 issue of the Australian Journal of Education is focused on early career teachers. Check out the articles here.
- The Program for International Student Assessment collects information on student motivation. A report from Catherine Underwood at the Australian Council for Educational Research presents results from Australian students and how they compare with students from 11 other countries.
- What is working in education for Aboriginal and Torres Strait Islander students? New analysis by a team of researchers from 10 universities has drawn on over 10,000 studies, dating from 2006 to 2018, to identify effective practices.
- The Media Literacy Project conducted by Dr Jocelyn Nettlefold and Dr Kathleen Williams provides a snapshot of media literacy in Australian schools.
- What do the outcomes for higher education graduates in Australia look like? Andrew Norton and Ittima Cherastidtham from the Grattan Institutepresent an analysis.
Schools Plus is a philanthropic body that supports schools around Australia. The organisation funds projects in “rural or remote areas, or schools in poor socio-economic areas, with students who speak languages other than English, who might have an indigenous background, or physical or intellectual disabilities.” Read on for an interview with CEO Rosemary Conn.
A Window Into Some Schools & The People In Them
Auburn North Public School has been recognised with a NSW Minister’s and Secretary’s Awards for Excellence for its work in supporting refugee students and their parents through a number of special programs for parents.
The World Architecture Festival has announced its 2018 short-list of inspiring school designs from around the globe. In addition to Melbourne Girls Grammar School, South Melbourne Primary School and Highgate Primary School (W.A.) is this school in Banten Province, Indonesia:
The Australian Mathematical Sciences Institute has announced the teacher and student awardees of the 2018 Choose Maths Awards. Check them out here.
For the second year running, Coolgardie Christian Aboriginal Parent-directed School has been awarded Secondary School of the Year by the Science Teachers’ Association of WA for excelling in science education.
Teaching is way more than just preparing lessons, turning up to class and marking work. Five years into the job, a teacher opens up about the emotional side to the role and the ongoing learning that’s involved.
The School Packs Project is an initiative started by Perth parent Fiona McMullen that provides school stationery to children in refuges who have escaped domestic violence. Check out the program here.
Education Policy & Politics
A nine year-old girl refuses to stand for the national anthem at school. She gets a lunchtime detention. Then things go a tad crazy. The national media, a shadow minister and even a federal senator weigh in against the girl’s actions and her parents. The girl gets death threats. What the?? From Ben Pobjie:
“Enforced patriotism is surely no patriotism at all, and a little girl who sings an anthem because she’s been ordered to isn’t respecting anything except the threat of punishment. The fact is, an anthem that you’re not allowed to stay seated for isn’t worth singing in the first place.”
The Australian Institute for Teaching and School Leadership has released its report as part of the National Review of Teacher Registration. The report contains recommendations that seek to “improve teacher quality, strengthen child safety, and streamline registration processes across Australia.”
N.S.W. is conducting its first K-12 curriculum overhaul in nearly three decades.
“Many of the debates triggered by curriculum reform are false dichotomies. Our students will need deep knowledge and to develop soft skills using that knowledge base. They will need to work intently on their own and collaborate in teams. They should cultivate a confidence in the classics and the creative opportunities of the latest technology.” — Mark Scott, the Secretary of the NSW Department of Education on the reforms.
“[O]nly 55 per cent of Year 12s [in South Australia]obtain the SACE, and more than a quarter leave with neither the high school certificate nor a vocational qualification.” The Education Department has now made a commitment to report statistics on SACE completion every year, yet principals say this won’t be enough.
The Tasmanian Government is investing $16.1 million to revitalise school farms across the state. As part of the investment, additional teachers will be employed at the school farms as a means of better supporting students into agricultural career pathways.
In an effort to prioritise critical and creative thinking, Victorian students are amongst the first in the world to sit a test assessing “whether they have the skills to detect fake news.” Read on.
Still in Victoria, the state government has launched a major campaign “ to promote public schools and drive up their enrolments, signalling a departure from the mantra of school choice.”
Education Around the World
England: In response to ongoing budget cuts over seven years, English headteachers have come together to petition the government to make a change.
France: A new law in France means that students under the age of 15 are banned from using phones, tablets and smart watches during school hours.
Japan: Meanwhile, nearly 400 kindergartens and nursery schools in Japan are using specially designed smartphone and tablet apps as part of a national initiative in ‘digital play’ to help prepare children for the digital age.
The Globe #1: A new study out of the National Center on Education and the Economy “finds that Australia, England, Finland, Hong Kong, the Republic of Korea and Singapore are pioneering new but remarkably different visions for early childhood education and care.”
The Globe #2: Using data on 121 173 teachers from 38 countries, research out of the University of Texas has found that “teachers responsible for students with special needs had, on average, lower qualifications, worked in itinerant positions more frequently and expressed greater professional development need than [other] colleagues.”
The Globe #3: How optimistic are young people about their futures? A survey by Ipsos and the Bill & Melinda Gates Foundation, has put the question out to teenagers across 15 countries.
New Zealand: A health and well-being survey of primary school principalsconducted by the New Zealand Educational Institute and Australian Catholic University found that “up to 37% of participants answered questions that had led to a ‘red flag’, which means they are undergoing a significant degree of distress.”
Scotland: in response to the difficulties faced by many women in affording sanitary products, the nation has become the first “in the world to guarantee free sanitary products to all students at schools, colleges, and universities.”
U.S.A.: “Some American public schools are turning to foreign teachersbecause Americans with college educations are increasingly uninterested in low-paid, demanding teaching jobs. …The need for mathematics, science, and special education teachers is especially dire in poor and rural schools throughout the country.”
Evaluation & Research Practices
“[I]n fields in which data are sparse or patchily distributed, or where studies vary greatly in design and generalizability — as is the case in biodiversity conservation, international development and education, for example — a different approach [than meta-analyses] might often be more appropriate” — William J. Sutherland and Claire F. R. Wordley from the University of Cambridge on the value of subject-wide evidence synthesis.
Maths, Science & Tech
Emmy Noether applied a new and elegant approach to mathematics, changing the face of algebra. A century on, her ideas and contributions to science are still having a profound impact.
“When you start at a new school or job, or move to a new city, how do you go about making new friends?” Patrick Honner uses the mathematics of networks to explore the options.
Not all numbers are real. As Kalid Azad explains, “Imaginary numbers perform rotations”. By looking at these numbers geometrically, you can see how imaginary multiplication differs from imaginary exponents.
“[S]ometimes maths produces answers that seem counterintuitive to our own experiences of the universe”. As Alexei Vernitski from the University of Essex explains, that doesn’t mean there’s something wrong with maths. Rather, it “show[s] us the limits of the useful range of using certain mathematical tools.”
Mathematician Lily Serna discusses the maths of luck — “From sharing birthdays to winning at blackjack; playing Aussie rules football to planning air sea rescues” — in this episode of Catalyst.
Academics Sarah Hamylton, Ana Vila Concejo, Luciana Esteves and Shari Gallop have written about gender inequalities in STEM. Refreshingly, in addition to talking about the problem, they present seven steps that can be taken to make improvements. For the full research paper, go here. Rose O’Dea and Shinichi Nakagawa from UNSW have examined the ‘variability hypothesis’ as a reason for the gender imbalance in tertiary STEM studies by analysing the school grades of more than 1.6 million students.
Artificial intelligence has proven superior to doctors’ assessments of whether comatose patients would wake up. The AI system was able to “trace brain activity invisible to the human eye.”
A pair of tiny robots has been successfully deployed on asteroid Ryugu. Their aim? To return to Earth with samples of Ryugu.