Introduction

There is a long-standing tension in mathematics and science curricula. In very broad terms, there is, on the one hand, the ‘traditional’ desire to develop the disciplinary knowledge and skills needed for higher education and scientific careers. In school science and mathematics education, though, the curriculum must also address the need to prepare young people with the scientific and mathematical understandings and dispositions needed to participate in society and an increasingly technical economy (Ball et al., 2017; Bøe et al., 2011). This tension is ever more apparent in version 9 of the Australian Curriculum, particularly through the explicit incorporation of the need to develop a STEM (science, technology, engineering, and mathematics) workforce in the rationale for both the science and mathematics curriculum (ACARA, 2022).

STEM has had an unusual curriculum path. While the quality and approach vary widely, over the last decade, STEM—as distinct from science, mathematics, and technology—has become a standard part of the enacted curriculum in most Australian schools. This is despite its absence from the Australian Curriculum documentation until now. The pathway for STEM into the regular activity of schools has been through policy interventions from outside of the Australian Curriculum processes, including substantial program development and implementation funding from other areas of government and directly from industry (Office of the Chief Scientist, 2016). This unusual pathway is interesting and worthy of critical analysis, so I will return to it briefly at the end of this paper. The primary concern of this short paper, however, lies in the epistemic capacity of teachers to fluently negotiate the tensions between the disciplinary and sociocultural/workforce (Collins & Evans, 2002; Grootenboer et al., 2021; Nugent et al., 2015) demands that are growing as the Australian Curriculum develops. To do this, I begin by offering some thinking on assessment, or how we know what is happening in teaching and learning.

Epistemic tensions and validity in assessment

The dominant view of school assessment, held by most teachers, students, and parents alike, is drawn from the psychometric tradition (Ercikan & Roth, 2009). The enactment of this tradition through standardised testing, formal examinations, and all the anxiety-promoting traditions that most people bring to mind at the mention of the words ‘maths test’ are built on a deep, ontological understanding of validity. To be a valid measure of learning within this view of the world, assessment must be abstract. To count as a legitimate measure of learning, there must be standardised conditions, standardised questions, and a standardised distribution of scores. Within the research world, we would call this approach to knowledge production ‘reductionist’. It draws from the purest vision of scientific validity—control all variables and ensure that the instrument is measuring what we want it to measure (Duncan et al., 2021).

This highly abstract approach to knowing about students was pioneered in the early twentieth century in trait, behavioural, and cognitive psychology and was readily transferred to measures of student disciplinary learning. This understanding of validity has become so entrenched that it is difficult to imagine schooling without it. However, it leads to some quite perverse outcomes. I will explain what I mean here by way of anecdote.

I did quite well in high school maths. This is not bragging. I was not top of the class or anything, but I got good marks. I was quite surprised, though, when I was studying for a science degree at university, to find that calculus was actually useful for a variety of things and not just a game one did for marks at school. Who knew? Now I realise that this anecdote is, at least in part, a testament to my own deficiencies as a learner. My mathematics teacher almost certainly did explain that determining the slope of a curve was useful for calculating the rate of change of real-world things and so on, but somewhere in the process that explanation did not ‘stick’.

To continue with another personal anecdote for a moment, I think there are many students today for whom the capacity to apply their mathematics is not sticking if indeed it was ever there. In a project looking to decrease the rate of failure or withdrawal in first-year university chemistry I was involved, for example, the chemistry lecturers had identified that the major issue was the insufficient mathematical capacity of the students. The problem, as they saw it, was the removal of a mathematics prerequisite from the degree. When we looked at the students’ records, however, the vast majority of those failing had actually done quite well in their high school mathematics and would have met the prerequisite requirements of a previous era.

Each of the stories above points to a problem with what might be seen as the ‘standard’ view—the standard epistemology—of assessment validity. That is, the assessment regimes it supports tend to tell us, with high confidence, about students’ capacities with respect to very specific skills or knowledge, at a very specific point in time. They are perhaps less valid, though, as representations of what those same students can do with respect to some of the ambitions we find in the rationale statements in our curriculum (ACARA, 2022). The reductionist approach to assessment simply cannot provide us with a valid representation of students’ capacity to use their mathematics or their science for tasks like ‘thinking critically and making sense of the world’, particularly when we are hoping they will do that thinking and sense-making throughout their lives. These are complex and emergent (Woolcott et al., 2021) practices that do not exist at specific points in time (Kemmis, 2019).

