Children are often intrigued by number patterns and games and so it makes sense for teachers to include them in their mathematics lessons. Puzzles encourage the use of critical thinking skills and provide practice in important skills areas. The use of games fosters mathematical learning and encourages the mathematical processes that children use.…

As students progress through primary school, they are introduced to a growing collection of notation and symbols. From a teaching perspective, before introducing new mathematical symbols it is important to consider the role they play. If students cannot see a meaningful relationship between these signs and symbols and mathematical concepts, coming…

Among the practical applications of statistics is the collection of data from manufacturing processes. Often collected in the form of a time series, data collected from a series of measurements show the variation in those measurements, such as mass of a product manufactured. Limits are set for quality control and if these are exceeded then a…

In May 2008, the first National Assessment Program for Literacy and Numeracy (NAPLAN) test was administered across Australia to determine the standard of literacy and numeracy achievement of Australia's students in Years 3, 5, 7 and 9. Some students did very well on the tests and some did not. This type of test can tell a great deal about…

Students write definitions or explanations of mathematical words or symbols in their own words. These can be collated and added to as the year progresses to form a class dictionary that all students can access as required, or students could create their own personal dictionaries. This article presents a collection of ideas for incorporating…

When children start school, they bring with them a variety of background skills and informal knowledge that can enrich their learning of new concepts and ideas. A major tenet of many learning theories is that the more children are able to connect a new concept with their existing knowledge and understandings, the more they feel confident and able…

Mathematical investigations are loosely-defined, engaging problem-solving tasks that allow students to ask their own questions, explore their own interests and set their own goals. The value of investigations for students lies in their complexity. Scaffolding plays an important role in supporting students' high-level engagement by encouraging…

The Task Types and Mathematics Learning project is investigating the opportunities and constraints that teachers experience when using particular types of mathematics tasks. Some assumptions underlying this aspect of the project are: (1) that teachers seeking a balanced curriculum choose to use a mix of types of tasks; (2) open-ended questions…

With teachers and students in Government and Catholic schools in three geographical clusters in Victoria, the Task Type and Mathematics Learning (TTML) project is investigating the best ways to use different types of mathematics tasks, particularly in Grades 5 to 8. This article describes Type 1 tasks and discusses how they contribute to…

Open-ended activities can be a powerful and engaging tool, promoting authentic learning and opportunities for formative as well as summative assessment. This article presents an activity that shows how an open-ended task--with a variety of solution strategies and multiple correct answers--can be an effective educational activity which also offers…

Teachers and researchers work hard to discover the most effective ways of teaching mathematics in the primary classroom. When searching for new tasks to teach or ways to adapt a task to fit the class's profile, they often "phone a friend," drawing on the know-how and knowledge of colleagues and experts. Other articles in this issue attempt to…

In this article, the authors discuss the use by teachers of "Type 2 tasks" within the Task Types in Mathematics Learning (TTML) Project, i.e., those in which the mathematics is situated within a contextualised practical problem. It is argued that these kinds of tasks have great potential for challenging and engaging students, and showing how…

Teachers do not want to have students simply marking time by completing tasks from which there is no new learning for them. Similarly, teachers do not want students struggling with tasks that are demoralisingly difficult. In one primary mathematics classroom, however, a teacher can expect to have a wide range in the levels of understanding of the…

Being numerate involves using mathematical ideas efficiently to make sense of the world, which is much more than just being able to calculate. What is needed is the accurate interpretation of mathematical information and the ability to draw sound conclusions based on mathematical reasoning. This skill may be called "critical numeracy", defined as…

Early algebraic thinking in a primary context is not about introducing formal algebraic concepts into the classroom but involves reconsidering how one thinks about arithmetic. Early algebraic thinking assists young students to engage effectively with arithmetic in ways that support engagement with arithmetic structure rather than arithmetic as a…