Abstract
Concern over the long-term decline in Australian students’ mathematics and science performance, as evidenced in results from international assessments (Thomson et al., 2019), and declining achievement and enrolments in STEM areas in post-compulsory education (Kennedy et al., 2014), have resulted in an increased focus on STEM in education. This, in turn, has prompted much debate on the ‘who, what, when, where, and how’ of teaching these disciplines, to promote an integrated approach for STEM education. Despite considerable research into teaching and learning, ‘much of the accumulated knowledge is neither readily accessible nor actionable, by most classroom teachers’ (Confrey et al., 2019, p. 76) in the primary and secondary years.
It is in this landscape that many researchers have been drawn to learning progressions and trajectories research (LP/Ts), to consider how these may be used to better inform student learning. LP/Ts research is based on the premise that students require timely instructional support targeted at their level of understanding. This special issue brings together mathematics and science education researchers to discuss LP/Ts research in the Australian context. The seven articles included showcase a range of theoretical perspectives and methods of investigation, reflecting the potential of using LP/Ts research in generating a closer link between research and practice. Our aim is to contribute to scholarly discussion on ways to bridge the theory-to-practice nexus and highlight the implications for curriculum reform and classroom practice.
Two key features of LP/Ts research are the priority given to the core concepts of domain knowledge, and the use of evidence-based assessment data to inform teaching. Teaching that is guided by quality data has been shown to be an effective means of meeting students’ learning needs (Furtak et al., 2014); however challenges abound in defining, assessing, modelling, and using learning progressions to inform teaching (Alonzo & Gotwals, 2012). Core knowledge or ‘big ideas’ are commonly used to frame the theories, concepts, discourse, frameworks, practices, and ways of thinking in which students are expected to learn (Sikorski, 2019), but how researchers define and select the core knowledge or ‘big ideas’ of domain knowledge may differ significantly and reflect their focus at the time. Early LP/Ts researchers often used the curriculum statements and/or standards to identify the ‘big ideas’ of mathematics (e.g., see Clements & Sarama, 2009). This approach can result in a superficial coverage of concepts learned, and the curriculum can become fragmented as a result (Mohan & Plummer, 2012). An example of this is highlighted in the article by Heather McMaster, Christine Preston, Hailan Wang, and Mersini Perivolarellis who identify a discrepancy in the use of certain terms between mathematics and science education (e.g., mass compared to density).
There is also the danger in LP/Ts being misconstrued as a synonym of the scope and sequence of year level outcome statements, as presented in many curricula documents, resulting in assessment tasks that may not fully capture what students can do and achieve. Such challenges, and variances in definition and approach to LP/T’s, are outlined in the article by Dianne Siemon that leads off this Special Issue. This article provides a useful introduction to the history and current status of LP/Ts research, and its use in mathematics and science, drawing on current policy documents and the literature to challenge current assumptions at the national level about what constitutes a learning progression.
As Siemon and other authors here note, LP/Ts are necessarily hypothetical in nature and context-bound, since learning takes place over periods of time and in contexts which may vary for all schools, teachers and students. It is hypothetical in that the researchers cannot know beforehand what the students’ responses will be, thus the initial progressions are plausible hypotheses of what researchers perceived students can do. With respect to the first key aspect of LP/Ts research (domain knowledge), it is suggested that the ‘big ideas’ should have broad explanatory power and be used to shape a vision of the domain knowledge in which curricula are designed (Mohan and Plummer (2012).
Several authors in this edition use a combination of curricular statements, research into the cognitive development of reasoning, and levels of discourse in forming their initial hypothetical learning progressions. Using a multiple perspective approach can contribute to our understanding of knowledge development. For example, Max Stephens, Lorraine Day and Marj Horne point out in their article that while the curriculum documents focus on noticing and describing regularities and patterns; and forming expressions in the algebra generalisation strand, the curriculum fails to capture the elements of understanding and using equivalence to work with algebraic expressions and use of explicit generalised reasoning.
