Maths skills need to serve students beyond the next 30 minutes

By Peter Sullivan, Professor of Science, Mathematics and Technology Education, Monash University. 

A lack of consensus about what works can make debates about education frustrating. This is especially true for the teaching and learning of mathematics. Not only is there a high level of disagreement about the teaching of the subject, but even the most fundamental approaches are debated.

One of the main areas of disagreement centres on whether students should be told explicitly what to do, or whether a problem-solving centred approach is more effective.

The first method, which some commentators support, involves teachers telling students what to do and having them practice multiple examples, which are then corrected. Such commentators see curriculum progress as climbing a series of micro-steps that are best taken in a particular order. This argument suggests that students work best by progressing through a textbook page-by-page and example-by-example.

As part of the same argument, it is recommended that students are taught in groups of similar levels of achievement, with students in lower groups being offered a limited mathematical diet. This approach is based, presumably, on an assumption that not all students can learn mathematics, and is most common in junior secondary classes.

However, a sample of Year 7 and 8 content that is on both the Year 7 and Year 9 NAPLAN assessments, reveals that students in those years hardly improve at all. (Schools can easily check this claim by comparing, for example, questions 5, 21 and 26 on the 2016 Year 7 Calculator paper that were also on the Year 9 paper). These items are explicitly on the content taught in years 7 and 8, yet, state-wide, the improvement is very limited. Even though these are not the same students, the comparisons give a clear indication that this approach is NOT working.

I, along with others, argue that a better way students can learn mathematics is through solving problems for themselves, by connecting related ideas together and working on tasks and experiences that are challenging, for which the solution path and type are not obvious, and which take time to reach. Through effective differentiation strategies, mathematics can be taught in mixed achievement groups, with students’ own solutions and solution strategies being a central part of the teaching. The assumption is that all students can learn mathematics given time and opportunity.

Those who support the former argument (that students need to be directed explicitly) claim that students give up quickly if not told what to do, that they will not persist long enough to find solutions, and that they do not like ambiguity and risk-taking, but want to get correct answers.

However, these are inappropriate orientations for the world of employment and life that we can imagine current students will experience. The responsibility of schools and mathematics teachers is to overcome such limiting self-beliefs.

Of course, there are some aspects of mathematics which students cannot be expected to come up with themselves, such as the formula for the relationship between the circumference and diameter of a circle or the theorem of Pythagoras.

But there are other aspects of mathematics which students can explore for themselves using the knowledge they already have. To give an example, imagine we are introducing middle primary students to the concept of measurement errors and how to avoid them. We might pose the following task for students.

Michael and Monica measured the basketball court. Michael said it was 20 rulers long. Monica said it was 19 ½ rulers long. How could this happen?

The teacher might ask the students to first work individually and then to collaborate with others to formulate a list of possible explanations for the discrepancy. There are many possible explanations that students can find for themselves. For example, when I have done this, students have suggested “one of them left gaps”, and others have suggested “one of them measured crookedly”. There are, of course, many other possibilities but note how these two suggestions could be turned into student generated rules for measuring such as “do not leave gaps” and “measure in the shortest straight line”.

The task, which the students can work on prior to any instruction, is accessible for all students and can be used as a prompt to stimulate collaborative discussion focusing on possible sources of measurement error.

The task can also be extended by posing a problem like:

Someone suggested that one of them left gaps. Who left the gaps: Michael or Monica?

The answer, by the way, is not obvious. Write your answer down before looking at the end of the article.

Note that this task also addresses another important measurement principle that students can see for themselves, that the larger the unit the fewer the number of units.

It comes down to this. Telling students how to answer mathematics questions might work well for the next 30 minutes but it does not enhance the chance of students remembering what they have been told, nor of transferring this particular learning to a different context. The challenge is to find ways to engage students in their own learning.

Hopefully the additional funding that many schools look likely to receive in new funding models might be allocated in ways that support such learning and teaching for the future.

(Monica left the gaps).


