Building the bridge between curriculum alignment and learning progression: an alignment analysis between assessment and instruction applying typical order of skills in multiplication and division

Concerns about the link between curriculum, instruction and learning progression guide this investigation. To align instruction to the students’ knowledge level, it is critical to build from how curriculum alignment has been examined. For the review of the literature, the relationship between curriculum alignment and student learning pathways remains underexplored. There has been an increased focus in the literature on the use of learning progressions to assess students’ level of knowledge to inform teaching (Masters, 2017). However, limited attention had been paid to the use of curriculum alignment tools to examine how pre-assessment results inform sequence of instruction. In addition, there is no evidence of the use of alignment tools adopting a learning progression to examine alignment in targeted interventions. This alignment study offers a new kind of thinking curriculum alignment by adopting a typical order of skills in multiplication and division to examine content coverage (Pearn and Ziebell, 2021) and cognitive demand (Ziebell and Clarke, 2018) between pre-assessment and instruction. Curriculum alignment can be defined as the consistency among all elements of an educational system, especially between (1) learning objectives, (2) assessments, and (3) instruction (Anderson, 2005). The central idea is that a coherent message about the desired content shapes teachers' instructional choices, which then informs their teaching practices and ultimately impacts student learning of that content (Porter, 2002, p. 5). Therefore, effective alignment is thought to improve curricular coherence and enhance student achievement (Wenzel, 2016). Curriculum alignment is intrinsically linked to standards-based curricula, which is adopted by many educational systems globally, including Australia. The standards serve as a benchmark for schools in planning their teaching and learning strategies, as well as for evaluating student progress. However, as curriculum alignment studies enter their third decade, there is well documented dissatisfaction with the quality of standards implementation, particularly cognitive skills are the weakest aligned curriculum component and that only a limited range of cognitive skills outlined in learning objectives are usually taught and assessed (Boesen et al., 2014). It is well known that Australian students have experienced consistent decline in mathematics performance in international and national standardized testing. De Bortoli (2023) found that 51% of Australian students reached the national proficient standard in PISA, which indicates that a substantial number of students are still struggling to demonstrate more than basic skills in mathematics. Thomson and colleagues (2016), when analyzing TIMMS results, found that by the middle primary years significant disparities in mathematics achievement among students become evident. These findings confirm that the skills and knowledge that each student accumulates within a class or grade level will likely vary significantly (Griffin, 2018). Thinking about other ways to define content and cognitive demand that would be more powerful and supports students’ academic growth in Mathematics is needed. The context for this study is a 1-1 Mathematics tutoring program in South Australia, Australia. Learning+ was a program designed to support students’ academic growth in mathematics and promote independent learning. The initiative was implemented by South Australian Department for Education in 2021-2022. The program offered online 1-1 mathematics tutoring sessions for students in years 6 to 9 with mathematics ability either above or below the Standard of Educational Achievement for their year level. The objective of the tutoring sessions was to accelerate student learning of the mathematics curriculum. Each student had two 30-minute one-on-one tutoring sessions per week for 10 weeks. Over two years a total of 2890 students benefited from the initiative, 277 tutors and 137 schools were involved. Key features of the program can be summed up under three headings: professional learning, targeted resources, and ongoing support to the team. To assist in identifying students’ learning needs and the sequence in which they should be taught, this study relies on Learning+ resources (Pearn and Ziebell, 2021): the pre-assessment Number Interview B, and the sequence of instruction on Multiplication and Division. In addition, the Growth Points framework for multiplication and division (Hoad et al., 2005) provides guidance to identify where students are on their learning pathways. In the sequence, this project utilizes a two-dimensional matrix where content descriptors prioritize the actual development of students’ thinking as opposed to a conventional standards orientation. The unit of analysis are the tasks on the pre-assessment and the tasks chosen by the tutors in subsequent tutoring sessions after the assessment application. Porter’s alignment index tool (Porter, 2002), largely used in alignment research, was adopted. It provides a quantitative analysis of alignment. Preliminary findings show the potential of using learning progressions in curriculum alignment studies. Anderson, L. W. (2005). Objectives, evaluation, and the improvement of education. Studies in Educational Evaluation, 31, 102–113. Boesen, J., Helenius, O., Bergqvist, E., Bergqvist, T., Lithner, J., Palm, T., & Palmberg, B. 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