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Championing maths by inquiry

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Authors: Jo Earp
Championing maths by inquiry

A new Australia-wide initiative promoting innovative approaches to mathematics teaching and learning that engage and challenge students is on the hunt for hundreds of teacher champions.

The reSolve: Mathematics by Inquiry project is developing units of work and classroom resources for Foundation to Year 10 linked to the Australian Curriculum: Mathematics, and professional learning modules for teachers.

In addition to the free materials, there will also be a ‘human legacy’ – 240 reSolve Champions working in all states and territories, sectors and in a variety of school contexts.

The project is a collaboration between the Australian Academy of Science and the Australian Association of Mathematics Teachers (AAMT). It’s also part of the National STEM School Education Strategy 2016-2026 and comes at a time when Australian student performance in maths is flatlining, a substantial proportion of Australian 15-year-olds are failing to meet the National Proficient Standard, and Year 12 high-level mathematics participation is declining.

reSolve Executive Director Dr Steve Thornton tells Teacher one of the thrusts of the project is to look at the real-world application of mathematics. It’s also about creating a spirit of inquiry and risk taking ‘encouraging students to think mathematically, to ask questions’ and encouraging teachers to use engaging pedagogies.

Thornton explains the central plank of the whole project is a maths by inquiry protocol that has been developed, highlighting three critical elements. ‘First of all, that mathematics is purposeful. And by that we mean that it’s not just about teaching the curriculum – it’s more than that, there’s a reason for doing it, maths is connected, coherent.

‘Secondly that the mathematical tasks are challenging and accessible. That’s emphasising that students ought to in maths lessons not do stuff that they already know how to do, because they don’t learn anything. It’s also about challenging [teachers] to push the boundaries in a way that is accessible to everybody.

‘Then the third element is that classrooms have a supportive knowledge-building culture. That’s to try to emphasise that interactions in the classroom, the way a teacher relates to the students, is all around building mathematical knowledge. … Australian classrooms are often nice places to be but often the deep learning that goes on is sometimes questionable.’

One of the major roles of the AAMT is to recruit and train the champions. A free 12 month online and face-to-face professional learning program, starting in July, is designed to give them the knowledge, experience and skills to use the approaches and materials and lead others.

Will Morony, Chief Executive Officer of the AAMT, says there’s no set view of what champions will do. The majority will be located in their schools, so they may just work with colleagues, but they could also link up with other local teachers or be a resource across a school cluster or hub. Education systems are also being encouraged to think about how they can best use the champions. ‘[They’ll] be taking the message of the protocol and the messages of Mathematics by Inquiry forward in ways that are locally designed and developed. So, we’re trying to create an ownership of these champions. They will be catalysts.’

You don’t need to be an award winner or a maths specialist be a reSolve Champion; indeed, educators who are teaching out of field will be welcomed with open arms. Reflecting on his own experience as a passionate maths teacher, Thornton says his way of thinking about the subject didn’t always connect with colleagues. ‘I think it’s actually really important that people communicate with … their group of colleagues and peers and likeminded people. So, that also extends to I think a deliberate strategy that we have to have a really good cross-section of champions – which might also include champions with particular interests in schooling, such as Indigenous education or special ed.’

Teachers interested in becoming a reSolve Champion are required to submit an expression of interest by 10 April, 2017. To find out more about the program and how to apply to become a champion, visit You can also keep in touch with project developments, including details on resources, through the Academy website.

How do you encourage students to take risks in their learning?

Think about a recent maths lesson you taught. Were students asked to tackle something they were already proficient in, or did the tasks challenge them?

In what ways do you provide students with opportunities to apply what they're learning in maths to the real world?

Greg 14 March 2017

I am not sure why the AAMT think that inquiry learning will help arrest Australia’s decline in mathematics. Inquiry learning has a long history of failure due to the fact that it does not align with what we know about cognitive science:

Moreover, evidence from PISA 2012 found an association between students’ reports of the frequency of inquiry-type activities and maths performance. The more of these activities students reported, the worse the performance. This was also found in the 2015 PISA results through a similar survey of learning experiences in science.