Move over, tennis mums, a new breed of tennis mom has arrived in the updated Oxford English Dictionary

You might remember the term tennis mum being used to describe women who returned to tennis after becoming mothers.

Now, tennis mom and tennis dad refer to parents who actively and enthusiastically support their child’s participation in the sport.

They are among the tennis-related, lifestyle, current affairs and educational terms included in the latest update of the Oxford English Dictionary.

More than 50 new words and 30 new senses related to tennis were added to the dictionary, after consultation with the All England Lawn Tennis and Croquet Club.

They included bagel, tennis slang coined by player Eddie Dibbs in the 1970’s, referring to a score in a set of six games to love due to the similarity of the numeral 0 to the shape of a bagel. Superbrat is also a word which is used in contexts other than tennis, but was famously applied to the tennis player John McEnroe by the British press in response to outbursts on court.

Forced error is used to describe a mistake in play which is attributed to the sill of one’s opponent rather than the player’s own misjudgment, while chip and charge refers to an attacking style of play, in which the player approaches the net behind a sliced shot.

What else is new to the OED?

A new usage of thing was introduced in the dictionary update, used in questions conveying surprise or incredulity, such as ‘how can that be a thing?’ This has been traced back to an early episode of television series The West Wing.

The new sense of woke, meaning ‘alert to racial or social discrimination and injustice’ has also been included. Its use by supporters of the Black Lives Matter movement, and in particular the phrase ‘stay woke’ is thought to have introduced the word to a broader audience, especially on social media.

Old sayings have also been tweaked, with footless (as in, footless drunk, an alternative to the more familiar ‘legless’) and son of a bachelor (a euphemistic alternative to ‘son of a bitch’).

Oxford Dictionaries announced post-truth as its 2016 Word of the Year, and since then, the huge increase in its usage has given the lexicographers enough evidence to add it to the OED.

In the educational sphere, the OED update included MOOC, an acronym for massive open online course, which you might have spotted on your social media feed and wondered about its meaning.

A range of words for wedding veils were added to the dictionary, including a birdcage veil, blusher veil, cathedral veil and fingertip veil.

Another lifestyle addition was the Danish trend and culture reference hygge, defined as ‘a quality of cosiness and comfortable conviviality that engenders a feeling of contentment or well-being’.

Finally, ZYZZYVA, referring to a genus of tropical weevils native to South America and typically found on or near palm trees became the new ‘last word’ in the OED.

You can find all the new new word entries, sub-entries and senses on the OED website.

For more on Australian dictionaries, visit the Australian National Dictionary.



Performance and retention – the value of textbooks

Textbooks can play an important role in student retention, according to Oxford University Press author James Arvanitakis.

In an article in The Conversation, James wrote about a new program at Western Sydney University in which first year students receive free access to digital textbooks. The pilot program was introduced at the start of 2017, following similar strategies in the US and the UK.

James wrote that he believed textbooks were an important pedagogical tool that could help keep students engaged.

“Success at university is a combination of pedagogical and social factors, which include support networks and university transition strategies. Student performance and retention is enhanced by access to high-quality resources that they can afford.

“Textbooks are a powerful pedagogical tool that can improve engagement. In my own teaching experience, a well-written and relevant textbook allows students to better understand the broader subject narrative,” he wrote.

“That is, it is not about learning individual topics such as gender, class, race and technology. Rather, it allows the student to see the story of arc of the complex and intersectional factors that shape our societies.”

In his own experience, James has seen the benefits of high quality texts on student performance and retention, citing a drop-out rate of 22% falling to less than 2% as a result of the introduction of a textbook, with feedback indicating repeatedly pointing to the value of the new textbook.

James edited OUP title Sociologic – Analysing Everyday Life and Culture. He is a strong supporter of the ‘inclusive access’ model of textbook purchase.



How to make maths memorable

By Annie Facchinetti

Recent research in the area of neuroscience has revealed that the brain has a greater ability to change and adapt than was previously thought. However, brain changes are generally not instant. For lasting neurological pathways to be built, much like wearing a physical pathway between one place and another, they need to be travelled multiple times.

