# data[].attributes.attachment_link.readable_text
Important information

The National AI Centre (NAIC) is transitioning from CSIRO to the Department of Industry, Science, and Resources (DISR) on 1st July 2024. You can find the latest NAIC content at industry.gov.au. For any NAIC-related questions, please email NAIC@industry.gov.au.

About

Educational Datasets have been created using data that is available on the CSIRO Data Access Portal. Each dataset has a linked teacher guide and comes in three different levels, novice, expert and programmer. Novice and expert data is intended for use with spreadsheet software, while programmer data is intended for use with programming languages.

The provided teacher guides describe the datasets for teachers and provide a range of lesson activities for students in Years 3 to 10. Datasets are grouped according to where the data's context fits into learning areas of the Australian Curriculum. All of the available dataset packages cover general data literacy content from the Mathematics and Technologies learning areas, as well as the science as a human endeavour and science inquiry skills strand of the Science learning area.

Available resources

Available datasets

Great Barrier Reef

The Great Barrier Reef Carbon Dioxide Measurements dataset records concentrations of oceanic carbon dioxide and atmospheric conditions along the Great Barrier Reef, taken aboard a moving ship.

This is a teacher and student resource for Science, Mathematics, Digital Technologies and Geography teachers, with activities for Years 7 to 10. It covers earth and space science, science as a human endeavour, science inquiry (Science) and processes and production skills (Digital Technologies).
Download resource PDF (813 KB) Dataset ZIP file ZIP (9 MB) Download Dataset - accessible version DOCX (1 MB)
Logan's Dam

The Logan's Dam Water Quality dataset records fortnightly observations of water conditions in a dam in South East Queensland. The dataset provides an opportunity for students to explore the way that water conditions change over time, examine potential hazards in water quality, compare related datasets and examine the interactions between water chemistry and biological life.

This is a teacher and student resource for Science, Mathematics, Design and Technology, Digital Technologies and Geography teachers, with activities for Years 7 to 10. It covers chemical sciences, earth and space sciences, science as a human endeavour, science inquiry (Science) and processes and production skills (Digital Technologies).
Download Resource PDF (756 KB) Download Dataset ZIP (18 KB) Download Dataset - accessible version DOCX (559 KB)
Sydney particle study

The Sydney Particle Study dataset records weather conditions and concentrations of different air pollutants, which were recorded at Westmead in Sydney.

This is a teacher and student resource for Science, Mathematics, Digital Technologies and Geography teachers, with activities for Years 7 to 10. It covers chemical sciences, science as a human endeavour, science inquiry (Science) and processes and production skills (Digital Technologies).
Download Resource PDF (493 KB) Download Dataset ZIP (13 MB) Download Dataset - accessible version DOCX (567 KB)
Mean sea level

The Reconstructed Global Mean Sea Level dataset records the average global sea level from 1880 to 2009. Measurements have been calculated using tide gauges located around the world and satellite readings. Using this dataset, students can explore changes in sea levels, compare measurement methods and create models and predictions based on identified long-term data trends.

This is a teacher and student resource for Science, Mathematics, Digital Technologies and Geography teachers, with activities for Years 7 to 10. It covers earth and space science, science as a human endeavour, science inquiry (Science) and processes and production skills (Digital Technologies).
Download Resource PDF (600 KB) Download Dataset ZIP (22 KB) Download Dataset - accessible version DOCX (680 KB)
Wheatbelt bird survey

The Wheatbelt Bird Survey dataset records every species of bird sighted at the 'Koobabbie' property in the northern wheatbelt of Western Australia between 1987 and 2016. Students have an opportunity to explore diversity, replicate a real-world experiment and examine seasonal differences in species observed.

This is a teacher and student resource for primary school teachers, with activities for Years 3 to 6. It covers biological sciences, science as a human endeavour, science inquiry (Science) and processes and production skills (Digital Technologies).
Download Resource PDF (513 KB) Download Dataset ZIP (187 KB) Download Dataset - accessible version DOCX (497 KB)
Income equality

The Income Inequality in Australian Regions Measurements dataset indicates levels of income inequality present in Australian Local Government areas in 2001 and 2011. The dataset provides an opportunity for students to explore differences throughout the country and consider contributing factors to high or low income inequality.

This is a teacher and student resource for Mathematics, Digital Technologies, Economics and Business and Geography teachers, with activities for Years 7 to 10. It covers science inquiry (Science) and processes and production skills (Digital Technologies).
Download Resource PDF (812 KB) Download Dataset ZIP (36 KB) Download Dataset - accessible version DOCX (973 KB)

# data[].attributes.attachment_link.description
CSIRO Educational Datasets are aimed at making it easier for teachers to bring real-world research data into the classrooms.

# data[].attributes.attachment_link.readable_text
Thuong Nguyen and Benjamin Watson

Photo: AsiaVision - Getty Images

Abstract

The results of the Reserve Bank's 2022 Consumer Payments Survey show that consumers continue to shift from using cash to electronic payment methods - a trend that was accelerated by the COVID-19 pandemic and consumers' preference towards using debit and credit cards and making payments online. Consumers are also increasingly using more convenient payment methods, particularly contactless card payments, by tapping their card or phone. Cards are now used for most in-person payments, even for small transactions that used to be made mostly with cash.

Introduction

The Reserve Bank conducted its sixth Consumer Payments Survey (CPS) in October to early December 2022. This article considers the results of the survey, with a particular focus on electronic payment methods. Livermore and Mulqueeney (2023) summarise the results on cash usage, including the drivers of declining cash use and the accessibility of cash services for Australians.

Survey methodology

Participants recorded every transaction they made for seven days in a payments diary and provided extra information on their payment preferences and attitudes in a post-survey questionnaire. The CPS provides unique insights into Australian consumers' payments behaviour and their changing preferences via both qualitative questions and quantitative analysis of the payments diaries. For the 2022 CPS, around 1,000 people completed the survey and recorded around 13,000 transactions.

The seven-day payments diary captured detailed information on every transaction that a consumer made in a week. The information included:

the payment method - for example, debit card, credit card, cash or bank transfer

the payment location - whether in-person or online

the execution of the payment method - for example, by inserting a card into the terminal, or tapping a physical card or mobile device

the payment purpose - for example, supermarket, household bills, leisure or transport.

The sample was collected to ensure it was representative of the Australian population across a range of demographics, including respondent age, sex, geographical location and household income.

Results overview

The results show that Australians continue to change the way they make payments, with the longer run shift to electronic payment methods accelerated by the COVID-19 pandemic. Australians are using cash less frequently; only around 13 per cent of payments were made using cash in 2022, which is half the share reported in 2019 (Table 1). Card payments made up the bulk of consumer payments, with debit cards accounting for half of all payments and credit cards another quarter. Other payment methods such as 'buy now, pay later' (BNPL) services made up only a small share of consumer payments. Cheque usage declined further in the 2022 CPS.

(a) Excludes payments over $9,999, transfers (payments to family and friends), transport cards and automatic payments. Totals may not sum to 100 due to rounding.
(b) Payments made using banks' internet or telephone facilities; does not include other payments made using the internet.
(c) 'Other' methods include prepaid, gift and welfare cards, bank cheques, money orders, BNPL and Cabcharge.

Source: RBA calculations, based on data from Colmar Brunton, Ipsos and Roy Morgan Research.

Cash usage

Australians continue to shift away from using cash for day-to-day transactions. Since the CPS was first conducted in 2007, the share of payments made using cash has declined in every subsequent survey - cash made up around 70 per cent of payments in 2007 and only 13 per cent in 2022. The pandemic accelerated the shift away from cash as consumers complied with social distancing requirements by making more payments remotely and because of hygiene concerns with handling cash. Cash has historically been used more frequently for low-value in-person purchases; however, card payments have now overtaken cash usage even for these small purchases.

