This paper contains an analysis of some early thinking of 94 young children aged 5 years 7 months to 6 years 5 months. These children were interviewed as part of a larger study of the multiplicative thinking of children who were midway through their first year of school in Australia. They had not been formally taught multiplication or division at…

Assessing and monitoring the mathematics progress of students is a key role for teachers. It is important for assessment tools to identify students who are not yet thriving and provide guidance for teachers about how to support these students. In our study, teachers assessed 396 Grade 1 students midway through the school year using the Mathematics…

Equal representation as a social issue is about the participation of one social group, in a particular context, in proportion to the numbers in the group within the total population. The proportion of women in parliament, and of the participation rate of students of lower socioeconomic status in higher education, are examples. The aims of this…

This paper explores the tensions between two influences that currently shape the design of textbooks and other teaching resources. Through a textual analysis of primary school curricula from Australia and Mexico, we document a "curricular trend" in which number is framed almost exclusively in terms of counting. We explain that this trend…

Informal Australian discussion suggests that calculators are still widely regarded as devices for calculation, consistent with their naming, and are rarely recognised as potentially helpful to support students learning mathematics. In this paper, Barry Kissane explores some of the ways in which modern calculators might support students learning…

We assessed a range of theoretically critical predictors (numerosity discrimination, number knowledge, counting, language, executive function and finger gnosis) of early arithmetic development in a large unselected sample of 569 children at school entry. Assessments were repeated 12 months later. Although all predictors (except finger gnosis) were…

This study investigated how six Year Four (9-10 years old) students interacted with a dynamic (zoomable) digital number line to demonstrate knowledge and understandings of decimal fractions. Results from a task-based interview indicated that the zoomable number line is able to assist students in developing conceptual understandings of decimal…

Building students' understanding of cardinality is fundamental for working with numbers and operations. Without these early mathematical foundations in place, students will fall behind. Consequently, it is imperative to build on students' strengths to address their weaknesses with the notion of cardinality.

Learning to count and to produce the correct sequence of number words in English is not a simple process. In NSW government schools taking part in "Early Action for Success", over 800 students in each of the first 3 years of school were assessed every 5 weeks over the school year to determine the highest correct oral count they could…

Specialised Content Knowledge (SCK) is defined by Ball, Hoover-Thames, and Phelps (2008) as mathematical knowledge essential for effective teaching. It is knowledge of mathematics that is beyond knowledge which would be required outside of teaching; for instance, the capacity to determine what misconception(s) may lie behind an error in…

Recent research has supported and extended earlier research on how and for how long Indigenous people of Australasia have been counting. This history values the long history of Indigenous knowledge and re-writes the limited and sometimes false history that many Australian teachers accept and teach about number systems. The current views on the…

There is a large body of research that suggests a sound understanding of rational number is vital for success in all areas of mathematics, at school and beyond. In the Australian Curriculum, fractions are formally introduced from Year 1, yet there is evidence to suggest that current approaches are not leading to deep understanding in later years.…

A study conducted with 25 Year 6 primary school students investigated the potential for a short classroom intervention to begin the development of a "Modelling" conception of mathematics on the way to developing a sense of mathematics as a way of thinking about life. The study documents the developmental roots of the cognitive activity,…

Mathematics educators and researchers have advocated for the use of manipulatives to teach mathematics for decades. The purpose of this article is to provide illustrative uses of a readily available manipulative rather than a complete list. From an Australian perspective, Pop-it fidget toys can be used across the mathematics curriculum. This paper…

In providing a continued focus on tasks and activities that help to illustrate key ideas embedded in the new Australian Curriculum, this issue will focus on Number in the Number and Algebra strand. In this article Derek Hurrell provides a few tried and proven activities to develop place value understanding. These activities are provided for…