The idea that practice assists with the retention of knowledge is not a new one, but our understanding of the importance of practice in learning has been deepened by neuroscientific research. For example, a 2013 study by the Norwegian University of Science and Technology specifically examined the role of practice in the acquisition of maths skills. According to Professor Hermundur Sigmundsson, one of the study’s authors, ‘We found support for a task specificity hypothesis. You become good at exactly what you practice’ (EurekAlert!, 2013).

The concept of practice is therefore an integral part of Oxford Maths. Each topic in the Student Books features a Guided Practice section that includes worked examples to support students in the early stages of learning about a concept or skill. The Independent Practice pages then allow students to use their skills and apply their knowledge, while the Extended Practice section provides the opportunity to apply learning in slightly more challenging contexts.

The Oxford Maths Student Book practice sections follow a gradual release of responsibility model, designed to scaffold students’ learning and build confidence to tackle more complex work. Many students, and indeed many adults, would assert that they are not good at maths, and the approach used in Oxford Maths is designed to ensure that every student can experience success at their level. An OECD presentation about the role of the brain in learning reached the following conclusion:

‘Concerning positive emotions, one of most powerful triggers that motivates people to learn is the illumination that comes with the grasp of new concepts – the brain responds very well to this. A primary goal of early education should be to ensure that children have this experience of “enlightenment” as early as possible and become aware of just how pleasurable learning can be.’ (Understanding the Brain: the Birth of a Learning Science, 2008)

To ensure that all students have the opportunity to feel successful in maths, the Oxford Maths Teacher Dashboards offer differentiated learning pathways to support students at their point of need. This includes teacher-led activities for students who require extra support, additional hands-on and collaborative learning experiences for students who are at standard, and a range of extension opportunities to challenge more able students. Suggestions for daily practice and ideas for whole-class activities offer a range of different opportunities to practise concepts and establish lasting neurological pathways. The pre- and post-assessment components also equip teachers to monitor student learning and make appropriate teaching adjustments.

In discussing the gradual release of responsibility model, Fisher and Frey (2008) assert that, ‘Structured teaching requires that teachers know their students and content well, that they regularly assess students’ understanding of the content, and that they purposefully plan interrelated lessons that transfer responsibility from the teacher to the student’. The structure of the Oxford Maths program also supports the ‘I do it; we do it; you do it together; you do it independently’ philosophy of the gradual release of responsibility model, by working through a structured series of activities that foster collaborative learning supported by ongoing snapshot assessment.

As teachers, it is easy to overlook the importance of practice as we rush to cover all the content required while meeting the high demands of busy school life. Oxford Maths provides a clear and comprehensive mathematics program that draws on current research to ensure that content is not just ‘covered’ but taught in a way that leads to sustained learning and the development of problem solving and reasoning skills.

Oxford Maths:

  • is a balanced approach including direct instruction, hands-on activities, small group and whole class tasks, skill practice and open-ended problem-solving.
  • incorporates key elements of inquiry, including making connections with mathematics in the real world, opportunities for higher-order thinking and multiple pathways for students
  • supports students to build foundational maths skills needed for complex critical thinking and problem-solving tasks.

Further reading

EurekAlert! 2013, No math gene: Learning mathematics takes practice. [online] Available at: [Accessed 28 June 2016].

Fisher, D & Frey, N 2008, Better learning through structured teaching, Association for Supervision and Curriculum Development, Alexandria, Va.

Sigmundsson, H, Polman RCJ & Lorås, H 2013, ‘Exploring Individual Differences in Children’s Mathematical Skills: A Correlational and Dimensional Approach’, Psychological Reports: Volume 113, Issue 1, pp. 23-30. doi: 10.2466/04.10.PR0.113x12z2

2008, Understanding the Brain: the Birth of a Learning Science, 1st ed. [ebook] Paris: OECD. Available at: [Accessed 28 June 2016]

Don’t underestimate the value of practice in maths education

By Annie Facchinetti

It is often easy to assume that because students appear to have understood an idea or demonstrated a skill on a particular day, they have mastered the associated concept. However, research is increasingly confirming the importance of practice in embedding learning in long-term memory.