Card payments

The 2022 CPS showed a further shift to electronic payments by Australians. This trend has been driven in recent years by the development of more convenient and seamless payment technology as well as changes in consumer payment behaviour brought on by the COVID-19 pandemic. Card payments now offer convenient contactless payments that speed up transactions; they have reduced the need for consumers to top up cash, have wide merchant acceptance facilitated by new payment providers, and have allowed for innovation in the payments space (such as storing cards in mobile wallets). As a result, three-quarters of payments were made with cards in 2022 - an increase of 13 percentage points from 2019 and three times the share in 2007 (Graph 1). The increase in card usage mirrors the decline in cash usage.

The increase in card usage since 2007 has involved both debit and credit cards. Since the CPS was first conducted in 2007, consumers have continuously increased their usage of debit cards; the share of payments made with debit cards is now around half of all payments - more than three times higher than in 2007. The increase over the past 15 years has been driven by the introduction of debit cards that provide much of the same payment functionality as credit cards, such as the ability to make contactless and online payments and to store them in mobile wallets (see below). By contrast, the increase in credit card usage since 2007 has been more moderate, rising 14 percentage points to be around one-quarter of all payments. The stronger uptake of debit cards partly reflects consumers preferring to use their own funds from a bank account, rather than borrowed funds from a credit card. In addition, the perceived attractiveness of credit card reward schemes has fallen in recent years and higher surcharges for using credit cards at some merchants may be driving consumers to use debit cards instead.

Cards are the dominant payment method for Australians of all age groups. Younger people use cards most intensively, with consumers aged 18-29 years using cards for around 85 per cent of their payments (Graph 2, left panel). Consumers aged 65 and above have historically been high cash users; however, they now use cards for nearly two-thirds of their payments. Compared with 2019, the share of transactions made using cards rose most strongly for those 40 years and older, with little change for those under 40, narrowing the difference between younger and older people. The increase in the use of cards for older consumers was strongest for low-value transactions; for those under 40, the share of low-value payments made using cards had already reached a high level in 2019.

The rise in the share of card payments between 2019 and 2022 was seen across all income groups (Graph 2, right panel). The rise in card usage was strongest in the middle-income groups (i.e. the second and third income quartiles). Higher income households have the greatest propensity to use cards, with cards accounting for 82 per cent of their payments, compared with 69 per cent for those in the lowest income quartile.

Lower income households use debit cards and cash more frequently than higher income households (Graph 3, left panel). Consumers in the lowest income quartile made 55 per cent of their transactions with debit cards, compared with 45 per cent for those in the highest income quartile. However, in value terms, middle-income households use debit cards for a slightly larger share of their spending than other income groups (Graph 3, right panel).

Conversely, higher income households use credit cards more intensively than other households (Graph 3). Consumers in the highest income quartile use credit cards for around one-third of their payments, which is three times the share for lowest income households. This may reflect higher income households being more likely to meet the lending standards for a credit card, as well as debit cards and cash being used as budgeting tools for lower income households.

The 2022 CPS shows that cards are the dominant payment method at almost all types of business (Graph 4, top panel). Cards account for more than 80 per cent of payments at supermarkets, food retailers, transport, and petrol and service stations. The high share of card payments at supermarkets may reflect the convenience of using a card at these businesses - for instance, supermarkets were among the first businesses to introduce contactless card terminals in Australia, and more recently have introduced self-service checkouts that do not accept cash. Also, many supermarkets do not surcharge card payments, making this payment method a more attractive choice than at businesses that directly recoup the cost of card payments. Card payments are used least for household bills, with consumers tending to use lower cost methods such as bank transfers and BPAY for these payments.

Since 2019, the increase in card use has been broadly based across types of business. There has been a significant shift away from cash at small food retailers, such as cafés, pubs and takeaway food outlets, with the share of payments made by card increasing by 18 percentage points (Graph 4, bottom panel). In addition to consumer preference to use cards, this trend could reflect wider card acceptance, enabled by plans offered by new payments providers catering to smaller merchants, as well as more convenient technology such as simpler point-of-sale terminals and portable payment terminals that connect to mobile phones. The decrease in the share of payments made using cards in the holiday category reflects increased use of other non-cash methods such as bank transfers, which can be used to avoid card surcharges.

Australian consumers are increasingly using cards for transactions of all sizes, from low-value transactions of less than $10 to larger transactions over $100 (Graph 5). Around 80 per cent of payments over $10 are made using cards. Historically, low-value payments of $10 or less were made mostly in cash; however, in 2022 more than 70 per cent of these payments were made using cards - up from around 50 per cent in 2019. The widespread acceptance of card payments, adoption of contactless functionality and changes in payment preferences in response to the COVID-19 pandemic have supported the sharp increase in the use of cards for low-value transactions over the past decade (Bullock 2020).

The use of contactless card payments, such as tapping a card or waving a mobile device at the payment terminal, increased further in 2022. Contactless card payments are used near universally by Australian consumers, making up 95 per cent of in-person card transactions in 2022, up from around 85 per cent in 2019 (Graph 6). By contrast, when the CPS was first conducted in 2007, almost all in-person card transactions were made by inserting the card into a terminal and providing a signature or personal identification number (PIN) for verification. The increase in contactless payments since 2019 was driven by a significant increase in the usage of mobile devices such as phones, watches and rings, to account for 30 per cent of all in-person card payments. Tapping a physical card, rather than a mobile device, is still the most common way of making an in-person card payment, despite its decline since 2019 as consumers switch to mobile payments.

In the 2022 CPS, more than one-third of consumers used a mobile device to make a contactless payment in the diary week - an increase of 25 percentage points from 2019. Adoption of payment-enabled mobile devices has increased substantially across all age groups over the past three years, particularly for younger consumers (Graph 7). Mobile payments were used by nearly two-thirds of Australians aged between 18 and 29 in 2022, up from less than 20 per cent in 2019. For consumers aged 65 and over, only 9 per cent made a mobile payment during the diary week - however, this was triple the share in 2019.

Mobile payments are facilitated by mobile wallets - that is, applications on mobile devices, like smartphones, that store card details. As well as in-person payments, mobile wallets can be used to make online payments. In the 2022 CPS, respondents were asked if they stored each of their payment cards in a mobile wallet, such as Apple Wallet, Google Wallet, Samsung Wallet or Alipay etc. Around half of respondents stated they had a card stored in a mobile wallet in 2022, with mobile wallet usage higher among younger people (Graph 8, top panel). Mobile wallets have become more popular for consumers of all age groups since 2019 (Graph 8, bottom panel). Having a single card stored in a mobile wallet is more common than having multiple cards stored.

Online payments

Online payments made up a higher share of retail payments in 2022 than in 2019, with consumers shifting away from in-person transactions. When measured by the number of transactions, the share of payments made online was 18 per cent - up from 12 per cent in 2019 and just 4 per cent in 2007. This reflects the long-term rise in e-commerce, spurred on more recently by lockdowns and social distancing during the pandemic.

Around two-thirds of respondents made at least one online payment in 2022, up from around 55 per cent in 2019 and more than double the share of people surveyed in 2007. Some goods or services are more difficult or more expensive to purchase online - including petrol, supermarket items and food retail - and so only a small share of these purchases are made online (Graph 9). For other types of services - such as leisure, bills and holidays - a high share of purchases are made online. More than half of leisure purchases - such as music, movies and sports tickets - were made online in 2022.

