This paper aims to broaden the scope of the construct concept image by addressing the mathematically oriented notion of "solution of an algebraic equation." The notion solution of an algebraic equation is not mathematical per se, but it is most prevalent in mathematical communications and in mathematics education. The paper describes…

Intellectual risk-taking, the act of engaging in learning by contributing an idea, question, or creative thought regardless of potential errors or judgments, is associated with many positive student outcomes; however, there is limited guidance on how to create an environment in which students feel empowered to be courageous in this way. In the…

This case study was undertaken to characterise the interventions made by a kindergarten teacher during a multiplicative structure problem-solving lesson. The study findings show that when she realised the children were having difficulty, she provided assistance to enable them to find the right answer. When the children gave an incorrect response,…

In recent decades, research has stressed the prominence of mathematics classroom discussions in productive instructional practices in mathematics instruction. In this context, problem-solving activities have been a common focus of research. Research shows that teachers need to deal with prerequisites and challenges such as norms, design of tasks,…

This paper introduces a model built upon the Method of Varying Inquiry, offering a didactical approach to problem posing and solving activities that stimulates inquiry-based learning in mathematics classrooms. The model combines the inquiry-based framework with the variation theory and with specific didactical and theoretical elements (the…

There has been an increase in the mental health concerns of students of all ages over the past several years. Specifically, since COVID-19, the social and emotional needs of students at the elementary school level have become drastically more evident. This qualitative action research study aimed to understand teachers' implementation of Morning…

In this paper, we first frame Sprague's vision in the historical context from which it emerged. From there, we explore some contemporary concerns instructional communication researchers must grapple with, and then propose some practical next steps for envisioning instructional communication research as a platform for meaningful contributions…

Science education researchers have highlighted how uncertainty can foster meaningful scientific sense-making, supporting students to re-evaluate their understandings of scientific phenomena and pursue deeper causal accounts. However, facilitating whole-class conversations motivated by uncertainty is complex and challenging, calling for further…

The COVID-19 pandemic has affected student learning; according to the National Assessment of Educational Progress (2022), scores for students in the United States have shown a decline in mathematics. . One way educators can strengthen students' current mathematical knowledge and bridge to new content is through Number Talks. Number Talks are brief…

Whole-class mathematical discussion in a problem-solving activity is recognized as a powerful pedagogical activity but also a challenge for teachers who must consider several difficulties that learners might face, particularly in terms of an overload of Working Memory and Executive Functions. This study investigates how the use of a digital…

The teaching and learning of mathematics in sub-Saharan African countries is dominated by teacher-centred pedagogies rather than student-centred ones. Observations of mathematics teachers at two private schools in South Sudan confirmed such practices. This inspired the researchers to design an intervention to help six primary mathematics teachers…

Often, mathematics teachers do not incorporate whole-class discourse of students' various ideas and solution methods into their teaching practice. Particularly complex is the in-the-moment decision-making that is necessary to build on students' thinking and develop their collective construction of mathematics. This study explores the…

In this paper I analyze a problem solving event in a secondary mathematics classroom. As the event unfolds, the teachers, including me, understand the event as involving interactions that were not related to learning. By adopting an expansive view of learning, I advance a different interpretation, that the interactions tell a story of student…

This quantitative study, administered at a higher education institution, looked at what variation exists among immigrant students, domestic students, and international students as determined by analysis in the HERI CIRP Freshman Survey as measured by responses to Habits of Mind questions. Habits of Mind is a framework of attributes that focus on…

Compelling research evidence shows benefits for student learning from explaining one's ideas and engaging with the ideas of others. However, whether certain patterns of group interaction may engender this productive student participation is unknown. Using data from two third grade mathematics classrooms, and over the course of six days during a…