This article illustrates and differentiates the unique role cognitive interviews and think-aloud interviews play in developing and validating assessments. Specifically, we describe the use of (a) cognitive interviews to gather empirical evidence to support claims about the intended construct being measured and (b) think-aloud interviews to gather…

This paper compares the counting and whole number knowledge and skills of primary school children in Australia and Germany at the end of Grade 1 and Grade 2. Children's learning was assessed using the Early Numeracy Interview and associated Growth Point Framework. The findings highlight substantial differences between the two groups that vary for…

Studies reveal that students as well as teachers have difficulties in understanding and learning of decimals. The purpose of this study is to investigate students' as well as pre-service teachers' solution strategies when solving a question that involves an estimation task for the value of a decimal number on the number line. We also examined the…

"Let's Count" is an early mathematics program that has been designed by The Smith Family and the authors to assist educators in early childhood contexts in socially disadvantaged areas of Australia to work in partnership with parents and other family members to promote positive mathematical experiences for young children (3-5 years). A…

In this article, I present an initial analysis of an empirical study that was undertaken in an attempt to elicit what subject-matter knowledge, pedagogic content knowledge and curriculum knowledge teachers bring to bear on decisions for teaching. The analysis is based on interview data with 46 Grade 3 teachers, who were presented with two…

If teachers are to adequately support development of their students' numeracy capabilities then they need to have an identity as a teacher of numeracy. A preliminary evaluation of a conceptual framework (Bennison & Goos, 2013) developed for use in a two-year study that seeks to understand this construct is presented. Initial findings about an…

The goal of this study was to investigate understanding of in-service elementary school teachers in Taiwan about number sense, teaching strategies of number sense and the development of number sense of students. Data were gathered through interviews of nine elementary mathematics teachers, regarding their understanding about number sense. The data…

The gap between young Indigenous and non-Indigenous children's capability within mathematics is widely acknowledged. This gap is conjectured to exist at all levels of schooling, including pre-school, and widens as children mature. Most of these findings are based on research relating to children's understanding of number and space. Little is known…

This paper presents the findings of an investigation into the influence primary teachers' knowledge of a researched-based framework describing children's cognitive development in early number has on their teaching practices. Survey and interview data from twenty-eight teachers were collected to determine teachers' perceptions of their…

Research investigating the cognitive effect of bilingualism on mathematical learning began just over 25 years ago and has progressed from there, although research focusing on the Asia-Pacific region is still quite limited. This paper presents details about a current project in this area. CARE's Riel Maths research project investigates ethnic…

This study contributes to a growing body of research on the development of elementary teacher's content knowledge of mathematics. Individual clinical interviews were conducted with preservice elementary teachers (N=21) enrolled in a professional development course called "Foundations of Mathematics for Teachers." An instrument that…