Consumers are increasingly using their debit cards to make online payments, in addition to BPAY and bank transfers, which have historically accounted for the largest share of online payments (Table 2). In 2022, the share of online payments made using mobile apps was little changed from 2019 at just under 40 per cent, with the remainder initiated through other means such as web browsers (e.g. Chrome or Safari).

(a) 'Other' methods include Paypal, prepaid, gift and welfare cards and BNPL services.
(b) 'Mobile phone' was recorded as a separate category of online payments only in 2013 and 2016, while in 2019 this was recorded as 'App'.

Sources: RBA calculations, based on data from Colmar Brunton, Ipsos and Roy Morgan Research.

The figures in Table 2 refer to online payments where participants initiated and made the payment during the diary week. The CPS also collects information on participants' automatic payment arrangements, such as household bills (e.g. rent or electricity) paid by direct debit, and recurring 'pay anyone' transactions via online banking. These arrangements are set up ahead of the payment occurring and are recorded separately in a post-diary questionnaire (participants review their bank statements when recording information on these payments). The share of payments made automatically during the week of the CPS has been steadily increasing over recent years, to 12 per cent of the total number of transactions (Graph 10, left panel). By value, nearly one-third of weekly spending was made automatically in 2022 (Graph 10, right panel). The growth in automatic payments reflects the changing way people pay their bills as well as the increasing use of subscription services, such as video streaming and meal services. Two-thirds of all household bill payments in 2022 were made automatically, which is around triple the share in 2013. This shift towards automatic payments for certain transactions is another way in which payments are becoming more convenient for consumers.

Other payment methods

In recent years, several other ways to make payments - besides cash, cards or cheques - have emerged in Australia. Some of these newer ways to pay use the same 'payment rails' as existing payment methods, but they are faster, more convenient or more secure.

The CPS gathered respondents' knowledge and usage of a number of these other ways to make payments (Graph 11). PayPal and BNPL had near universal consumer awareness, while Beem (previously called 'Beem It') and Alipay/WeChat Pay had little awareness or usage in Australia. Many people were aware of cryptocurrencies, but only a very small share had used them to make a payment in the past year.

QR codes

The 2022 CPS asked respondents for the first time about their awareness of using quick-response (QR) codes for making payments. Some merchants now offer QR codes that direct consumers to a mobile wallet, typically funded by the consumer's debit or credit card, to complete a payment at the terminal. About one-third of respondents had heard of this payment method and around 10 per cent reported using it to make a payment in Australia in the past year. In some other countries, merchants are providing QR codes that allow their customers to pay by transferring funds directly from their bank account through fast payment systems. Adoption of this payment method in Australia could provide consumers with a low-cost alternative to card payments.

PayID

PayID is a way of using a mobile number, email address or Australian Business Number to address an account-to-account bank transfer, with the funds available to the recipient almost instantly. In 2022, around half of Australians had heard of PayID and 30 per cent had used it in the past year. PayID is more convenient than using the traditional Bank-State-Branch (BSB) and account number, which require consumers to correctly key in 15 digits. Another benefit of PayID is that the payer receives confirmation of the name of the person or business being paid, reducing the risk of fraud. PayID was introduced in 2018 as part of the New Payments Platform (NPP). Consumer uptake of PayID has been slower than initially expected, and currently not all Australian bank accounts are connected to make or receive a payment using PayID (Connolly 2022). The Payments System Board continues to encourage financial institutions to roll out PayIDs for all bank accounts, which will be necessary to achieve their full potential. In the diary, payments using PayID made up around 10 per cent of bank transfers, with the remainder addressed using BSB and account numbers (Graph 12). Consumers under the age of 50 had the highest share of bank transfers addressed using PayID.

Buy now, pay later

BNPL services allow customers to purchase goods on credit and make interest-free instalment repayments. While offering benefits for consumers, BNPL services are typically an expensive way for merchants to accept payments, costing on average around 4 per cent of the value of the transaction, compared with 0.5-1.5 per cent for traditional card payments. Almost one-third of Australians had used a BNPL service in the past year, up around 8 percentage points from 2019. Usage was highest among younger Australians: over 40 per cent of 18-39 year olds had used a BNPL service in the past year, compared with only 10 per cent for those aged 65 and over (Graph 13). However, usage increased across all age groups from 2019. While a large share of Australians had used BNPL in the past year, BNPL payments made up just 0.7 per cent of the number of payments in 2022 up from 0.5 per cent in 2019.

For the first time, the 2022 CPS also collected data on the number of BNPL accounts consumers had with different BNPL providers. On average, Australians had 0.7 BNPL accounts per person, with people aged 18-39 having nearly one account on average (Graph 14, left panel). Those aged 65 and over were the least likely to hold a BNPL account. Of those consumers with a BNPL account, BNPL users held two accounts on average (Graph 14, right panel). Consumers with access to multiple accounts may encourage competition in the BNPL market, as providers compete to entice consumers to use their service. However, BNPL firms typically do not allow merchants to pass on the high cost of accepting their service directly to BNPL users through a surcharge. So, the benefits of competition in the BNPL market may accrue to BNPL users, subsidised by non-users as merchants recoup the cost by raising the price of goods and services generally.

Conclusion

The 2022 CPS showed a further increase in the use of electronic payment methods, with consumers further reducing their use of cash. This partly reflects both a continuation of existing trends and changes induced by the pandemic. Australians mostly use cards to make payments, even for smaller transactions that used to be made with cash, with debit cards alone accounting for half of all payments. At the same time, consumers are continuing to embrace a range of more convenient ways to pay, such as contactless payments using mobile phones and automatic payments, although such methods often use the existing payments infrastructure (such as the card networks).

# data[].attributes.attachment_link.title
Consumer Payment Behaviour in Australia | Bulletin - June 2023

# data[].attributes.attachment_link.description
The results of the Reserve Bank's 2022 Consumer Payments Survey show that consumers continue to shift from using cash to electronic payment methods - a trend that was accelerated by the COVID-19 pandemic and consumers' preference towards using debit and credit cards and making payments online.

# data[].attributes.attachment_link.description
ANZ Credit Card Education provides practical tips on managing credit cards, including understanding interest rates, balance transfers, and budgeting strategies.

# data[].attributes.body
VCAA

# data[].attributes.attachment_link.title
Planning - Victorian Curriculum and Assessment Authority

# data[].attributes.body
Resources and competition

# data[].attributes.attachment_link.description
Our secondary school free elearning resource teaches in a fun and engaging way how the Australian tax and super systems work

# data[].attributes.attachment_link.title
The Amazing Maths Race – Felstead Education

# data[].attributes.headline
Someone talking about Florence Nightingale

# data[].attributes.subject
Someone talking about Florence Nightingale

# data[].attributes.attachment_link.readable_text
Robyn Williams: Today's talk is a conundrum, at least at the start. Don't worry if you can't guess the answer, few can. But the questions posed by our Chief Scientist, Alan Finkel, are highly significant.

It's about the power of numbers, often to save lives - thousands of lives. It's also about the perils of underestimating a famous figure. Some are much more significant than their image may indicate.

Professor Alan Finkel.

Alan Finkel: Who am I?

I was born in 1820 into a wealthy and well-connected British family. As a child, my hobby was building statistical tables, in which I captured trends in the vegetable output from our garden.

At my request, I was tutored in mathematics for two hours every day. I became a maths tutor myself, before applying for a position as a Superintendent in the British military.

I was deployed to the battlefield, where I collected extensive data on soldier mortality rates. And this formed the basis of an 850 page report that I published in 1858. My report saved countless thousands of lives by prompting major reforms in hospital practice.

