This study identified appropriate pedagogy for computational thinking in K-12 computer education. The Delphi technique was employed to collect different views, ideas and opinions derived a consensus from a panel of 12 international experts through a series of questionnaires. The experts have various experiences in computer science, computer…

It is widely acknowledged that communicating mathematical thinking is complex, difficult, and often messy. In this article, the authors explore how mathematical thinking is communicated, providing examples of strategies for teachers and students to use in the mathematics classroom.

Mathematics and spatial reasoning are inextricably linked. While this is increasingly recognised, a clearer understanding of how spatial reasoning improves your mathematics performance is needed. We sought to explore the role of spatial reasoning strategy use across a range of mathematics assessment tasks with Grade 7 and 9 students. Interviews…

Gap reasoning is an inappropriate strategy for comparing fractions. In this article, Patrick Sullivan and Joann Barnett look at the persistence of this misconception amongst students and the insights teachers can draw about students' reasoning.

Learning strategies are crucial to student learning in higher education. In this paper, there are comparisons of student engagement, feedback mechanism and workload arrangements at some typical universities in Australia and China, which are followed by practical suggestions for active learning. First, an inclusive class would allow learners from…

Teaching and learning research since the 1980s has established a trend in students' learning approach tendencies, characterised by decreasing surface learning and increasing deep learning with increasing age. This is an important trend in higher education, especially at a time of increasing numbers of older students: are we graduating more deep…

Legal reasoning is a type of problem solving, and is situated within thinking skills, one of the six threshold learning outcomes established under the auspices of the Australian Learning and Teaching Council's Bachelor of Laws Learning and Teaching Academic Standards Statement. The threshold learning outcomes define what law graduates are…

The conventional lecture has significant limitations in the higher education context, often leading to a passive learning experience for students. This paper reports a process of transforming teaching and learning with active learning strategies in a research-intensive educational context across a faculty of 45 academic staff and more than 1,000…

This research was designed to investigate the conceptualisations and thinking strategies Indigenous Australian students use in counting tasks. Eighteen Aboriginal students, in years 1 to 11 at a remote community school, were interviewed using standard counting tasks and a "counting" task that involved fetching "maku" (witchetty…

Mental computation--that is, calculating in the head--is a relatively new topic in mathematics curricula for primary-age children. It is an important skill because it enables children to learn more deeply how numbers work, make decisions about procedures, and create strategies for calculating, thus promoting number sense--a well-developed…

The ability to solve linear equations sets students up for success in many areas of mathematics and other disciplines requiring formula manipulations. There are many reasons why solving linear equations is a challenging skill for students to master. One major barrier for students is the inability to interpret the equals sign as anything other than…

As part of individual interviews incorporating whole number and rational number tasks, 323 grade 6 children in Victoria, Australia were asked to nominate the larger of two fractions for eight pairs, giving reasons for their choice. All tasks were expected to be undertaken mentally. The relative difficulty of the pairs was found to be close to that…

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…

The theme of the 38th meeting of the International Group for the Psychology of Mathematics Education (PME 38) and the 36th meeting of the North American Chapter of the Psychology of Mathematics Education (PME-NA 36) was "Mathematics Education at the Edge." Academically, the theme provides opportunities to highlight and examine…

Estimation is an important skill for everyday living. Good estimators usually have a sound knowledge of basic facts, understand place value and use a variety of strategies to make their estimates. This paper describes an activity which is designed to provide students with opportunities to practice their rounding strategies with addition and…