In response to the limitations of the standard view of assessment validity, we have seen the rise of alternatives that can be seen as ‘situated’ and ‘sociocultural’ (Reay, 2004). To many scholars who work in this space, situated and sociocultural are essentially synonyms. To others, there are important differences. In short, and with no clearly agreed definitional boundaries, the situated description tends to signify an extension of the psychometric tradition with some context tacked on (e.g. Patel, 2018). The sociocultural approach, on the other hand, tends to arise from interpretative traditions within sociology and the humanities and seeks to assess human activity and practice as it occurs within social and historical contexts (Roth & Lee, 2007).

From the ‘synonymous’ camp, the linguist James Gee (Mislevy et al., 2009) explains the situated/sociocultural understanding well with reference to his own interest in trout fishing. Trout are, apparently, quite fickle, and the bait or lure that catches a fish one day may not interest them the next. The finding then, that a trout has been caught with a particular lure on a particular day cannot be readily generalised. More generalisable are more complex models like ‘this kind of lure tends to be more successful on cloudy days when the water is cold’. The purpose of this story is to illustrate that there are fields of human endeavour, not only fishing, where we find it quite normal to consider not only the individual but their context. Their ecosystem. This consideration of the ecosystem is what the situated/sociocultural approaches to assessment seek to achieve.

In relating his fishing experiences back to education, Gee argues the need for a diachronic rather than a synchronic approach to (reading) assessment. That is, point-of-time information is of marginal usefulness and needs to be understood in terms of each student’s trajectory. A low score in early reading decoding, for example, might mean very different things for different students, and discerning that meaning requires consideration of factors such as the emergent literacy situation at home before the student started school, and what are the affective concerns that give meaning to a given activity. With respect to the latter, he asks what we should make of the validity of the test when a child fails a third-grade reading test, then goes home and successfully plays Pokemon, a game requiring a sixth-grade reading ability.

The kinds of validity questions that Gee raises with respect to reading and literacy education are no less complex when we consider mathematics and science. The curriculum suggests, correctly in my view, that mathematics education provides an important foundation for the development of complex capacities such as computational thinking (ACARA, 2022). But where is it valid to measure the use of computational thinking? In an abstract test? In a more situated task like the development of an algorithm that can be situated in a real-world problem, where a well-defined answer will exist? Or would a more grounded situation like working out the steps required for tidying a bedroom be suitable? Or when we seek to assess science inquiry practices, should our assessment focus on clearly ‘scientific’ contexts such as the separation of two chemicals? Or is it valid to explore scientific inquiry in the context of an integrated STEM activity, like designing an insulated ‘keep cup’?

Epistemologies and what counts as valid learning

While the stories and anecdotes above have focussed on assessment validity, they point also to the wider challenges of determining what counts as ‘valid’ learning, particularly when a curriculum is designed to achieve quite different epistemic objectives. That is, this revision of the Australian Curriculum is continuing—and actually expanding—a curriculum ambition to simultaneously support very different learning trajectories. This is, of course, a necessary feature of a national, universal curriculum settlement. Some students are going to use their school science and mathematics as a basis for a scientific career, some will use it to move into the broader STEM workforce, and others will not be seeking a vocational outcome but will simply learn more about the world (Kennedy et al., 2018). Catering to these diverse demands is, broadly speaking, appropriate. Doing so, however, places a high epistemic burden on teachers. It asks our teachers to be able to think about the curriculum they are enacting in fundamentally different ways and to be able to fluently move between those ways of thinking.

The ability to move between different ways of thinking is called epistemic fluency (Goodyear & Markauskaite, 2018; Leonard & Fitzgerald, 2018). Such fluency is not easy or common (Barnes et al., 2020; Lunn Brownlee et al., 2017), and it suggests a high level of expertise around the content. For teachers, it essentially requires that they must be able to deploy and move between different sets of pedagogical content knowledge. Some recent research my colleagues and I conducted points highlights this challenge well.