Rosemary Callingham, Jane Watson and Greg Oates show how LP/Ts can complement and support curriculum development, by developing targeted teaching advice that is zone-based rather than year-level based, thereby helping teachers to support students’ development of increasingly sophisticated reasoning, understanding, problem solving and fluency, with respect to the mathematical proficiencies of Statistics and Probability.
Debra Panizzon, John Pegg, Dagmar Arthur, and Gerry McCloughan use the cognitive-based, evidenced-informed Structure of the Observed Learning Outcome, more commonly known as the SOLO model, when analysing the technical and non-technical language of chemical sciences, thereby ensuring a systematic and objective rigour in their learning progression. Rebecca Seah and Marj Horne highlight the limitations of relying solely on curriculum statements when constructing a geometric reasoning learning progression. They emphasise the importance of visualisation and language and discourse when engaging in geometric reasoning.
Using evidence-based assessment data to inform teaching is a second feature of LP/Ts research. The contributors in this edition use a variety of methods, such as combining the use of Rasch analysis and fine-grained analysis of students’ discourse, to better determine the level of understanding required for different domain knowledge. Joan Burfitt presents a large-scale analysis of 5000 United Kingdom and 1200 Australian early secondary students’ responses related to understanding of proportional reasoning. She reports that measuring students’ incorrect responses at scale enhanced the descriptions of the likely behaviours of students at the various levels of learning progressions, and this can be informative for teachers in the planning of learning activities.
McMaster and colleagues use variation theory and task-based interviews of Year 5 and six students to reveal their thinking about mass and volume in a Science context. Through a fine-grained analysis of students’ responses to a task that included a coordination of knowledge of transformation by enlargement, Cartesian coordinates, and area measurement, Seah and Horne show the importance of helping students to move between different representations of a problem situation, so that they can use diagrams, calculations, and language to see the connections between them.
A common thread through all the articles in this special issue is the value of LP/Ts in highlighting the need for linking of curricula content, both within, and between subjects. Callingham and colleagues, for example, propose a curriculum which integrates learning progressions with the key content and the mathematics proficiencies, but acknowledge that such an approach requires a shift in mindset on the part of curriculum developers. Siemon proposes using LP/Ts as boundary objects, in reconnecting and rebalancing the curriculum, pedagogy, and assessment relationship to support reform at scale. First proposed by Star and Griesemer (1989), boundary objects are abstract or concrete objects that ‘inhabit several intersecting social worlds’. Drawing on perspectives of Communities of Practice, Siemon describes how the ‘big ideas’ and learning progressions can serve as boundary objects between curriculum and assessment, while the design of the tasks and scoring rubrics, developed through LP/Ts research, can bridge the boundary between pedagogy and assessment. The resultant teaching advice can then act as boundary objects for curriculum and pedagogy between different communities of practice.
While Siemon concludes that at the present time it is not clear what impact, if any, evidence-based learning progressions may have on planned curricula developments, collectively the authors in this special issue make bold claims for curricula reform, informed by LP/Ts research and LP/Ts-informed instructional approaches. Importantly, effort in curricula reform will be fruitless unless they result in a corresponding change in classroom practises. While we remain optimistic that the potential of LP/Ts for developing students’ conceptual understanding and reasoning will become more widely recognised and valued, we recognise the importance of further research into LP/Ts’ applications in the classroom context.
Two key questions are worth pursuing. Firstly, how does LP/Ts research assists teachers in planning activities and implementing differentiated instruction to support the diversity of needs within the classroom? Secondly, considering the increasing emphasis on STEM education, what is the potential for LP/Ts research as a framework for interdisciplinary collaboration between mathematics and science disciplines, to explicitly nurture its growth from the early childhood years onwards. Such research will account for the growth in knowledge and aptitudes needed to improve educational outcomes for all students.