Students encounter difficulties in solving areas of triangles and quadrilaterals due to a lack of conceptual understanding of the topic. The researchers have developed the following activities and the hypothetical learning trajectory (HLT) through the design research approach focusing on developing activities for students to learn the concepts…

One of the greatest conceptual difficulties faced by middle level mathematics students is developing a rich understanding of irrational numbers that includes recognizing that irrational numbers are truly real numbers with an exact value and an exact place on the number line. Developing a deep conceptual understanding of irrational numbers is…

When it comes to choosing tasks, values can have a significant impact. This study explores teachers' values as they choose one task from among three that they believe will have the most potential to occasion mathematical creativity in the classroom. Participants' analyses of each task, as well as their reasons for choosing one task as most…

In this paper, motivated by the desire to understand which forms of parent-initiated activity are productively implicated in young children's mathematics learning, we present a methodological critique of recent research. Many such studies, based on assumptions that parent-initiated activities can be categorised as formal or informal, direct or…

How can we engage all primary school students in rich mathematical learning, support them to make connections, and develop their mathematical language and reasoning? In this article, we draw on one school's experience in considering an approach to mathematics instruction that could support teachers in addressing this question, specifically…

The reality is that textbooks and state standards have more content than can reasonably be covered for proficiency in most classrooms. In years past, this typically meant cutting the last unit or two or moving along regardless of who was keeping up, in many cases resulting in cutting statistics from the curriculum. This article provides five…

This article deals with an introduction of probability at school through sensory modalities. This approach is based on sampling fluctuation with empirical observations of frequencies. Initially, we analyze how students from high school work on such a task by using dice, pencil, and paper. We then identify the use of schemas and data visualization…

In today's fast paced early childhood classrooms, mathematics play activities in prekindergarten settings are not consistently supported. Administrators and educators have discussed with great intensity and passion about incorporating mathematics play in prekindergarten classrooms. Both groups discussed the benefits and reservations of…

This study examines a Technology, Pedagogy, Content Knowledge (TPACK) training framework for pre- and in-service mathematics teachers that enables them to experience inquiry-based learning as learners in a dynamic geometry environment that serves as a mathematics laboratory. We investigate the effect of this experience on the teachers' TPACK,…

This paper presents a qualitative study developed with a group of 16-year-old students who were asked to estimate large numbers of elements on a bounded surface. Taking the realistic mathematics education framework as a reference, we presented the students with an activity sequence comprised of four different tasks--each one with a different…

Quadratic functions are explained in the three equivalent formats: Standard (or Expanded), Vertex and Factorised. However, cubic functions are represented only in the two equivalent formats: Standard (or Expanded) and Factorised. In this article, the author shows how cubic functions can be expressed in three equivalent formats like quadratic…

This article builds on the work of Professor Robyn Jorgensen and Associate Professor Peter Games and others on social justice and mathematics and links to the Ethical Understandings capability of the "Australian Curriculum." Presented in this paper is an argument for the importance of a social justice approach to teaching mathematics,…

In this study, it was aimed to examine the argumentation structures of 5th-grade middle school students, while they were structuring geometric concepts in argumentation-based activities of geometric shapes. To this end, 7 fifth-grade students studying in a public middle school were included in the study. In the study, five geometry tasks involving…

In this article, the authors present a task that promotes mathematical creativity. The task focuses on defining new geometric concepts, whilst providing students with creative thinking opportunities. They discuss prospective mathematics teachers' experiences while conducting a geometric definition task. Prospective mathematics teachers who…

Mathematical spaces extend far beyond the classroom and physical environments into virtual spaces. Today's students have more to consider than just their face-to-face experiences with mathematics inside or outside the classroom; they have the online perspectives of others to consider as well. To gain critical insight, we conducted this research…