The adage ‘practice makes perfect’ is proving particularly relevant in the field of neuroscience, where studies show that exposure to repeated experiences of a topic are more likely to build lasting neurological pathways. Hohnen and Murphy (2016, p. 79), for example, found that repetition or practice results in what they call ‘myelination of that circuit’ (myelin is described as the insulating sheath around many nerve fibres, which increases the speed at which impulses are conducted), resulting in students developing greater efficiency with the target skill.

Practice, with a view to mastery, therefore underpins the spiral approach used in the Maths Plus program, both within and across year levels. In a 2007 report, Pashler et al concluded, ‘Research has shown that delayed re-exposure to course material often markedly increases the amount of information that students remember. The delayed re-exposure to the material can be promoted through homework assignments, in-class reviews, quizzes, or other instructional exercises’ (p. 5). Maths Plus offers students the opportunity to revisit mathematics topics at different points in the year, supported by the extra practice afforded by the Mentals and Homework Books.

The Maths Plus Teacher Dashboard also provides access to a range of resources that will enable students to experience mathematical concepts in a variety of different ways. These include digital interactives to introduce and explore topics, as well as support, extension and reflection activities. Problem-solving challenges included in the Student Books allow for skill application in a variety of contexts.

The final step in the Maths Plus process is assessment. Another of Pashler et al’s (ibid., p. 21) findings was that, ‘… the act of recalling information from memory helps to cement the information to memory and thereby reduces forgetting. By answering the questions on [a] quiz, the student is practicing the act of recalling specific information from memory’. The comprehensive post-assessment components available as part of the Maths Plus program help consolidate learning, and allow teachers to gauge student understanding, while the simple marking system provides evidence for A–E grading.

According to the UK’s National Centre of Excellence in the Teaching of Mathematics, ‘All pupils should become fluent in the fundamentals of mathematics, including through varied and frequent practice, so that pupils develop conceptual understanding and are able to recall and apply their knowledge rapidly and accurately to problems (NCETM 2014). The Practise, Master, Assess approach used in Maths Plus covers all these aspects, using proven strategies to develop the knowledge and skills to become proficient in mathematics.

Maths Plus:

  • Provides spiralling content where concepts are explored, then built on throughout the year and across year levels. This helps learners make connections over time, supporting recall and fluency.
  • Offers varied learning experiences such as interactive concept exploration, learning, practice and consolidation activities, problem solving tasks, extra support and extension activities, and mentals and homework activities.
  • Assessment Books (bundled with Student Books) provide post-assessment tests that are simple to use and quick to administer, and allow teachers to track and review student learning.
  • Series is explicitly aligned to the new Victorian Curriculum, as well as the Australian Curriculum and New  South Wales syllabus.

Further reading

Bruner, J 1960, The Process of Education, Harvard University Press, Cambridge, Mass.

Hohnen, B & Murphy, T 2016, ‘The optimum context for learning; drawing on neuroscience to inform best practice in the classroom’, Educational & Child Psychology, 33(1), p. 79.

National Centre of Excellence in the Teaching of Mathematics 2014, Mastery Approaches to Mathematics and the New National Curriculum, Sheffield, United Kingdom.

Pashler, H, Bain, P, Bottge, B, Graesser, A, Koedinger, K, McDaniel, M & Metcalfe, J 2007, Organizing Instruction and Study to Improve Student Learning (NCER 2007–2004). Washington, DC: National Center for Education Research, Institute of Education Sciences, U.S. Department of Education. Retrieved from [Accessed 19 July 2016]


Why flipped learning makes sense in the STEM classroom

By Andrew Douch

The current generation of STEM teachers is the first that must choose between teaching important skills and teaching urgent skills. In the past, there was no difference — the important skills were the urgent skills. Now there is a fork in the road, presenting a threshold challenge for STEM teachers that flipped classrooms can help us overcome.