In this research (Marrone et al., 2022), we asked the teachers and students of a large kindergarten-year 12 school, to provide a list of words in response to a very specific question: ‘When you think about mathematics, how do you feel?’ We then used a process of semantic or sentiment analysis. As you would expect, there were positive affective responses like fun, excitement, and happiness, and there were negative responses like anger, sadness, and hate. Less expected, although upon reflection quite reasonable, was the strong presence of words that spoke not to the emotions that the question sought to elicit but more directly to the ability to do mathematics. Mathematics was complex, complicated, easy, or difficult.

This tendency to link emotional response to self-efficacy was present in all groups of students (male, female, primary, and secondary) and all groups of teachers (male, female, primary, and secondary). Notably, though, it was most common for nonspecialist teachers to make this particular connection. By ‘nonspecialist’, we mean teachers with no specialist background in mathematics. This includes almost all primary school teachers and an increasing number of secondary teachers teaching ‘out of area’ due to endemic workforce shortages.

Another striking finding in this research was a strong correlation between teachers using ability-based words to describe their own feelings about mathematics and the reporting of negative emotions about mathematics by female students. This finding demands further research, but it suggests that teachers’ personal understandings of mathematics and mathematics education can have a particularly strong impact on female students, among whom mathematics anxiety is common.

Also striking in terms of the argument I have been making in this paper is what is not present in this research. The teachers ‘broke out’ of the specific question on their emotions to instead describe mathematics processes. In doing so, they presented mathematics as an individual and rather abstract activity, but they did not give any indication of the sociocultural ambition of the curriculum. In their reports, mathematics did not empower critical thinking or making sense of the world. It was not connected to vocational outcomes like jobs in STEM. In these initial responses from both teachers and students, mathematics existed disconnected from the world. This was actually true in the responses of both specialist and nonspecialist teachers; the specialist teachers were just far more positive about mathematics—we could not identify a single negative feeling about mathematics from any of the specialist mathematics teachers.

What this research highlights is that in a context where teachers and students are reporting on mathematics without thinking too deeply about it when they go just to their immediate emotional response, they are responding from within one specific understanding or ‘epistemic positioning’ of mathematics. They are positioning mathematics as an individualistic and abstract activity that aligns well with the ‘traditional’ curriculum settlements with a focus on disciplinary skills and knowledge leading to higher education within the discipline. The alternative, sociocultural epistemic positions within the curriculum are not present. This suggests that if the multiple epistemic aims of the Australian Curriculum are to be realised, there will be an ongoing need for both teachers and students to increase their epistemic fluency (Suh et al., 2022).

A final word on the introduction of STEM

To conclude, let me return to the explicit inclusion of STEM within the sociocultural ambitions of the mathematics and science curriculums. As I noted above, STEM has found its way into the curriculum via an unusual path. It has become such a strong component of the everyday discourse of Australian education that its inclusion in the formal curriculum documents now seems natural, even overdue. This pathway to inclusion, however, should raise some ‘red flags.’

The pathway that has been taken in developing STEM as a part of the curriculum in Australia has largely depoliticised (Sharma & Hudson, 2021) what might otherwise have been a quite controversial shift in the sociocultural direction of the science and mathematics curriculum. As an alignment of related subjects, STEM makes sense as a way to provide greater context to each of its component parts (STEM Task Force, 2014). STEM, though, is much more than an integration of subjects that we might previously have referred to as ‘the sciences.’ The sciences, as a term, has generally not excluded mathematics and applied science. STEM though, must be seen as a wider discourse that aligns the sciences with the needs of a specific image of future industry. It aligns the school subjects of science and mathematics not only with vocational outcomes but emphasises the future workforce needs of global capital. It frames science and mathematics within a neoliberal agenda. The imperative of STEM can perhaps be most readily seen when one considers the emerging ‘meta theme’ that it has largely displaced from school science: sustainability.

STEM has entered the Australian curriculum as some vague statements in the preamble. These statements will not change much in the way curriculum is enacted. Its inclusion is significant, though, because it shows that a well-funded and directed policy initiative from industry can bypass the normal forums of curriculum debate and gradually normalise radical curriculum change.