In this study we analyse the Australian Curriculum: Mathematics (ACM), with a focus on how mathematical proficiencies are represented from Foundation year through year 10.
The ACM is organised around the interaction of two different types of strands: the content strands and the proficiency strands. The proficiency strands are understanding, fluency, problem solving, and reasoning, which describe the thinking and doing of mathematics (i.e., how the content is explored). The focus on proficiencies are in line with international mathematics curriculum reform movements, where a movement has occurred from emphasizing only content, with the risk of limiting learning activities to procedures and memorisation, to include a variety of more sophisticated types of mathematical activities described through proficiencies.
The ACM describes a structure of progression for the content strands through different sub-strands, which are introduced in different year levels. However, the ACM does not include a structure for illustrating the progression for the proficiency strands. References to proficiencies exist in content descriptions in the ACM, making it possible to analyse any potential progression also for proficiencies, which is the purpose of our study, where we explore if and how the stated aim of the ACM to ensure that students develop increasingly sophisticated mathematical proficiencies is evident.
One view of learning mathematics is that students (within a certain content strand) first need to master basic facts and procedures (i.e., to master aspects of fluency) before they can understand why given facts are true or how and why given procedures work, and before they can progress to activities involving reasoning and problem solving. However, empirical research has increasingly shown this fixed type of learning sequence to be inadequate, especially in regard to equity, as there is always the risk that certain groups of students are restricted from opportunities to learn more than facts and procedures. It is therefore of importance to examine how different types of proficiencies are depicted in the ACM. In particular, we aim to answer two research questions about the ACM:
1. How are the different proficiencies emphasized across year levels? What kind of structure exists to ensure the development (a type of progression of sophistication and depth) of the proficiencies throughout the year levels?
2. How are the different proficiencies emphasized across content strands (both within and throughout year levels)?
We are using a type of linguistic analysis to locate descriptions of activities/abilities in the ACM that signify proficiencies.