“Importance” is about how much something matters. “Urgency” is about how soon it matters. In previous generations, it was understood that the more knowledge students had when leaving school, the better their career prospects. The urgency of exam preparation incentivised students to learn the important skills that would later underpin their career success. But that is no longer true.

There is a growing, collective understanding among STEM teachers that the skills that prepared yesterday’s students to thrive in a knowledge economy are inadequate preparation for today’s students. As information continues to be commoditised and processes automated, retaining knowledge is less important than it once was. It is still helpful for a student to know the first 20 elements of the periodic table, but failing to know them is a much smaller handicap than it was 20 years ago. After all, you can ask Siri what the atomic mass of copper is, should you ever need that information.

I’m not saying, as some do, that knowledge has no value, or that looking something up (no matter how efficiently) is as good as remembering it. If students are ignorant on a topic, they have no filter through which to sift new information. In a “post-truth” world, critical thinking is more valuable than ever and critical thinking is problematic for someone who lacks the context that knowledge affords. Nevertheless, YouTube is a pretty effective knowledge prosthesis.

Creativity, problem-solving, resourcefulness, computational thinking; these are skills that have always been valuable but are now at a premium. Teachers get this. Every time I mention it in a presentation I notice teachers nodding. But there seems to be a disconnect between that understanding and the way many teachers plan their classes. Many of us still spend a large portion of our class time teaching knowledge. Why? Because in November, students will sit an exam to answer questions that in any other context would be Googleable! If we have failed to prepare them for that we will have let them down. We won’t have done any favours for our own reputation, either.

Personally, I don’t think exams effectively measure student learning in any meaningful way in 2017. But as a science teacher, I have no influence over the state’s assessment processes (“God grant me the serenity…”). For as long as exams are the gate through which students must enter to pursue a STEM career, we need to hold that gate open for them.

Therein lies the dilemma we face. Do we spend our valuable class time on the most important or the most urgent things? Do we equip our students with the skills that will matter to them most, or those that will matter to them first? Do we prepare them to thrive in the economy of the future, or to thrive in the exams of November?

I don’t think we can neglect either. But clearly there is insufficient time to do both.

Since we are unlikely to be given more time, we need to make more efficient use of the time we have.

This is where the flipped classroom comes in. A common criticism of the flipped classroom model is that it is still a fundamentally didactic, teacher-centred approach. I don’t disagree with that —if done well, I do think that it is much more student-centred than it might seem.

Nevertheless, it is not my aim in this article to discuss different approaches to the flipped classroom model, how to do it well, nor to explain how it can be student-centred (we will look at those things in my presentation at the Oxford University Press STEM Conference). The point I want to make, rather, is that the flipped classroom is much more efficient than traditional approaches.

By taking didactic learning out of the classroom, class time is reclaimed for more “important” learning tasks, those that prepare students for the economy of their future. At the same time, it allows students to cover the “urgent” content they need for exams much more efficiently. They can, for example, listen to a lesson at double speed, while multi-tasking by washing the dishes (or some other mindless chore), thereby saving precious at-desk study hours for other tasks. It also makes that kind of learning demonstrably more effective.

In many ways, I think the term “flipped learning” does a disservice to the concept of flipped learning by implying that it is the wrong-way-around. On the contrary, I think it should be the new normal — at least until we do away with high-stakes standardised testing.

Nobody races to the bank during lunchtime anymore to withdraw cash during bank hours. Instead, we enjoy lunch with our colleagues in the staff room and multi-task cash-withdrawal with our grocery shopping that evening when the bank is closed. We don’t call it “flipped banking”, but that is what we are doing! We are using technology to time-shift a necessary, “urgent” errand to make more efficient use of our time, while also reclaiming our lunchtime to rest and cultivate rapport with colleagues — both of which, are important but not urgent.

