Q&A: Evidence-based learning progressions in mathematics

Professor Dianne Siemon is an Emeritus Professor at RMIT University and has worked in mathematics teacher education for over 30 years. She is a Keynote speaker at ACER’s upcoming Research Conference which has the theme ‘Excellent progress for every student: What will it take?’.

In this Q&A, she gives Teacher readers a taste of what she will be sharing with delegates.

You’re a Keynote speaker at ACER’s Research Conference 2021 and will be delivering your Keynote, Excellent progress for all – A function of year level curriculum or evidenced-based learning progressions? on Monday 16 August. Can you give us a taste what you will be speaking about?

Australian students’ performance on international assessments of mathematical literacy such as Program for International Student Assessment (PISA) and Trends in International Mathematics and Science Study (TIMSS), and declining rates of participation in the more advanced mathematics courses in the senior years of schooling, suggest we are not serving all of our students well. While some students are doing very well, there is a ‘long tail’ of students, who may be up to seven years behind their higher achieving peers in curriculum terms, and who disproportionally come from disadvantaged or lower socio-economic backgrounds – this is inequitable in a country that prides itself on a fair go for all and aspires to ‘excellent progress for all students’.

We need to be doing a better job if we are to ensure all students have the opportunity to maximise their life choices and chances. One known way of doing this is to use formative assessment to identify where learners are in their mathematics learning and to better target teaching to point of need. Research-based learning progressions or trajectories can inform this process by identifying the ‘big ideas’ of mathematics, the connections between them, and their likely development over time. They also offer assessment tools that identify where students are in relation to what is important, and targeted teaching advice to help teachers progress student learning.

Insisting that all students irrespective of where they are in their particular learning journey should master all aspects of the mathematics curriculum at their year level is a recipe for disaster. Having said that, I am firmly of the view that all students have the right to be exposed to the curriculum at their year level, but this needs to be done in ways (e.g., accessible but challenging tasks in mixed ability settings), and in contexts (e.g., a culture that supports growth mind-sets) that provide opportunities for all students to learn, if not immediately, then ‘down the track’.

Is learning progressions a new idea?

It depends on what you mean by a learning progression. If we regard the curriculum as a learning progression, it is definitely not a new idea. If we expect a learning progression to be research-based, then learning progressions in the form of learning assessment frameworks such as Count Me in Too, the Early Years Numeracy Project, and First Steps in Mathematics have been around for some time.

Research-based learning progressions that consider the development of big ideas and the connections between them over time are a relatively new phenomenon. They have become possible because of developments in educational measurement that enable item difficulty and student performance to be measured using the same unit and placed alongside each other on an interval scale. Known as Rasch analysis (Bond & Fox, 2015), the advantage of this is that it can identify what students who perform at a particular point on the scale are able to do and what is likely to be within their grasp with teaching targeted to learning need. Detailed analyses of items located at similar points on the scale can be used to develop teaching advice about where to go to next.

In your experience, do lots of teachers understand learning progressions?

Australian teachers of mathematics are familiar with the general notion of learning progressions in the form of year level content descriptors, scope and sequence charts, and, more recently, numeracy continuums. These are learning progressions to the extent that they specify what needs to be learnt over time, but the curriculum is a socially negotiated document that has been built up over time to satisfy various stakeholders. As it evolves, some aspects might be modified on the basis of research evidence, but the curriculum as a whole cannot be said to be research-based. If we expect learning progressions to have some basis in research, then I would say there are many teachers who are aware of evidence-based learning and assessment frameworks, although the extent to which these are used to inform practice on a day-to-day basis may vary considerably.

What does excellent progress look like? Does the function of a year level curriculum meet the requirements for supporting all students to make excellent progress?

That is a really good question. One view of what this might look like is given in the Gonski (2018) Report of the Review to Achieve Educational Excellence in Australian Schools. That is, that we should aspire to ‘deliver at least one years’ growth in learning for every student every year’. But my question is growth in relation to what? All aspects of the year level curriculum or what research suggests are the key ideas needed to sustain and support further learning in mathematics?

The trap with the Gonski notion is that if a years’ growth is defined in terms of year level curriculum, it serves to maintain the status quo. For example, a Year 4 student who is five or so years behind their high achieving peers, will still be five or more years behind their high achieving peers in Year 8 even if they have all achieved at least one year’s growth in all of the intervening years. This is not excellent progress.

Another problem with the Gonski view is that ‘at least’ suggests something a bit more than one year rather than a lot more. We can and should be aspiring to deliver whatever it takes to ensure all students have the opportunity to engage productively with the curriculum at their year level or beyond.

Teaching all aspects of the curriculum and grouping by ability is not the answer. Identifying where students are in relation to important mathematics and focusing on what is known to make a difference through targeted teaching and creative mixed ability teaching is what is needed. And this is where research-based learning progressions, like the ones we have developed for multiplicative thinking (Siemon, 2019) and mathematical reasoning (Siemon et al., 2018) can contribute.

What are you hoping teachers and school leaders take away from your Keynote?

That they come to a deeper understanding of what is involved in developing evidenced-based learning progressions for key aspects of school mathematics and how these can be used to identify student learning needs in relation to important mathematics, support teachers to navigate curriculum expectations, and to make more informed pedagogical decisions than might otherwise have been made in the absence of these learning progressions and their related diagnostic assessments.

Anything else you’d like to mention?

I am encouraged by the 2021 review of the Australian Curriculum: Mathematics. There are many areas where research-based learning progressions appear to have been taken into account and understanding is valued as much if not more so than simply applying procedures. Students are expected to be able to identify and explain relationships and reasoning is more of a focus.

While recent criticism has suggested that the revised curriculum ‘delays and devalues fluency’, this is not the case. Indeed, it could be argued that the revised curriculum expects more of students at an earlier age in relation to fluency by attending to the need to build on from known (e.g., doubling and additive strategies) and the associativity, commutativity and distributivity laws, all of which are now introduced at the primary level.


Bond, T. & Fox, C. (2015). Applying the Rasch model: Fundamental measurement in the human sciences (3rd Ed.). Mahwah, NJ: Lawrence Erlbaum Associates

Gonski, D. (2018). Through growth to achievement: Report of the Review to Achieve Educational Excellence in Australian Schools. Commonwealth of Australia. https://www.dese.gov.au/quality-schools-package/resources/through-growth-achievement-report-review-achieve-educational-excellence-australian-schools

Siemon, D. (2019). Knowing and building on what students know: The case of multiplicative thinking. In D. Siemon, T. Barkatsas & R. Seah (Eds.), Researching and Using Progressions (Trajectories) in Mathematics Education (pp. 6-31). Leiden, The Netherlands: Brill-Sense.

Siemon, D., Callingham, R., Day, L., Horne, M., Seah, R., Stephens, M., & Watson, J. (2018). From research to practice: The case of mathematical reasoning. In J. Hunter, L. Darragh & P. Perger (Eds.), Making waves, opening spaces, Proceedings of the 41st annual conference of the Mathematics Education Research Group of Australasia, (pp. 40-49). MERGA. https://www.merga.net.au/common/Uploaded%20files/Annual%20Conference%20Proceedings/2018%20Annual%20Conference%20Proceedings/Siemon.pdf

Research Conference 2021 ‘Excellent progress for every student: What will it take’ runs from 16-20 August, and features 20 sessions, four keynote addresses and one intensive Masterclass. Click on the link to explore the full program and register for the event.