I helped to establish the International Statistical Congress and I served as a data consultant to the US Army in the American Civil War. I also invented the polar area diagram, and I pioneered the infographic.

I was elected to the Royal Statistical Society [and here's a big clue...] I became the first female member at the age of just 38. I died a legend amongst statisticians at the age of ninety.

I am, of course, Florence Nightingale: mathematician.

Yes, Florence Nightingale - the Lady with the Lamp. She ought to be the Lady with the Logarithm. She saved far more lives by her grasp of numbers than by her gift for nursing. And she put data at the heart of healthcare as we know it today.

So throw out your history books, I am correcting the record! Florence Nightingale is henceforth our patron saint of mathematics. And I will pay my personal tribute by drawing out four lessons from her story to guide us today.
Lesson One: Maths is critical
Imagine a world without maths. You have to cast your mind back more than five thousand years, to a world barely crawling from the Stone Age. Take away numbers, and you take away commerce, farming, medicine, music, architecture, cartography, cooking, sport... and every other activity we've invented since 3000 B.C.

The first thing you looked at today was probably the time. The second was probably the temperature. The third, perhaps the nutrition panel on the side of the cereal box.

There is nothing so disempowering as ignorance of the numbers like these that make it possible to navigate our world. Never forget, the weakest person in a negotiation is always the person who can't add up in their head. Maths is the language of science. Maths is the language of progress! Maths is the pre-requisite for learning, and for life. And no-one knew it better than Florence Nightingale.
Lesson Two: learning maths is hard
It is hard in the sense that it demands our early persistence. Learning in maths is a continuum - always building the next lesson on the skills mastered in the lessons before. To fall behind is often to stay behind. And to drop out in school is to kneecap your opportunities in later life. It is very difficult to retrofit the mathematics foundations into your brain at university, if you have failed to develop them in school.

I understand the temptation for schools to lighten the content in the maths curriculum, in the dubious belief that easy things are more attractive to students, and any maths is surely better than no maths. I also understand the incentives that lead students to study maths at a level below their true ability. But a lighter load is really a heavier burden: it is the burden of low expectations.

Florence Nightingale understood this reality from an early age. She didn't consider herself to be naturally gifted in maths, but she did believe she had the capacity to learn. And so she refused to settle for the level of maths education thought fitting for girls of her time. She demanded from her parents the support to raise herself to something higher: something that would make it possible to participate fully in public life.

She should be our role model for the education of all students: regardless of gender, regardless of postcode, regardless of cultural background and regardless of family income.

And surely, the most effective way to raise expectations in schools is to start at the endpoint of the education continuum: that is, start with universities. Implement maths prerequisites in all the courses that need, you know, a grasp of maths! At a stroke, we would signal to principals at primary and secondary level that they simply can't afford to drop the ball. Maths has to be a priority for every student, from kindergarten to graduation. But that brings me to...
Lesson Three: compulsion is not enough
Some children seem to fall in love with maths at birth and, like Florence, are hungry to be taught. Others need help to turn an arranged marriage with maths into a genuine passion. That is the role of the teacher: to make a subject not just compulsory, but compelling. But, of course, it is very difficult for any teacher to inspire a passion that they don't feel themselves. It is also extremely disrespectful to the teaching profession to discount the time, the talent and the training that it takes to teach maths well.

Maths teachers should, in the first instance, be experts at maths. It's that simple - and yet, it seems, that hard. In far too many schools, out-of-field teaching remains the norm; peer networks are thin; and professional development is an impossible dream. We seem locked in to a cycle of poor outcomes and diminishing expectations: passing on to each generation of teachers, students, and parents the frustration we feel ourselves. Entrenched practices are hard to break; and they are demoralising to report.

But just because the problems run deep, that does not mean that we should shy from solving them. Which brings me to my...
Final lesson from Florence: using evidence to make a difference
Imagine the situation Florence Nightingale confronted in the Crimea. Everyone knew that, in a war, soldiers get shot. Everyone knew that people who are shot tend to die.

What they didn'tknow was that the vast majority of deaths in the Crimean war weren't caused by wounds at all - they were caused by diseases like cholera and typhus. And so military leaders didn't implement the basic sanitary precautions in field hospitals and military barracks that would save lives by stopping the spread of disease.

Florence Nightingale saw the problem - but she needed her own ammunition. So she counted the dead, collected the data, and displayed it in a polar area diagram. It was a credible and compelling display of the causes of death.

And suddenly the problem was crystal clear. It was fixable. That is how a woman - a nurse - took on the top brass of the British military and won.

Think of Florence Nightingale the next time you feel that speaking up for meaningful reform is like the Charge of the Light Brigade: riding nobly into the Valley of Death. Evidence can give leaders the impetus and the confidence to act. But it can only do so if we present it in an actionable form.

It cannot just be a statement of problems. It cannot just be a statement of demands. It has to be written, and read, as a statement of opportunities. Only then can it point us to solutions.

So here's to Florence Nightingale, the Lady with the Logarithm.

Let's remind this country that there's strength in numbers. Let's commit to starting maths education early. To keeping it going. To treating our education system as a continuum. To keeping the bar of student aspiration high. To helping students clear the bar. To fighting the incumbency bias. And above all, to taking our research beyond observations, into the realm of solutions.

Robyn Williams: Solutions. Yes, solving problems as well as identifying them.

Our federal Chief Scientist Professor Alan Finkel. And if you want to hear the voice of Florence Nightingale recorded in 1890 - yes 1890 - just go to this week's Science Show where a scratchy wax cylinder recording can be heard. Her words are there:
"When I am no longer even a memory, just a name, I hope my voice may perpetuate the great work of my life. God Bless my dear old comrades of Balaclava and bring them safe to shore."
Florence Nightingale - her voice 127 years ago. Just go to the Science Show website and you can hear the very thing.

Next week: we worry about smells and their effects. Something that's been troubling our famous writer Kate Grenville. I'm Robyn Williams.

# data[].attributes.attachment_link.title
Florence Nightingale: Mathematician - ABC Radio National

# data[].attributes.attachment_link.description
Robyn Williams: Today's talk is a conundrum, at least at the start. Don't worry if you can't guess the answer, few can. But the questions posed by our Chief Scientist, Alan Finkel, are highly significant. It's about the power of numbers, often to save lives - thousands of lives.

# data[].attributes.attachment_link.title
What would Florence Nightingale make of big data? | BBC Ideas

# data[].attributes.attachment_link.readable_text
What do you get when you cross a mathematician on his summer holidays with the Marvel Cinematic Universe back catalogue?

A Christmas spent binge-watching superhero films, and a statistical analysis of why the Marvel movies are so popular.

"It started almost as a joke," said mathematician and self-confessed Marvel fan Matthew Roughan of the University of Adelaide.

"It started as 'I'm going to watch the Marvel movies over Christmas, I bet I can get a paper out of this'."

The Marvel Cinematic Universe (MCU) is "arguably the most successful movie franchise of all time" reported Professor Roughan and his co-authors in PLOS ONE last week.

Its films have grossed more revenue than the two next successful franchises, Harry Potter and Star Wars.

"The numbers of people who've watched these movies is just amazing. The amount of money involved is phenomenal," Professor Roughan said.

To try to explain why the Marvel movies are so popular, Professor Roughan calculated the effective cast size of the first 21 films by counting how many conflict situations each character was in throughout the film.

He then compared this number against the profitability ratio of the film (the box office returns divided by the movie's budget), and whether the movie was an origin story, a sequel or a team-up, where you get all of the superheroes coming together.

"The most obvious thing you see is a correlation between the size of the cast, the effective number of characters in the movie, and the profitability," Professor Roughan said.