In the same way, the flipped classroom can lead us to a more efficient, effective future for students, equipping them with the urgent and important skills they need.


Andrew Douch is an education technology consultant at



Connecting with Law Short Film Competition 2017

The Connecting with Law Short Film Competition is an annual event run by Oxford University Press Australia & New Zealand. Now in its tenth year, the Connecting with Law Short Film Competition is open to all tertiary students currently enrolled in a law unit at an Australian university.

This year, we are asking students to create film about Groundbreakers. To enter, you should create a two to five minute film about people, cases or judgements that have been ‘groundbreaking’ and have changed the shape of Australian law. Your film should educate, entertain and engage fellow law students and help them connect with law.

Your entry should be creative (no snails in a bottle!) and it can be in any style, including a  music video, animation, documentary, interview, talking head or performance.

Get your name known in law and win great prizes!

1st Prize – $1,500

2nd Prize – $500

3rd Prize – $250

Want to learn more?

Visit the Connecting with Law Short Film Competition homepage to read our terms & conditions and submission guidelines, download an entry form or see last year’s winner!

Previous winning and commended entries can be viewed online at the Connecting with Law Film Library.

Entries close August 25th 2017.

Oxford Word of the Month: June – Kangatarian

WotM header

noun: a person who eats kangaroo meat but avoids eating other meat. Also as adj.


In early 2010 a number of news organisations, both in Australia and internationally, reported on a new diet trend happening in Australia:

There’s a new semi-vegetarian wave emerging in Australia: people who exclude all meat except kangaroo on environmental, ecological and humanitarian grounds. They call themselves kangatarians and are slowly growing in numbers. (Sydney Morning Herald, 9 February)

A number of these reports referred to a group of university students who were actively promoting this new diet:

Then, about 12 months ago, one group in Sydney decided to begin spreading the word about the benefits of kangaroo meat. ‘They coined the phrase kangatarians, it was a bit of a joke initially’, said Peter Ampt, a lecturer at the University of Sydney and a kangaroo meat advocate. (Calgary Herald, 13 February)

The evidence suggests the term is linked to these stories from early 2010.

Kangatarian is modelled on the word vegetarian. The -arian suffix means ‘having a concern or belief in a specified thing’. Vegetarian is also the model for other recent neologisms such as pescatarian ‘a person who eats fish but avoids eating meat’, and the jocular meatatarian ‘a person who eats meat as a significant part of their diet’. The kanga- element in kangatarian of course comes from kangaroo, a name for any of the larger marsupials of the Macropodidae family, with kangaroo entering English via the Guugu Yimithirr language of north-eastern Queensland.

Some of the appeal of eating kangaroo meat in preference to other meat is because it is thought to be healthier (it is a naturally lean meat), but kangatarians chiefly find the diet appealing on environmental grounds, because it does not rely on large-scale husbandry practices as other meat production does. Attempts to encourage a reluctant Australian public to eat more kangaroo meat, however, would probably entail the adoption of some of these practices.

Achieving the objectives of the review, then, would require the kangaroo industry to shift to farming techniques, but this would be in breach of kangatarian values. And a CSIRO report has dismissed kangaroo husbandry as a tedious and costly endeavour, on account of the animals’ nomadic habits, their low reproduction and slow growth rate, and behaviour patterns that generally prevent herding. (Crikey, 2 May 2012)

The reference to ‘kangatarian values’ illustrates that the term does not simply denote a dietary behaviour but, like vegetarianism, is often based on a set of ethical choices. Indeed, the word kangatarianism is also making its way into the Australian lexicon:

City newspapers and foodie magazines are swooning over the new wave of semi-vegetarianism that is emerging in Australia—Kangatarianism—excluding all meat except kangaroo on environmental, ecological and humanitarian grounds. (Alice Springs Centralian Advocate, 12 February 2010)

Kangatarian (and kangatarianism) will be considered for inclusion in the next edition of the Australian National Dictionary.