Learning progressions/trajectories in mathematics: Supporting reform at scale

In recent years, attention has turned to the development of evidenced-based learning progressions/trajectories as a means of identifying the likely paths learners might take in developing a deep, well-connected understanding of key aspects of mathematics. However, the extent to which this work influences what happens in mathematics classrooms varies greatly depending on the prevailing relationship between curriculum, pedagogy and assessment. This article will draw on current policy documents and the literature to challenge current assumptions at the national level about what constitutes a learning progression. It will draw briefly on the results of a recently completed, large-scale study on mathematical reasoning in the middle years of schooling to make a case for evidenced-based learning progressions/trajectories as boundary objects in reconnecting and rebalancing the curriculum, pedagogy and assessment relationship to support reform at scale.

LEARNING PROGRESSIONS IN LOWER-SECONDARY SCHOOL SCIENCE EDUCATION IN JAPAN

This research examined whether incorporating learning progress (LPs) in teaching can help Japanese lower-secondary school students systemically understand science concepts. A teaching plan incorporating the learning progressions (LPs) concept was developed. Next, a lesson was conducted for 36 third-year students of a public lower-secondary school in Japan (Hiroshima Prefecture) from the unit of “Ions and Atoms.” Then, the portfolios used in the class and the assessment questions after the class were analyzed. The results show that some students understood the concepts systemically at the grade level indicated by the LPs; however, some students did not. The results of this study suggest the following: (1) teachers should examine the appropriate teaching methods in the target unit and incorporate teaching to allow students to engage with what they are learning; (2) students should understand the lower-level concepts related to the target unit based on LPs, and if the level of understanding is insufficient, teachers should incorporate time to review and reconstruct the concepts. Keywords: lower-secondary school science, scientific concepts, learning progressions (LPs), systemic learning

The SWANs/ABLES Project: A resource developed by and for teachers to support the teaching and learning of students with additional learning needs

The inclusion of students with additional learning needs in schooling is part of policy and practice in Australia. However, it has been well documented that teachers lack the resources and training to meaningfully include students with additional learning needs in the full range of learning in their classrooms. The SWANs program of work aimed to fill this gap through the development of assessments based on learning progressions that provide teachers with targeted information to support the teaching and learning of all students including students with additional learning needs. The development and implementation of the SWANs/ABLES suite of resources illustrates how a practical assessment tool can support teachers to target the learning of students with additional learning needs regardless of their point of readiness to learn.

Learning progressions and the Australian curriculum mathematics: The case of statistics and probability

Mathematics curricula have traditionally focused on content knowledge, often in the form of a scope and sequence of increasingly difficult mathematics. The importance of using and applying mathematics is recognised in the current Australian Curriculum Mathematics (AC: M) as ‘proficiencies’ that are intended to be integrated with the content. There is little support for teachers to develop these proficiencies – reasoning, understanding, problem solving and fluency. Learning progressions are sequences of learning that focus on cognitive processes, and thus provide a useful basis for curriculum development. Using an empirical Statistical Reasoning Learning Progression as an exemplar, a new approach to curriculum development is suggested that links content knowledge with the proficiencies. The outcome is a zone-based, rather than year level based, curriculum that allows teachers to target their teaching, so that students develop increasingly sophisticated understanding of statistics and probability.

Using partial knowledge to inform the creation of learning progressions

The aim of this study was to show that some of the errors made by students when responding to mathematics assessment items can indicate progress in the development of conceptual understanding. By granting partial credit for specific incorrect responses by early secondary students, estimates of the difficulty of demonstrating full and partial knowledge of skills associated with the development of proportional reasoning were determined using Rasch analysis. The errors were confirmed as indicators of progress, and hence partial knowledge, when the thresholds of achievement followed a logical order: The greater the proficiency of the students, the more likely they were to receive a higher score. Consideration of this partial knowledge can enhance the descriptions of the likely behaviours of students at the various levels of learning progressions and this can be informative for teachers in their planning of learning activities.

Learning progressions as models and tools for supporting classroom assessment

Like all models, learning progressions (LPs) provide simplified representations of complex phenomena. One key simplification is the characterisation of student thinking in terms of levels. This characterisation is both essential for large-scale applications, such as informing standards, but potentially problematic for smaller-scale applications. In this paper, I describe a program of research designed to explore the smaller-scale use of LPs as supports for teacher classroom assessment practices in light of this simplification. Based on this research, I conclude that LP levels may serve as a generative heuristic, particularly when teachers are engaged with evidence of the limitations of LP levels and supported to use LPs in ways that do not rely on their levels.