That doesn't mean that if you put more characters in a movie it will suddenly be more profitable, as can be seen in the case of Avengers: Infinity War (the point on the far right of the graph), but the movies with the bigger casts tended to be the ones that made more money.

The researchers also noticed a strong relationship between the type of movie and its profitability, which they think reflects the overall structure of the MCU.

The franchise has smaller origin movies like Iron Man and Captain America which introduce the individual superheroes and explain some of their back story.

These characters then go onto to appear in the larger Avengers team-ups.

"You get fans of Iron Man and you get fans of Captain America who each have their own little piece of the puzzle that they want to see, and then when they come together, all those fans come together in one big group," Professor Roughan said.

Sequels and team-ups generally out-performed origin movies, with Black Panther and Captain Marvel being clear exceptions to this trend.

"It's really clever of them to be willing to do these smaller [origin] movies," Professor Roughan said.

"They make money, they're great movies but they're not quite so big press, exciting things in order to build towards the really big movies, which then break all box office records.

Science in your inbox

Get all the latest science stories from across the ABC.

# data[].attributes.attachment_link.title
The maths behind what makes Marvel movies so popular

# data[].attributes.attachment_link.description
What do you get when you cross a mathematician on his summer holidays with the Marvel Cinematic Universe back catalogue? A Christmas spent binge-watching superhero films, and a statistical analysis of why the Marvel movies are so popular. "It started almost as a joke," said mathematician and self-confessed Marvel fan Matthew Roughan of the University of Adelaide.

# data[].attributes.attachment_link.title
LM - MTM 50 Ways Math Can Solve Real-World Problems

# data[].attributes.attachment_link.authors[].name
Matt Martino, Julian Fell, Ben Spraggon, and Cristen Tilley

# data[].attributes.attachment_link.title
The census is big data — we’ve turned it into 100 dots to sift out the good stuff

# data[].attributes.attachment_link.description
Australia is a diverse and complex country, but if we use census data to turn it into 100 dots, it can tell us a lot about who we are and how we’re changing.

# data[].attributes.attachment_link.description
These beautiful flash cards use spaced repetition to teach multiplication facts. Achieve fluency with just five minutes of practice per day!

# data[].attributes.attachment_link.readable_text
Looking for maths games and interactives for Year 6 students to use in the classroom? These popular resources deal with fractions, decimals, statistics, percentages, area, grids, probability, data analysis, symbols, time, measurement and much more.
Playing an interactive game together as a group is a great way to introduce and start learning a concept. Problem solving together can lead to lots of fun classroom discussion.

Games can also help reinforce and deepen understanding of a concept.

Students can play these games by themselves at home or together in the classroom.

Here are popular maths games, as decided by teachers and students!

How well do you understand decimal place value with numbers that include hundredths? You'll be given a starting number, such as 46.87, which you then need to turn into a target number, such as 85.32. Try to achieve the target with as few additions or subtractions as possible. (Topics: addition, decimals, number lines, place value)

Use this tool to match different types of clock times. Adjust the time on 12-hour and 24-hour digital clocks to match the time on an analog clock. Some of the times will go right down to the minute. Try to finish each challenge in the least number of adjustments. (Topics: time, digital clocks)\

Do you want fly soup or bug burgers? In this awesome game, the Foul Food Maker randomly creates several kinds of disgusting meals. Work out the likelihood of getting a certain meal. Run simple probability experiments and compare the results with theoretical probability. (Topics: sampling, probability, statistics)

Ready for a trading challenge in the world of pet fish? Your ultimate goal is to buy a fizzer fish, but you'll have to do some smart trading to make enough money to buy it. Compare prices, supply and demand in different trading markets, and make sure you maximise your profit and reputation as a smart trader. (Topics: profit, loss, discounts)

These thought-provoking infographics helps students understand how data representation builds knowledge and influences decisions about social issues. Statistics are presented using the full range of graphs included in the syllabus requirements of the Australian Mathematics curriculum. (Topics: statistics, data representation, percentages)

Mark the route for a walking track on a rainforest map. Choose a section of track based on instructions about distances, compass directions and grid references. Keep adding sections of track to get to the rest house. (Topics: symbols, maps, grid references)

Help an archer to hit an apple with his arrow by building two fractions that equal one whole. Use the Fraction Fiddle Tool to see what happens when you change the numerals in a fraction. Students build fractions and compare them on a number line to find out which one's larger. (Topics: addition, denominators, subtraction)

You're a contestant in a quiz show, and you need to solve worded mathematical problems about nature. To collect a prize, you need to listen to the suggestions from the panel and identify the correct answer for each step in the problem-solving process. (Topics: problem solving, multiplication, mental arithmetic)

Using a grid, help a town planner design two site plans for a school. Assign regions of a 10 x 10 grid for different uses, such as a classroom, playground, canteen, car park or lawn. Calculate the percentage used for each region, and practise different ways to represent fractions. (Topics: area, proportions, grids, number operations)

Explore how kids use their leisure time. Create a survey, and then choose the best way to display the results, whether a pie chart, bar graph or histogram. Use the data to answer questions and write a report based on the survey results. (Topics: tables, data analysis, sampling, statistics)

Use a strategy to help you solve divisions, such as 157 divided by 6 (you may have remainders). Split a division into parts that are easy to work with, use times tables, then solve the calculation. Strategies like this help you do complex arithmetic in your head. (Topics: factors, division, number patterns)

You need to recreate a photo of a group of 3D objects. Rotate the scene on the grid until you have matched the same viewpoint. This interactive helps you explore visual perspectives of solids, such as cylinders, spheres, cones and cuboids. (Topics: geometry, solids, translation, perspective)

Explore facts about the life of cassowaries, such as their physical characteristics, diet, habitat and life cycles. Answer fraction questions as you interact with graphs and work through the ecology notes. (Topics: number operations, simple fractions, measurement, mental arithmetic)

A frequency graph shows the results of a spinner. Your job is to build a new spinner that recreates the results. Work out the proportions of colour you need, and then test your spinner and compare your graph to the graph of the spinner. Are the results similar? (Topics: sampling, statistics, data analysis, probability)

Work out how many acrobats you need to form square-shaped human towers. You'll learn about squared numbers too. Examine a table and graph, and look for a pattern that will help you predict the number of acrobats needed to build bigger towers. Describe how the number pattern is formed. (Topics: number patterns, composite numbers, perfect squares)

Find more classroom resources for Year 6 maths on ABC Education.

# data[].attributes.attachment_link.title
Top maths games for Year 6 students - ABC Education

# data[].attributes.attachment_link.description
Looking for maths games and interactives for Year 6 students to use in the classroom? These popular resources deal with fractions, decimals, statistics, percentages, area, grids, probability, data analysis, symbols, time, measurement and much more.

# data[].attributes.attachment_link.title
Brain Breaks Zoom Edition - Institute of Positive Education 2020

# data[].attributes.attachment_link.title
Lily Serna loves her fans, but there’s one thing she hates them saying - ABC Everyday

# data[].attributes.attachment_link.description
It’s been almost a decade since the last episode of Letters and Numbers was filmed, but people still stop co-host and mathematician Lily Serna on the street to chat about it.

# data[].attributes.body
nrich activity

# data[].attributes.attachment_link.readable_text
Which countries are most "sporty"?

Below, we have provided the London 2012 Olympics medal table.

Do you think the medals table alone offers enough information to answer this question fairly?

What other information do you think could be taken into account?

Make a plan of the information you will collect and the calculations you will perform. Then carry out your plan to decide which countries are most sporty.

Send us your top-rated countries, together with your justification for the data and criteria you chose to include in your analysis.

