Learning trajectories (LTs) can inform teaching by contributing a variety of pedagogical and content-related insights and strategies. They support sequencing topic introduction and development. Because ideas evolve gradually and often rely on a careful introduction of new representations, operations, cases of numbers, structures, and definitions,…

According to Jim Knight, learning something new--such as a new instructional approach or other innovation--and applying it in practice is complex and involves adaptations that take time. Knight describes the five stages he believes people go through in learning and practicing any innovation, from "non-use," gradually up to the stage of…

Given that the primary task of teaching is to teach the content of physical education, attention to how instructional tasks operationalize the curriculum and progress learning is essential knowledge for teachers. Task progression in physical education occurs when tasks are designed to successively and incrementally present physical education…

The importance of multiplicative thinking in supporting students' learning of key topics and success in further mathematics is widely and clearly stated in mathematics education literature. However, multiplicative thinking is not clearly stated in curriculum documents of many countries including Australia. In the "Australian Curriculum:…

Dyslexia is a specific learning disability caused by a neurological problem. It is a worldwide problem with a prevalence of 5-10% of the population. It is described mainly by difficulties in reading, spelling, accuracy, fluency, and decoding abilities. This article is chiefly concerned to provide an overview of dyslexia, some key issues based on…

This article describes how a teacher orchestrated a productive mathematics discussion to draw out mathematical knowledge and connect different areas of mathematics following a geometric sequences task. Whenever teachers succeed to engage their students in producing mathematics, it is advantageous for their moves to be analysed, discerned and…

BKT and other classical student models are designed for binary environments where actions are either correct or incorrect. These models face limitations in open-ended and data-driven environments where actions may be correct but non-ideal or where there may even be degrees of error. In this paper we present BKT-SR and RKT-SR: extensions of the…

Purpose: The purpose of this paper is to review the variation in methods used to analyse lessons in order to improve teaching and learning. Design/methodology/approach: It addresses the question of how observations of lessons can be analysed, and what approaches and methods are applicable in the analysis of collected data in lesson and learning…

The article introduces a software application (MATH) supporting an education of Applied Mathematics, with focus on Numerical Mathematics. The MATH is an easy to use tool supporting various numerical methods calculations with graphical user interface and integrated plotting tool for graphical representation written in Qt with extensive use of Qwt…

Recent years have seen a growing interest in intelligent game-based learning environments featuring virtual agents. A key challenge posed by incorporating virtual agents in game-based learning environments is dynamically determining the dialogue moves they should make in order to best support students' problem solving. This paper presents a…

The learning cycle has been embraced as a teaching approach that is consistent with the goals of the "National Science Education Standards" (National Research Council, 1996). Science teacher educators may be disappointed to find, however, that preservice teachers may fail to grasp this model, even after extensive instruction (e.g., Settlage,…

When teaching geography to students in the primary grades, teachers should provide firsthand experiences that young children need to make meaningful sense of their world. David Sobel, author of "Mapmaking with Children: Sense of Place Education for the Elementary Years," suggests that teachers in the early grades adopt a small-world approach to…

This article is written from our perspective as both researchers and mathematics teacher educators, and describes how our knowledge has grown as we engage concurrently in both teaching and research. Reflection-on-action is a means for us of approaching the relationship between theory and practice that comes out of the development of our work as…

We are researching actions that teachers can take to improve mathematics learning for all students. Structural elements of the lessons being trialled include making aspects of pedagogy explicit to seek to overcome differences in familiarity with schooling processes, and sequencing tasks with the potential to engage students. This article reports…

Social studies teachers face pressures from demands for greater emphasis in the areas of multicultural aspects of the world population, expansive technological changes, citizenship and moral education, and accountability for basic competence. The latter demand offers an opportunity to return to the broad perspective of teaching students not "what…