Due to the learning paradox, students cannot have real difficulty in understanding a mathematical concept that they have not yet understood. There is a gap between real difficulties, directly experienced by students, and illusionary ones, only observed by researchers. This paper aims to offer a critical reflection on our understanding of the term…

Research studies are abundant in pointing at how the transition from additive to multiplicative thinking acts as a core challenge for students' understanding of proportionality. This said, we have yet to understand how this transition can be supported, and there remains significant questions to address about how students experience it. Recent work…

Though there is an extensive research literature on understanding and assessing individual modeling competencies, less attention has been given to characterizing the social context of the classroom in which modeling occurs. Yet a classroom's culture of modeling--its negotiated system of beliefs and values about the nature of modeling and what…

Given the rapid growth of research-practice partnerships (RPPs), we need a framework that helps the field understand how RPPs can facilitate organizational learning in service of local educational improvement and transformation. Drawing on sociocultural and organizational learning theories, we argue that learning can happen for the organizations…

Given the rapid growth of research-practice partnerships (RPPs), we need a framework that helps the field understand how RPPs can facilitate organizational learning in service of local educational improvement and transformation. Drawing on sociocultural and organizational learning theories, we argue that learning can happen for the organizations…

Prior to the 2010 release of the Common Core State Standards for Mathematics (CCSSM), the curricular landscape in the United States consisted of an assortment of individual state standards that as a collection reflected little consensus as to the grade placement of specific mathematical content. As CCSSM has now been used as the foundation for…

Ambiguity is a natural part of communication in a mathematics classroom. In this paper, a particular subset of ambiguity is characterized as clarifiable. Clarifiable ambiguity in classroom mathematics discourse is common, frequently goes unaddressed, and unnecessarily hinders in-the-moment communication because it likely could be made more clear…

Visualising positive and negative numbers on a number line is helpful for exploring problems involving operations with positive and negative numbers. This is because number lines lend themselves to exploring problems involving continuous linear contexts such as travelling distances and temperature. Teachers in a professional development program…

In this article, we describe a software system for assessment development in online learning environments in contexts where there are robust links to cognitive modelling including domain and student modelling. BEAR Assessment System Software (BASS) establishes both a theoretical basis for the domain modelling logic, and offers tools for delivery,…

This paper explores the use of a mediated field experience (MFE) for teacher candidates in a middle school setting, a small laboratory school. This work focuses on adjustments made for the MFE to function in an online environment during remote instruction caused by a worldwide pandemic. Teacher candidates completed a learning cycle focused on…

Positioning students as competent is a teaching practice that uses specific, explicit affirmations to note that students have contributed something meaningful to the community of learners. It supports student agency in the mathematics classroom and contributes to the development of a positive mathematics identity. In this article, the authors…

There is a large body of research that suggests a sound understanding of rational number is vital for success in all areas of mathematics, at school and beyond. In the Australian Curriculum, fractions are formally introduced from Year 1, yet there is evidence to suggest that current approaches are not leading to deep understanding in later years.…

"University of Chicago School Mathematics Project (UCSMP)" is a core mathematics curriculum that includes materials and a routinized instructional approach with an option for teacher training. The curriculum uses an inquiry-based approach with a focus on active learning where students frequently engage in hands-on activities and…

"University of Chicago School Mathematics Project (UCSMP)" is a core mathematics curriculum that includes materials and a routinized instructional approach with an option for teacher training. The curriculum uses an inquiry-based approach with a focus on active learning where students frequently engage in hands-on activities and…

"University of Chicago School Mathematics Project (UCSMP)" is a core mathematics curriculum that includes materials and a routinized instructional approach with an option for teacher training. The curriculum uses an inquiry-based approach with a focus on active learning where students frequently engage in hands-on activities and…