In the author's experience, lessons that are clearly meaningful for students beyond the classroom can foster positive attitudes, increase enjoyment, and enhance learning. In this paper she offers suggestions on how to plan for meaningful mathematics lessons using the topic of map skills as an example. She also presents some specific ideas for…

When asked to calculate the area of a particular shape, one student responded by asking, "Is that the outside or the inside?" while another student replied, "I think it's the one where you put a little 2 next to it." Both of these responses indicate a lack of conceptual understanding of area and reinforce the research findings that students…

It is not often that one can introduce primary school students to a problem at the forefront of mathematics research, and have any expectation of understanding; but with magic squares, one can do exactly that. Magic squares are an ideal tool for the effective illustration of many mathematical concepts. This paper assumes little prior knowledge on…

One way of providing middle-school students with the opportunity to engage in realistic activities is to ensure that mathematical concepts and ideas can be taught and expressed in contexts closer to students' own experiences. Students are expected to learn serious, substantive mathematics in classrooms in which the emphasis is on thoughtful…

Drawing upon research, theory, classroom and personal experiences, this paper focuses on the development of primary-aged children's computational fluency. It emphasises the critical links between number sense and a child's ability to perform mental and written computation. The case of multi-digit multiplication is used to illustrate these…

Research has established that children's development of addition and subtraction skills progresses through a hierarchy of strategies that begin with counting-by-one methods through to flexible mental strategies using a combination of knowledge of basic facts and understanding of place value. An important transition point is the shift from the…

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 still have…

Traditionally, primary schools place minimal emphasis upon relations and transformations as objects of study. In their research, the authors have found the young children can engage in conversations about equivalence and equations (Warren & Cooper, 2005a) and functional thinking (Warren & Cooper, 2005b). Fundamental to relations and…

Teachers assume that by the end of primary school, students should know the essentials regarding shape. For example, the NSW Mathematics K-6 syllabus states by year six students should be able manipulate, classify and draw two-dimensional shapes and describe side and angle properties. The reality is, that due to the pressure for students to…

During Term 3 2004, 19 teachers and more than 400 students in six Catholic parish primary schools in the Archdiocese of Melbourne trialled the new mathematics and numeracy "learning objects" from The Learning Federation (TLF). Learning objects are small, reusable digital resources that can be used with a web browser. Teachers in the trial used…

Gradually Internet-based educational resources are making their way into the school mathematics curriculum. Online resources are potentially useful compared to normal courseware because of their abundance, availability at no cost, platform-free accessibility, and wide reaching accessibility. On the other hand, a major limitation of online…

Statistical literacy is defined as "the ability to read and interpret data: the ability to use statistics as evidence in arguments. Statistical literacy is a competency: the ability to think critically about statistics" (Schield, p. 2). When a definition of statistical literacy is considered it can be seen that all students can manage a level of…

Teachers who believe "practice makes perfect" may engage students in repetitive, perhaps timed, computational exercises. If educators teach students to understand the procedures they practice, however, they will not need as much drill and they will have more flexible use of the computations they perform. Three-quarters of a century ago, William…

Calculators can be used in primary schools in a number of situations. They are most beneficial when working with large numbers, dealing with real data that leads to complex calculations, performing repetitive calculations, developing concepts, estimating and checking, problem solving, and looking for patterns and/or relationships. But what if the…

Over the past three years, Richardson Primary School has transformed its entire educational program based around the widespread introduction of interactive whiteboards (IWBs) into the school. A review of this initiative states that "Richardson is the first school in the ACT, and probably Australia, where the total school community, the students,…