In the London 2012 Olympics the final medal table was as follows ( spreadsheet CSV form)

You could use data from previous Olympics to see the extent to which your criteria give a constant list of most sporty nations over time.

# data[].attributes.attachment_link.description
Which countries are most "sporty"? Below, we have provided the London 2012 Olympics medal table. Do you think the medals table alone offers enough information to answer this question fairly? What other information do you think could be taken into account? Make a plan of the information you will collect and the calculations you will perform.

# data[].attributes.body
Resolve activity

# data[].attributes.attachment_link.description
Resources for teaching STEM to students.

# data[].attributes.body
nrich activity

# data[].attributes.attachment_link.readable_text
Above are two sets of data that were gathered by school children in 1986 for what was called the Domesday Project. This project took place throughout the U.K. celebrating 900 years since the Domesday Book. You can find out more about it here.

In the data you see what two schools found out about the pets owned by some of the children. The Domesday Project took place in the early days of computers and so there were not many ways to display the information.

Here is a collection of seven such surveys which you can download as a pdf (data.pdf). These seven include the two above. Have a good look at them. You could focus on just the two above or on all seven.

What did the various school children find out?

These seven schools were all from very different areas of the UK. Does that surprise you? How might that have affected the data?

What differences do you notice in the ways that the data is displayed?

Which survey do you think is presented in the best way? Why?

Which survey do you think is not presented in a helpful way? Why?

You could do a similar survey in your class and compare the results.

# data[].attributes.attachment_link.description
Above are two sets of data that were gathered by school children in 1986 for what was called the Domesday Project. This project took place throughout the U.K. celebrating 900 years since the Domesday Book. You can find out more about it here.

# data[].attributes.body
Resolve activity

# data[].attributes.attachment_link.description
Resources for teaching STEM to students.

# data[].attributes.attachment_link.readable_text
We have been collaborating with our 2 neuroscience advisors, Christian Battista and Lang Chen, on new papers releasing the fascinating new evidence on the ways our brains learn mathematics, that are shared on this page.

In the labs at Stanford they have developed some really interesting new knowledge on the ways brains work mathematically. Prof Vinod Menon and his team have shown that our brains are made up of 5 different networks that are involved when we think about maths. Two of the networks are visual pathways - one is the ventral and one the dorsal visual pathway. Neuroimaging has shown that even when people work on a number calculation, such as 12 x 25, with symbolic digits (12 and 25) our mathematical thinking is partly visual.

The different evidence that is coming from the neuroscientists tells us that our brain wants to think visually about maths. Building students' mathematical understanding doesn't just mean strengthening one area of the brain that is involved with abstract numbers, it means strengthening connections between areas of the brain and strengthening the visual pathways.

We at youcubed believe that every mathematical concept can be represented visually to students, and that this would help them greatly. In our teacher paper, called "Seeing as Understanding," we not only discuss the visual research but also include visual activities for all grade levels. Some of the other papers and news articles share some fascinating new research on the importance of fingers. The visual activities shares different K-12 visual math activities, as examples of ways to make maths more visual.

# data[].attributes.attachment_link.description
We have been collaborating with our 2 neuroscience advisors, Christian Battista and Lang Chen, on new papers releasing the fascinating new evidence on the ways our brains learn mathematics, that are shared on this page. In the labs at Stanford they have developed some really interesting new knowledge on the ways brains work mathematically.

# data[].attributes.attachment_link.title
Mathematical Mindset Teaching Guide, Teaching Video and Additional Resources - YouCubed

# data[].attributes.attachment_link.description
We have designed a Mathematical Mindset Guide to help teachers create or strengthen a growth mindset culture. This guide contains five Mathematical Mindset Practices along with links to teaching videos. […]

# data[].attributes.attachment_link.readable_text
The Maths Inside project offers a series of eight maths lessons that are based on real research projects that are undertaken by CSIRO researchers and mathematicians. They offer insights as to how maths is used to solve research problems.

It is hoped teachers and students will find these examples to be interesting applications of the maths they have been studying and that they will stimulate the students' curiously to study more. The project was conducted by AAMT in collaboration with the University of Technology, Sydney, and CSIRO.

# data[].attributes.attachment_link.description
Maths Inside The Maths Inside project offers a series of eight maths lessons that are based on real research projects that are undertaken by CSIRO researchers and mathematicians. They offer insights as to how maths is used to solve research problems. It is hoped teachers and

# data[].attributes.body
Integrated program

# data[].attributes.attachment_link.readable_text
Say their names:

Al-Khwarizmi. Aryabhata. Bhaskara. Germain. Agnesi. Galois. Zhenyi. Mirzakhani. Shijie. Al-Haytham. Nightingale. Hypatia. Pingala. Noether. Lovelace. Easley. Brahmagupta. Uhlenbeck.

Whether you realize it or not, simply reading and saying the names of the mathematicians in the thumbnail is an important process in cultivating identity and attribution. Each of those 18 people have a story to tell that contributes to the massive and seemingly endless braid of the history of mathematics. And yet, simultaneously - and paradoxically - they only represent a mere fraction of the lore of mathematics.

Regardless, individually and collectively, they represent potential spaces for connection, identity, and belonging for our students and teachers. The diversity of faces, clothing, customs, and religions not only contributes to the kaleidoscope of mathematics, it provides a powerful snapshot for students to quickly see the magnitude of time in the thematic development of mathematics.

Each of those 18 profile pictures were pulled from this beautiful "Timeline of Mathematics" found at Mathigon. The time line is populated with mathematicians and important artifacts of mathematics. But, more importantly, it is not a static resource. It is constantly being updated with more mathematicians, more stories, and just more magic. As you explore this free resource, you will notice that situating students immediately in some kind of rich, historical narrative - giving origin and purpose - is what anchors all the courses.

There is much mythology and mysticism in mathematics. That in itself is a tantalizing allure to dive deeply into the rich history of mathematics.

For the past few years, I have written extensively about an urgency in broadening our ongoing discussions in math equity with actual mathematics from various cultures, races, and civilizations.

My last four articles related to the topic can be found below:

This article is all about resources( I will continually update this article with them) And, regardless of what grade you teach, there is something here for any teacher to begin the long, but wonderful journey of bringing inclusiveness and more anti-racism ideas into our classrooms.

Here is a wonderful reflection piece by author and teacher, Alice Aspinall. It is a short, but powerful read, to firmly establish the vector that all of us need to move in the direction of for the future of math education.

We all know that when children first start school, they are enamoured with storytelling time. Just the idea of sitting on a floor, anticipating a story from your teacher, are some of our favorite memories of school.

With much gratitude to the people at Math Minds, a wonderful flip book is available for K-1 teachers, calledDisappearing Moon, based on the oldest known math artefact, the Lebombo bone. Another story that has a historical element is , a nod to how a young Gauss added up numbers.

For middle school, Buzzmath has been teaching students about math history for over 10 years, through their Missions, a gamefied part of their platform that not only immerses students in a historical context, but also promotes resilience with challenging problems. Free access to one of their Missions can be found here.

As well,a link to their math history cards can be found here.

What is important about math history is that serves the purpose of fostering deep curiosity. Storytelling plays a part in that cycle.

Amplify is a company that is working with this immersive process in bringing the power of narrative/storytelling to math classrooms.

A link to the math profile cards pictured above can be found here.

In addition, if you would like to read more about the importance of bringing math history inside our classrooms, an ebook that I authored can be found here.

I am working closely with Amplify to ensure that compelling mathematical stories are fixtures in the platform - that they are inextricably baked right into the curriculum. A complete sample unit can be found here. As well as a link to feedback and interest in participating in fields trials of these narrative-rich units.

