Recent solar eclipses provide relevant real-world contexts for learning about the scientific phenomena of the lunar phases. News coverage of the phenomenon may have raised questions such as, "Why does the Moon look different at different times, and sometimes as if it is not there?," and "What patterns can be found in the lunar…

This article aims to show some activities based on non-routine problems with different levels of difficulty and from different classes that are integrated into the curriculum, additionally two spaces were opened for students to interact with recreational mathematics activities with the purpose of providing opportunities to all students access the…

This article presents activities focused on developing some essential Year 1-3 fraction understandings (i.e., joining/composing, decomposing/ partitioning) while aligning these activities to the Australian Curriculum content strands and content descriptions. Additionally, the authors describe the materials/resources needed, the key vocabulary…

In this set of tips, parents and caregivers will learn how to: (1) support children's understanding of fractions at home with activities on dividing objects (recommended for grades K-5); (2) support children's understanding of fractions at home with measurement activities (recommended for grades K-4); (3) support children's understanding of…

This study investigates the use of manipulatives by elementary students working on a fraction task. Extending previous work on the role played by the manipulatives in students' activity, we aim at describing how the choices made for the task design disrupt students' activity, creating opportunities to learn. The theoretical underpinnings allow…

Generative activities have been shown to support students to engage in space-creating play and exercise their conceptual agency to generate a mathematical space (e.g. Stroup et al. 2004), yet these studies implement generative activities only with their resonating counterpart, classroom networks, technological infrastructures that connect…

Without a doubt, fractions prove to be a stumbling block for many children. Researchers have suggested a variety of explanations for why this is the case. The introduction of symbolization and operations before the development of conceptual understanding of fractions, a lack of understanding of the role of the numerator and denominator, and an…

Background: Fractions continue to pose a critical challenge for students and their teachers alike. Mathematics education research indicates that the challenge with fractions may stem from the limitations of part-whole concepts of fractions, which is the central focus of fractions curriculum and instruction in the USA. Students' development of more…

Tzur and Simon (2004) postulated two stages of concept development, participatory and anticipatory. The distinction between the two stages was exemplified by what they termed "the next-day phenomenon" in which learners who could solve a task one day in the context of the activity through which they made the abstraction, could not solve…

In this article, the authors describe classroom use of technology that successfully engaged fourth grade students (typically aged 9-10) in the United States in learning about fractions. The activities involved the use of an interactive simulation designed to support student learning of fractions, and whole-class discussion where students were…

The concept of exponents has been shown to be problematic for students, especially when expanding it from the domain of positive whole numbers to that of exponents that are negative and later rational. This paper presents a theoretical analysis of the concept of exponentiation as a continuous operation and examines the deficiencies of existing…

When solving mathematical problems, many students know the procedure to get to the answer but cannot explain why they are doing it in that way. According to Skemp (1976) these students have instrumental understanding but not relational understanding of the problem. They have accepted the rules to arriving at the answer without questioning or…

Find out how to use photographic images to support the conceptual development of proportional thinking. This paper provides insight into a sequenced activity that promotes student engagement and makes links to familiar and unfamiliar contexts.

Maree Skillen provides a practical guide to using the free, Skitch app to promote mathematical exploration and understanding. Five activities are provided, with links made to the Australian Curriculum: Mathematics.

This guidance report focuses on the teaching of mathematics to pupils in Key Stages 2 and 3. It is not intended to provide a comprehensive guide to mathematics teaching. We have made recommendations where there are research findings that schools can use to make a significant difference to pupils' learning, and have focused on the questions that…