Investigating whole number place value in Years 3-6: creating an evidence-based developmental progression
Creators: name: Rogers, Angela
Publisher: name: RMIT University
Year: 2024

description: Place value is the foundation of the base ten number system and, as such, plays an essential role in understanding almost every aspect of primary school mathematics. The majority of place value literature tends to focus on the early years and/or describe the significant difficulties students have understanding this construct. However, analysis suggests that there is a lack of clarity associated with the meaning of place value in the context of teaching and learning in upper primary school. This leads teachers to focus on a small range of fairly superficial aspects of place value, such as reading, writing and comparing numbers, resulting in a shallow appreciation of the construct by many students. <br><br>Six critical aspects of place value, namely: Calculate, Count, Compare/Order, Make/Represent, Name/Record and Rename were identified from the analysis of the research literature. These aspects combine to provide a clear definition of place value and provide an important framework for future research. With all six aspects in mind, this research sought to design, construct and trial both a comprehensive paper and pen and an online place value assessment tool. The resulting Place Value Assessment Tool (PVAT) and PVAT-O (online) were trialled at two Catholic Primary schools in Victoria, Australia with around 600 Year 3-6 students. Rasch modelling and qualitative insights gathered from student interviews were used to produce two internally consistent parallel forms of the PVAT and a comparable online version of the test. In its final form, the paper and pen PVAT was used to measure the learning of 227 Year 3-6 students over a 10-week period at a third Catholic Primary school. The results suggested that students made substantive gains over this time. The insights gathered from the qualitative teacher survey suggested that a short professional development session related to the test and the six aspects encouraged teachers to modify their instruction over the 10 weeks. As a result, the PVAT was seen to be a quality, formative assessment tool with the potential to support teachers to improve their place value instruction.<br><br>Using the PVAT Rasch data, an empirically based Developmental Progression was constructed. The progression describes four key stages to help teachers formatively monitor and guide their student’s place value learning. The progression had several important implications for the teaching of place value. These included the critical nature of developing student understanding in the rename aspect and the finding that the difficulty of items is more related to the aspect of place value it addresses, rather than the size of numbers involved. This project presents qualitative and quantitative evidence that the PVAT, PVAT-O and the PVAT Developmental Progression provide teachers with a valuable resource for teaching place value. It also highlights the importance of taking a unified systematic approach to place value research to facilitate more comprehensive understanding of what is involved in teaching and learning this construct. <br><br>