Steve 14 March 2017

In response to Greg’s really important comment: in the article I am quoted as saying that the project aims to create “a spirit of inquiry”. I see this as very different to the inquiry described in Kirschner, Sweller and Clark’s paper. It does not diminish at all the importance of teacher activity, not only as a provocateur, but also as the responsible adult whose job includes explicit teaching. A spirit of inquiry is about cognitive activation - getting students to do maths with the brain switched on, if you like. A recent OECD working paper Teaching Strategies for Instructional Quality “explore(d) the relationships between mathematics teachers’ teaching strategies and student learning outcomes in eight countries, using information from the TALIS-PISA link database”. The paper said “Results show that cognitive activation strategies and, to a lesser extent, active learning strategies, have a strong association with students’ achievement in mathematics.” The link is
The reSolve: Mathematics by Inquiry project, and especially the three elements of the Protocol described in the above article, are all about cognitive activation strategies. Hence we take the view that inquiry is a state of mind, or an orientation to learning, that should permeate every maths lesson, rather than a defined approach as described by Kirschner et al. Incidentally, in the edition of Education Psychologist following the publication of Kirschner et al.‘s paper, there is a rejoinder by Hmelo-Silver et al. See which takes issue with the way that Kirschner et al. have defined inquiry.

Greg 14 March 2017

Given that the Hmelo-Silver et al paper has been referenced, it seems only fair to link to the original authors’ reply to to Hmelo-Silver’s commentary:

The original Kirschner, Sweller, Clark paper was of such significance that a conference developed out of it which was eventually followed-up with a book that I highly recommend - Constructivist Instruction: Success or Failure? Edited by Tobias and Duffy.

Having reviewed the re(solve) protocol above, I see no reason why the Kirschner, Sweller, Clark criticism would not apply to it. In fact, it seems more on the extreme end of the inquiry spectrum than many ‘guided discovery’ approaches given its talk of knowledge-building and problem solving. This would cognitively overload novice learners and likely lead to differential effects where those with the least prior knowledge learn the least..

I have read the PISA evidence on cognitive activation and don’t see why this would be particularly associated with an inquiry learning approach. Explicit instruction could easily create these conditions. And yet the PISA evidence on *actual* inquiry learning is pretty stark. It therefore seems a strange thing to promote as a way of improving international test scores.

Narinderjeet Kaur 15 March 2017

With a balanced Mathematical curriculum which is built on a secure foundation of Mathematical facts and concepts, it is possible to develop an inquiry learning approach. Pupils needs to be guided through inquiry approach however this should never be a stand alone style as pupils in the classroom will have different type of learning styles and needs. To ensure empowering of Maths, teaching approaches and styles need to be fluid, rigorous and responsive to pupils’ learning needs.

