There is growing interest in mathematics learning progressions in early childhood education. Counting is a skill usually developed early in life. The application of the counting principles in early childhood typically entails counting objects. This poses challenges for learning about zero. Indeed, the word "zero" is seldom used in the…

Place value is one of the 'big ideas' in number and plays a critical role in helping students develop their number sense, problem solving and computation skills. Yet, the elegant simplicity of our place value system belies the abstract nature of the construct. This paper presents data from 606 Year 3-6 students (ages 8-12) from two metropolitan…

In Asia, some children are taught a calculation technique known as the 'mental abacus'. Previous research indicated that mental abacus experts can perform extraordinary feats of mental arithmetic, but it disagrees as to whether the technique improves working memory. The present study extended and clarified these findings by contrasting performance…

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.

It is frequently surprising to new teachers (and even those with experience) when they find that not only do some children need to recount the group they have just counted to be assured of the total but also that this need seems to be resistant to intervention. Although moving from "counting-all" to "count-on" is sometimes…

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…

Advances in technology have seen a proliferation of touch-screen interfaces available to young children. These screens have changed the way in which young children engage with digital technology; with increased exposure and use, it raises debates about the suitability of integrating digital technology within early childhood settings. There are…

This paper reports on results of a targeted and extended (two school terms) program for building Grade 3 and Grade 4 students' facility with number facts and application for mental computation. As part of a larger project, this paper reports results from two schools. Results indicated strong gains in number fact recall and mental computation for…

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…

This research was designed to investigate the conceptualisations and thinking strategies Indigenous Australian students use in counting tasks. Eighteen Aboriginal students, in years 1 to 11 at a remote community school, were interviewed using standard counting tasks and a "counting" task that involved fetching "maku" (witchetty…

As part of individual interviews incorporating whole number and rational number tasks, 323 grade 6 children in Victoria, Australia were asked to nominate the larger of two fractions for eight pairs, giving reasons for their choice. All tasks were expected to be undertaken mentally. The relative difficulty of the pairs was found to be close to that…

Translating numerals into number words is a tacit task requiring linguistic and mathematical knowledge. This project expanded on previous number production models by examining developmental differences in children's number naming errors. Ninety-six children from grades one, three, five, and seven translated a random set of numerals into number…

Presents a case study with an at-risk second grade student on counting and numbers. Discusses counting stages that the student went through. (ASK)

Literature at national and international levels argues the importance of including mental computation in a mathematics curriculum that promotes number sense. However, mental computation does not feature in importance in the current Queensland mathematics syllabus documents. Hopefully, with the writing of a new mathematics syllabus, mental…

Estimation is an important skill for everyday living. Good estimators usually have a sound knowledge of basic facts, understand place value and use a variety of strategies to make their estimates. This paper describes an activity which is designed to provide students with opportunities to practice their rounding strategies with addition and…