What is also critical when using math history as a resource, are the multitude of unsolved - yes, unsolved - problems that can be shared with students to bring more context, relevance, and admiration for the work that mathematicians do. Thanks to Gord Hamilton(@gamesbygord), he has curated the small fraction which are accessible to our K to 12 students. Click on the link below.

There are, of course, some wonderful books that I would recommend to start adding to your library of math history/storytelling resources.

The Crest of the Peacock

This book(third edition) is the gold standard to find the roots of mathematics and correctly relay the trajectories of where we are today - especially with scholarly attribution of mathematical discoveries.

I was lucky to come across this book a few years ago, and it does a beautiful job of showing the history of mathematics through some well-known - and some others not as much - puzzles. There is a rich commentary in the opening of the book, and each puzzle has an answer with a detailed solution.

If this book were hardcover, you would put it on your coffee table! Absolutely gorgeous with rich illustrations, the book is a chronological tour of some of the most important discoveries in mathematics. Obviously not an all encompassing compendium, but has a nice balance in its time line of unpacking some of mathematics' most major milestones.

Ying and the Magic Turtle

As always, where and how children get introduced to the imagination of mathematics lies is beautiful storytelling. As you can see, I was one of the reviewers of the above book, as were some highly respectable math educators from North America. If you are an elementary teacher, this one is definitely a must have.

One of our generation's best storytellers in mathematics is Marcus du Sautoy, a world-renowned author and professor of mathematics at Oxford University. He narrated the brilliant 4 part series, The Story of Maths, which is a must watch.

Speaking of "must watches", I would strongly recommend that you watch Keith Devlin, Stanford University, and his enthusiastic storytelling of Algebra. In a time where the debates regarding algebra as a school topic are distilled down to a tasteless arguments about usefulness, Devlin tells a rich and compelling story of its birth and migration, indirectly supporting the notion that algebra - taught in a rich, historical context - is an invaluable area of knowledge that not only progressed mathematics, but society as a whole.

As exhaustive as this article might seem with resources, it is meant only as an initial invite into our journey in this magic labyrinth of stories, that when braided together, rightfully color mathematics with magic, mysticism, and mythology.

To be continued...!

# data[].attributes.attachment_link.title
How To Begin Bringing Rich and Inclusive Math History Resources Inside K to 12 Classrooms

# data[].attributes.attachment_link.description
Say their names: Al-Khwarizmi. Aryabhata. Bhaskara. Germain. Agnesi. Galois. Zhenyi. Mirzakhani. Shijie. Al-Haytham. Nightingale. Hypatia. Pingala. Noether. Lovelace. Easley. Brahmagupta. Uhlenbeck. Whether you realize it or not, simply reading and saying the names of the mathematicians in the thumbnail is an important process in cultivating identity and attribution.

# data[].attributes.attachment_link.description
Welcome to 52 weeks of math! The list of activities is below, or there is a blog view here. Enjoy! Week 1 - Embroider Curves with Lines Week 2 - Spiral of Theodorus Week 3 - Sonobe Origami Octahedron Week 4 - Polyhedral Study Week 5 - Tell a Tale (or Comic) Week 6 -...

# data[].attributes.attachment_link.readable_text
Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

# data[].attributes.attachment_link.description
Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

# data[].attributes.attachment_link.description
Maths Inside
Maths Inside consists of a series of maths lessons that are based on real-life scenarios. For each lesson there is a video of a maths practitioner who explains how they apply maths to their work. Growing Mathematically
Growing mathematically introduces teachers to learning progression…

# data[].attributes.attachment_link.readable_text
Introduction

Growing Mathematically is an initiative that supports and promotes the use of learning progressions, formative assessment and targeted teaching as effective teaching strategies for mathematics.

The current project applies Growing Mathematically to multiplicative thinking. The aims of the project are to provide:

An up-to-date and evidence-based learning progression (Learning and Assessment Framework, LAF) that describes the stages of development of multiplicative thinking skills

A mapping of the LAF to the Australian Curriculum: Mathematics and the National Numeracy Learning Progression

Validated assessments for teachers to locate their students on the LAF

Teaching advice and targeted teaching tasks that help teachers progress their students from one LAF level to the next

Background and research information

The project is currently in a trial phase. These web pages provide information about the trials and the procedures for the schools participating in them. All the relevant documentation, including the Teacher's Manual, can be downloaded from the links in the Documents section. The Teacher's Manual is a consolidation all the documents required for participating in the trials.

At the end of the trial process, the final materials will be published here.

# data[].attributes.attachment_link.description
Introduction Growing Mathematically is an initiative that supports and promotes the use of learning progressions, formative assessment and targeted teaching as effective teaching strategies for mathematics. The current project applies Growing Mathematically to multiplicative thinking. The aims of the project are to provide: An up-to-date and evidence-based learning progression

# data[].attributes.attachment_link.readable_text
DR. GINA A. ZURLO

Co-Director, Center for the Study of Global Christianity

When the World as 100 People graphic went viral a few years ago, I knew this could be replicated with data on global Christianity. With the help of CSGC research assistant Amanda Perkins and designer Brad Coon, we developed the graphic above and published it on the first page of the World Christian Encyclopedia. There are 2.5 billion Christians in the world - that's a big number. So big, it can be hard to conceptualize. But 100 is different. You've probably been in a room with 100 people. You can probably list 100 people by name. What if those 100 people represented all the beauty and diversity of World Christianity?

If 100 Christians represented all of global Christianity, 67 would live in Asia, Africa, Latin America or Oceania, while 33 would live in Europe or Northern America. Most would be found in urban areas (65) as opposed to rural (35). Linguistically, 16 would speak Spanish as their mother tongue, 10 English, 8 Portuguese, 5 Russian and 3 Mandarin Chinese. Most (64) would be between the ages of 15-64, while 26 would be under 15. Eleven Christians would be illiterate, and 35 would have little to no access to secondary education. Roughly half of Christians would have access to the internet. Fourteen would have no access to safe water, and five would have malaria. Most Christians (79) would live in countries with moderate to high corruption; 35 would live in countries with low development. A typical Christian today is a non-white woman living in the global South, with lower-than-average levels of societal safety and proper health care. This represents a vastly different typical Christian than that of 100 years ago, who was likely a white, affluent European.

The World Christian Encyclopedia describes the friction of Christian diversity with its divisive tendencies, as well as the harmonious balance when Christians work together across differences. There is indeed a "World Christianity" to speak of - as opposed to "Christianities" - and it is a portrait of a complicated yet united whole.

Learn more about the World Christian Encyclopedia and our upcoming conference here.

Technical notes: The World as 100 Christians graphic draws on a number of sources to depict the proportion of various of subjects if the world consisted of 100 Christians. The outer ring of continent, gender, density, age, tradition and language comes mainly from data found in the World Christian Database ( WCD). The inner ring of 12 global issues comes from the intersection of United Nations and the World Health Organization (WHO) with the WCD's data on Christianity.

# data[].attributes.attachment_link.description
When the World as 100 People graphic went viral a few years ago, I knew this could be replicated with data on global Christianity. With the help of CSGC research assistant Amanda Perkins and designer Brad Coon, we developed the graphic above and published it on the first page of the World Christian Encyclopedia.

