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…

Learning the meaning of number words is a lengthy and error-prone process. In this review, we highlight outstanding issues related to current accounts of children's acquisition of symbolic number knowledge. We maintain that, despite the ability to identify and label small numerical quantities, children do not understand initially that number words…

Background: The present study delves into the debate surrounding the effectiveness of homework, focusing specifically on the use of online homework in teaching decimal numbers to 5th and 6th grade primary school students. It highlights the challenges students face in representing and identifying decimal numbers, a concept that is often difficult…

Identifying and addressing the knowledge gap in early numeracy is crucial, given the strong associations between early numeracy skills and later school success. The purpose of this study is to establish current viewpoints and ideas on children's numeracy development via three forms of representation: manipulative, symbolic, and static. The…

Math fact fluency involves the quick, accurate retrieval of basic arithmetic combinations and the ability to use this fact knowledge efficiently. Math fact retrieval is typically considered fluent when performed accurately within 2 to 3 seconds, and "efficiency" refers to students' ability to apply fact knowledge to more complex…

Background: Poor mathematics performance in South Africa is well known. The COVID-19 pandemic was expected to exacerbate the situation. Aim: To investigate Grade 7 learners' mathematical knowledge at the end of primary school and to compare mathematical performance of Grade 7 and 8 learners in the context of the pandemic. Setting: Data were…

In this article Jessica Hunt explores the use of clinical interviews to gain a deep understanding of students' knowledge. Examples of clinical interviews are provided and advice for planning, giving and interpreting the results of interviews is also included.

Activity-based instructional strategies promote physical interaction with manipulatives to represent abstract concepts. As a means to improve student achievement in mathematics, educational researchers and practitioners often recommend instructional strategies that capitalize on the assumed benefits of manipulatives. Recent research has indicated…

This study concerns pupils' experience of unit and non-unit fractions of a discrete quantity during specially designed lessons. The aim was to explore pupils' understanding of operations such as "b/c of a" in lessons where the teachers were aware of some pupils' difficulties beforehand and what needed special attention.…

In the present research, we evaluated the effectiveness of a multi-year professional development program in mathematics for elementary teachers. Each year the program focused on a different domain of mathematics. We found the program increased teachers' knowledge of (a) number and operations, (b) measurement and geometry, and (c) probability and…

The introduction of negative numbers should mean that mathematics can be twice as much fun, but unfortunately they are a source of confusion for many students. Difficulties occur in moving from intuitive understandings to formal mathematical representations of operations with negative and positive integers. This paper describes a series of…

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…

Many elementary and junior high school students do not become proficient with common and decimal fractions because they have established few connections between the form they learn in the classroom and understandings they already have. (Author/GC)

Offers 3 teaching designs developed for 12- to 16-year-old pupils taking into account personal differences in gender, culture, knowledge, and use of calculators. The designs concern the representation of three-dimensional objects in the plane, directions and great circles on the sphere, and exploration of the integrating calculator. (Contains 31…

A broad range of research efforts are currently examining the quality and nature of the mathematics instructional program in the early grades. The purpose of this paper was to report on the assessment of a teaching-learning program in grade one classrooms. The major goals of the study were to: (1) identify patterns and change in children's…