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…

In this article, the authors describe a reform-based activity concerning multiplication, developed within the context of the children's story "The Wonderful Pigs of Jillian Jiggs" by Phoebe Gilman. They also provide vignettes of informal multiplicative thinking by Grade 2/3 children that occur during these activities. The informal multiplicative…

"Scratch" is a media-rich digital environment that utilises a building block command structure to manipulate graphic, audio, and video aspects. It incorporates elements of Logo including "tinkerability" in the programming process. In "Scratch" students use geometric and measurement concepts such as coordinates, angle, and length measurements. It…

In 2010, St. Leonards Primary School in Tasmania, along with other selected schools throughout Australia, trialled the draft Australian Curriculum: Mathematics. Mathematics had been a whole school focus at St. Leonards Primary School for several years, and the school found that the opportunity to be part of the trial strongly connected with their…

Finding patterns, and making and justifying conjectures are considered the building blocks of mathematical reasoning and proof. Curriculum revisions in the United States and Australia place increased emphasis on problem solving and reasoning in the primary school curriculum. A number of curriculum resources for teachers are available but under…

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…

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…

Virtually all mathematics is based on pattern and structure. A mathematical "pattern" is any predictable regularity, usually involving numbers or space. In every pattern, the various elements are organised in some regular fashion. The way a pattern is organised is called its "structure," which may be numerical or spatial. In this article, the…

Good questioning techniques have long been regarded as a fundamental tool of effective teachers and research has found that "differences in students' thinking and reasoning could be attributed to the type of questions that teachers asked" (Wood, 2002). Past research shows that 93% of teacher questions were "lower order" knowledge-based questions…

There are many classroom activities that can be implemented with primary students that introduce and immerse them in ratio investigations. Some enjoyable tasks include finding the ratio of tongue rollers to non-tongue rollers in the classroom; left-hand dominant to right-hand dominant; right-thumb over left-thumb when clasping the hands to…

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…

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…

The author recently read a research paper by Padberg (2002), in which the development of understanding associated with decimal fractions was studied. Padberg (2002) outlined the situation that existed in Germany, where students were introduced to decimal fractions in the sixth year of school. He claimed that it was assumed students would have a…

The authors discuss proportional reasoning as a challenging yet central concept for students in the middle grades that lays a foundation for mathematics studied later in high school. Four types of proportional reasoning problems are discussed: (1) Part-part-whole (comparing a subset (part) of a whole with its complement (other part) or the whole…