The authors define two mathematical cognitive verbs which are fundamental to the development of mathematical thinking and reasoning. They distinguish between 'describing' and 'explaining' in relation to doing mathematics, rather than using them interchangeably.

The learning of multiplication facts has long been an important focus of the primary grades, but lasting mastery of facts requires a meaningful approach that develops all four components of mathematical proficiency (understanding, fluency, problem-solving, and reasoning). This article shares how visual imagery in the form of Quick Looks with dot…

Planning mathematics learning sequences as a team is becoming increasingly common in Australian primary schools and is often referred to as "team planning" or "collaborative planning." The purpose of this article is to illustrate how a multi-age Year 5 and 6 primary school teaching team, authors Scott, Rai and Kristyn, grappled…

Creative thinking in mathematics is an essential 21st Century skill that can be developed and encouraged through an exploration of mathematical concepts. In the context of the new "Australian Curriculum: Mathematics," this article explores the possibilities that are unlocked when students engage with tasks creatively in mathematics. By…

This activity provides students with opportunities to practice addition strategies and explore probability in this adaptation of the classic probability game Greedy Pig. To play, you will need a 6-sided dice, a number chart, and a brown counter to represent the mouse, and a yellow counter to represent the cheese. The game is suitable for two or…

In this article the author describes an intervention program for students who were approximately six months behind expected standards. The program, "Prepare 2 Learn," had four components: building prior knowledge; developing mental computational fluency; encouraging a growth mindset; and meta-cognitive strategies. The qualitative data…

Effective planning lays the foundations for effective teaching in mathematics (Smith & Stein, 2018). The planning decisions made by teachers are many and varied and ultimately inform what, how and why students learn mathematics (Kilpatrick et al., 2001). Critically, these decisions affect students' opportunities to engage with mathematics in…

This paper explores Year 3 Irish students' problem-solving strategies when responding to a skyscraper growing pattern problem. Students' strategies reveal their understandings of multiplicative thinking, pattern, and algebraic reasoning. The version of the growing pattern lesson was that a 'teaching through problem solving' approach was taken,…

In order to investigate pre-service teachers (PSTs') understandings of the terms mathematics and numeracy, the authors conducted a study at one Australian university. The PSTs were enrolled in a mandatory unit about numeracy across the curriculum, in which both teachers' and students' numeracy capabilities were considered. The study took place…

Peter Sullivan and colleagues present a report on an initiative at a Victorian primary school which embraced opportunities offered by purposeful collaborative professional learning communities. They utilised a form of Japanese Lesson Study as part of their approach. There are three parts to the story of this initiative: (1) a description of the…

In this article the authors overview how the recently revised (version 9) Australian Curriculum (Australian Curriculum Assessment and Reporting Authority, 2022) and student difficulties with fractions relate to five developmental Fraction Schemes developed from multiple research projects in the literature. The article shares research findings from…

The teaching of measurement concepts typically follows a learning sequence of: (1) identifying the attribute, (2) comparing and ordering, (3) measuring using non-standard units, (4) measuring using standard units, and (5) applications. This sequence is entrenched in many curricular documents and textbooks (Australian Curriculum Assessment and…

This article illustrates one of several learning sequences from the Interdisciplinary Mathematics and Science (IMS) Learning project, connecting science and mathematics learning in the primary school. Investigating Body Height involved a series of investigations conducted in Years 5 and 6 across six classes in one school. The project teachers…

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…

This article presents activities focused on developing some essential Year 1-3 fraction understandings (i.e., joining/composing, decomposing/ partitioning) while aligning these activities to the Australian Curriculum content strands and content descriptions. Additionally, the authors describe the materials/resources needed, the key vocabulary…