andrew 16 March 2017

As a parent busting to have my 9 yo CAPABLE IN STEMS (and systems) in central west nsw you need to heed this…
Strand 2. Yr 4. 32 kids in 3/4 class. No aid. 10 mins 4 days a week maths. Printed sheets. Wed is no math. Sport. Art. Non scripture 2nd assembly… i had had to hassle for 4 weeks to get kid to use a computer instead of read or twiddle to do or mit sketch. Assembly. I am going to only take kid for sport. Science this year ‘is it alive or dead’.
Tried for 3 years to get a teacher to do fibonacci. Ticks all the boxes smails or rabbits anyone?
Assisted my kid to do garbage analysis locally after garbage missed. One truck 2 people. 12 days   2 people 1 truck to clean up unacceptable. How many trucks / people / acceptable time frame. Figure was within 20% of reported cost by coucil to cleanup. Kid realised they could be boss of council. Near wet themselves.
Took analysis… 7pgs to teacher who is also hd of sg 1 n 2. 1pg text. 5 simple addition multiplication simple divsion. 1 page summary with total… to hd teacher. Asked if such analysis done in class. ‘Oh yes. Second term. I ask questions seek answers BUT I DO THE CALCULATIONS”! Pity those still struggling w times table, 2 digit multiply.. and division… i hear crickets chirping. No integration with science. No botgraphs. My kid only learnt what average or mean was last week AS I AM NOW USING A TUTOR. Lost money to publc ‘system’.
One teacher left school last yr formed tutor co. Is doing 4 kids per hr at $40/hr 2 hrs per day 5 days a week. Ie approx $80 GONE TO PRIVATE NOT SCHOOLS.
Same idiocy as arguing about phonics. We dumb time poor parents get it. The alphabet needs 43+ symbols. Der… I hated school left yr 10 became a tradie.
And reSolve site you mention above not updated since 2016 funding gone. Videos great but expose poor training. And inquiry based maths! And apps paid by school draining human budgets and skills.
Teach them and help them dontput inna class of 32 mixed yr 3 n 4 age range 8-10 and hope they get it.
Tutor IN SCHOOL kids not up to speed. Eg… 2 kids next door with granny, icey mum, rabid dogs barking all night, no working memory next day. IT IS A SYSTEM NOT A SUBJECT!!!
Facilitate direct instruction until self inqiry able to be done by student. How many kids to you see starting thier own biz… many are capable but need inquiry AND explicit teaching.
Oh, and stop arguing about funding…DO IT FOREVER COS LEARNING ISNT A fad, it is essential. I know you know this yet we are in danger of having only inherently gifted or tutoried kids with skills required.

pat 17 March 2017

this is all very interesting - my focus is on the families of these students and the wider community.  part of the problem that families have especially when their children go to high school is that their own poor understanding of maths becomes patently obvious.  even more of a problem is that if you say that you enjoy maths, then you’re a fruitcake.  could some attention be paid to letting the wider community to participate in these innovations, please - we would like to learn too.

Elaine 21 March 2017

As retired Infant/Prim BEd now in charge of legal accounts I notice some Legal graduates have not developed a good memory (abandon GPS) which influences their transfer of learning and being about to ‘join the dots’ and see there is more than one solution to a problem. Kids learning tables need time on task till they are mastered. Kids can be encouraged to see the maths in other subjects and many situations e.g. why does the garbage truck only have one driver? If kids develop this awareness maths will become more relevant and interesting.

Jill 21 March 2017

One of the difficulties with ‘Inquiry’ is that the term has been widely used over decades to mean a multitude of approaches from ‘discovery’ through to ‘knowledge building’. It is important that the definitions are clarified. For example, there are few that would argue that Inquiry (discovery) is successful as a form of learning. Children require teacher guidance and challenge, monitoring and support, and these are largely absent in pure discovery. However, there are far more rigorous forms of guided inquiry that have demonstrated success in classrooms - enhancing affective, behavioural and cognitive engagement of students. The protocols of MbI and the work the AAMT is undertaking is far more aligned to the notions of guided inquiry in which students are scaffolded, challenged and so forth in order to make connections across domains of mathematics, from mathematics to its applications. There are also enhanced opportunities for students to engage in communication of their solutions and processes (enhancing the application and language usage of mathematics in context), and for students to use and draw upon many forms of representation….further enhancing both cognitive links and the application of mathematical conceptual understanding…not merely procedural.

Darren 24 March 2017

I recognise the view of the supporters of explicit instruction because there is evidence that it can achieve significant improvement in student results. However, the Australian Curriculum proficiency strands of problem solving and reasoning can be taught more effectively with a guided inquiry approach. I’m sure the students will testify this approach improves their disposition to mathematics, which is a global hurdle to higher achievement. If I am trying to increase student confidence in reasoning and problem solving (Australian Curriculum proficiency strands), I am trying to develop resilience and perseverance with complex unfamiliar questions (QCAA). I think this is most effective with a guided inquiry approach.

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