# data[].attributes.body
Collect data and represent it

# data[].attributes.attachment_link.title
Education resources for schools teachers and students - ABC Education

# data[].attributes.attachment_link.description
ABC Education has 5000+ educational games, videos and teaching resources for schools and students. Free Primary and Secondary resources covering history, science, English, maths and more

# data[].attributes.body
Problem solving to consolidate understanding of Pythagoras

# data[].attributes.attachment_link.keywords[]
md pythagoras' theorem & trigonometry

# data[].attributes.attachment_link.title
Pythagoras' Theorem and Trigonometry - Short Problems

# data[].attributes.attachment_link.description
A collection of short problems on Pythagoras's Theorem and Trigonometry.

# data[].attributes.attachment_link.description
Use logic to solve visual, interactive mathematical puzzles. Create your own puzzles to share with your friends or the SolveMe Community.

# data[].attributes.body
exponential loss approaching zero

# data[].attributes.body
Youcubed recommended by Sandra

# data[].attributes.attachment_link.readable_text
It's hard for kids to remember a string of arbitrary numbers. from www.shutterstock.com.au

Lots of kids have trouble remembering their times tables. Learning them by rote can mean a child can accurately recite the times tables, but has no idea what the numbers actually mean or how to apply this knowledge in a maths problem.

Practice is essential to effective learning, but it is important to keep a balance between practice and application.

Children need to know why they need to learn times tables

The number system underlying the times tables can often seem fairly arbitrary. A child can be forgiven for thinking it's just a complex system of numbers that they have to learn because the teacher says so.

If you have no idea why you are required to learn something, it is very difficult to develop sufficient motivation to persist with the practice that is often necessary to master the material.

One way to demonstrate the usefulness of the times tables is to engage a child in a counting task. The task could be timed, such that determining the number of elements quickly will mean something for the ultimate result (for example, beating a time limit results in a positive outcome, failing to beat the limit means the task starts again).

The multiplication facts in the times tables can then be demonstrated as short cuts in the counting process (if you can arrange the elements into four groups of eight, then knowing the answer to "4 x 8 = ?" will result in faster performance than having to rely on counting all of the 32 elements).

Many computer games and apps (like IXL Maths) possess this feature. They also involve many other features designed to maintain the interest of a child, which can help keep them motivated enough to persist with the task. Ultimately, the more practice, the better the knowledge.

Get to know the sums individually, not as a song lyric

Memory can often be a good reflection of what we do. If we regularly sing along to a favourite song, each line tends to remind us of the next line. However, if we then try to sing the song by ourselves, without the aid of an accompanying recording, we often find that forgetting one line means subsequent lines also can't be recalled.

A similar thing can happen if we engage in rote recitation of the times tables. This method is only useful if we want to have a method to fall back upon when all other methods fail. Basically this method can only produce the equivalent of a song lyric where, remembering what "4 8s" are is only possible if you can remember "4 6s are 24" and "4 7s are 28".

A better form of knowledge is one where a child knows the answer to each multiplication problem as soon as they see it, much like being able to read a word as soon as you see it.

Knowing the answer to each problem is then independent of knowing the answer to other times table problems. This type of knowledge can be gained only by practice at producing the answer.

One method for undertaking this type of practice is something like the old flash-card method. Write a problem on one side of a card (4 x 8 = ?), and the answer on the other side. With a shuffled deck of cards representing all of the problems in the times tables, a child can practise producing the answer to each problem, and then check their response by turning over the card.

Occasionally an adult can ask the child to do this out loud to ensure they are doing the task correctly. Initially the child may have to guess the correct answer, or work it out with their fingers or some other method. But they always have the benefit of immediate feedback by turning over the card.

Eventually, with enough practice, the constant association of the problem with the correct answer will begin to stick in their memory. A similar method can be easily programmed on to a computer or tablet. Plenty of commercial apps are available that will mimic this procedure.

Apply the times tables knowledge

Knowledge of the times tables is not useful by itself. A child must learn to apply the knowledge in a mathematical context.

It is important, though, that a child's knowledge of the times tables is not allowed to remain as a list of independent facts. A child needs to engage in activities that demonstrate the connections between the multiplication facts in the times tables. It is important to see how 4 x 8 and 8 x 4 are connected.

Ultimately they will also need to see how 4 x 8 = ? and 32 ÷ 8 = ? are connected. To achieve this the child should be provided with activities that require the application of their arithmetic knowledge in a way that can demonstrate and lead the child to uncover these connections.

Practice with this sort of material can help kids develop a knowledge base that results in reliable retrieval of facts and the sort of flexible application of this knowledge that is required in higher-order problems, such as solving for x in 2x + 3 = 11. If you struggle to come up with an answer to this problem, I would not suggest relying on a times tables song to help you out.

# data[].attributes.attachment_link.title
Here's how to get kids to remember times tables

# data[].attributes.attachment_link.description
Lots of kids have trouble remembering their times tables. Learning them by rote can mean a child can accurately recite the times tables, but has no idea what the numbers actually mean or how to apply this knowledge in a maths problem.

# data[].attributes.body
no websites, just an idea

# data[].attributes.attachment_link.readable_text
Resource finder
The most efficient way to search for teaching resources on nzmaths. Filter resources by level, strand, achievement objective, LPF aspect or resource type. Login to add search results to your teaching plans in the Planning Space.

Problem solving activities
An extensive collection of problem solving sessions. Each session includes a problem, a suggested teaching sequence, and possible extensions.

Rich learning activities
A collection of activities in engaging contexts in which to explore the achievement objectives from the NZC at levels 1-5.
Several differentiated approaches to engage students with varying levels of understanding are described and useful prompts for the teacher are included.

e-ako maths
More than 200 interactive student modules linked to strands and levels 1-5 of the NZC. These pedagogically sound modules illustrate best teaching practice and include authentic New Zealand contexts. Teachers can tailor learning pathways and monitor student progress.
Information about e-ako maths.

Picture books are an effective way to engage and entertain students. Books with mathematical content are linked to level and strand of the NZC. Suggested teaching activities are included for many of the books.

Figure It Out is a series of mathematics curriculum support books designed to supplement existing classroom mathematics programmes. Download teacher notes, or use the carousel interface to download individual student activities with teacher notes.

The Take This collection is based on the idea that you can 'take something' of interest to students and use it as a context to flexibly connect mathematics across the strands.

The Connected series promotes scientific, technological, and mathematical literacy and covers curriculum levels 2, 3, and 4.

Digital Learning Objects developed to support teaching and learning, now available password-free.
Access learning objects by strand and/or curriculum level.

Early childhood education
Support for early childhood educators to use everyday interactions with children to foster the development of mathematical thinking. Includes early learning progressions, questions to pose, things to watch for, and ways to extend children's thinking.

Links to teaching and learning guides on TKI, NCEA resources, and other useful sites.

Ask and discuss questions relating to NCEA in the professional learning communities. Online discussion threads for each achievement standard are moderated by Secondary Mathematics and Statistics advisers.

Planning space
Create and manage teaching plans using resources from nzmaths. Plans include a summary and copies of all resources selected, and can be printed or emailed. You need to be logged in to use the planning space.

# data[].attributes.attachment_link.description
Resource finder The most efficient way to search for teaching resources on nzmaths. Filter resources by level, strand, achievement objective, LPF aspect or resource type. Login to add search results to your teaching plans in the Planning Space. Problem solving activities An extensive collection of problem solving sessions.

# data[].attributes.attachment_link.title
Classroom resources / Better teaching / Home - Australian Association of Mathematics Teachers

# data[].attributes.body
Funny grab from Would I Lie to You Ep3 ABC TV

# data[].attributes.attachment_link.description
How high up the tree was he? 🤷‍♀️ #WILTY

# data[].attributes.body
Essential Maths - differentiated problems
Developmental maths - good for explanations of terms (linked to language)

# data[].attributes.attachment_link.title
Counting Games for Years 7 and 8 (Kester Lee)