Evidence suggests that some students have learned procedures with little or no underpinning understanding while others have a much more connected and conceptual levels of understanding. In this article, the work of four primary students is discussed in terms of their contextual understanding of multiplicative concepts. The difference between…

A robust understanding of place value is essential. Using a problem-based approach set within meaningful contexts, students' attention may be drawn to the multiplicative structure of place value. By using quotitive division problems through a concrete-representational-abstract lesson structure, this study showed a powerful strengthening of Year 3…

The importance of laying a foundation for algebraic reasoning at a young age is increasingly being emphasized. In this article, the authors report on an activity that elicits in a natural way algebraic strategies that in a later stage of learning algebra are crucial for solving equations. The activity brings about the students' spontaneous use of…

This article proposes a framework for classroom teachers to use in making pedagogical decisions regarding which mathematical materials (concrete and digital) to use, when they might be most appropriately used, and why. Two iPad apps ("Area of Shapes (Parallelogram)" and "Area of Parallelogram") are also evaluated to demonstrate…

Use of technology in the mathematics classroom has the potential to advance children's learning of mathematics and enhance their attitudes about mathematics. When used in conjunction with purposeful planning, teachers can use technological tools to reinforce their pedagogical intentions and to facilitate relevant learning activities for students.…

Primary teachers play a key role in their students' future mathematical success in the early secondary years. While the word "algebra" may make some primary teachers feel uncomfortable or worried, the basic arithmetic ideas underlying algebra are vitally important for older primary students as they are increasingly required to use "algebraic…

It is over 12 years since "APMC" published Bob Perry and Peter Howard's research on the use of mathematics manipulative materials in primary mathematics classrooms. Since then the availability of virtual manipulatives and associated access to computers and interactive whiteboards have caused educators to rethink the use of mathematics…

As part of the project titled "Hands-On Heads-On: The Effective Use of Manipulatives Both Virtual and Physical" being undertaken at Edith Cowan University, there was an investigation into the use of virtual manipulatives and the interactive whiteboard (IWB). Virtual manipulatives may be defined as a virtual representation of a physical…

In the middle years of primary schooling, the teaching of common fractions frequently involves written activities that use abstract representations of numbers, symbols, and images. Many students, however, still need the benefit of concrete materials and sensory motor experiences to enhance their understanding of the concepts associated with common…

Young students often struggle with abstract concepts in mathematics, causing primary teachers to continue to search for ways to help teach such concepts. "Principles and Standards for School Mathematics" (NCTM, 2000) recommends using concrete models and physical materials before moving on to more abstract ideas. However, some children…

Perimeter and area are important real-world concepts in their own right, and their relationship certainly is no less important. This relationship can be intuitively challenging for both children and adults. In this article, the author explores the relationship between perimeter and area with students from grades 4 to 6. The study of perimeter-area…

The authors discuss mass as one of the three fundamental measurements (the others being length and time), noting that estimation of mass is little taught and assessed in primary schools. This article briefly explores the reasons for this in terms of culture, practice, and the difficulty of assessing estimation of mass. An activity using the…