Toulmin's argumentation model is an effective tool in the description of one step of an argument. However, there is a need to consider more than this model to portray a comprehensive argumentation process. The purpose of the study is to investigate types of global argumentation structures that emerged while prospective middle school mathematics…

Many mathematics educators believe a goal of instruction is for students to obtain conviction and certainty in mathematical statements using the same types of evidence that mathematicians do. However, few empirical studies have examined how mathematicians use proofs to obtain conviction and certainty. We report on a study in which 16 advanced…

The motion equations of a body under gravity and resistance linearly dependent on speed are usually analysed by solving differential equations. In this paper we report a derivation not explicitly involving differential equations but instead based on some elementary mathematical operations. The derivation uses only knowledge covered in a typical…

The aim of this study is to investigate the change of prospective mathematics teachers' pedagogical content knowledge (PCK) on the linear equation and slope subject based on the lesson plan development and implementation process based on the 4MAT model. The concept of PCK was discussed in three components as content knowledge, knowledge of student…

In this paper, the construct of 'uncertainty' in professional mathematics is investigated in relation to mathematical creativity. Specific focus is on 'Big C' research mathematicians' conceptions of what uncertainty means and ways in which it influences their research. Based on the hypothesis that uncertainty is both a catalyst and a necessary…

This study explores narratives about critical moments in mathematics learning written by K-8 pre-service teachers' (PSTs) in the United States over a 20-year period. These critical moments, such as a single memorable task, course, test, or comment from a teacher, had a powerful and sustained impact on PSTs' mathematics identities, which they…

To increase possibilities for listening respectfully to Indigenous educators, there is a need to identify conversational prompts which are used to raise alternative views of social justice about mathematics education for Indigenous students. Using Nancy Fraser's description of abnormal social justice, an analysis was made of transcripts from round…

Students exhibiting mature number sense make sense of numbers and operations, use reasoning to notice patterns, and flexibly select the most effective and efficient problem-solving strategies (McIntosh et al., 1997; Reys et al., 1999; Yang, 2005). Despite being highlighted in national standards and policy documents (CCSS, 2010; NCTM, 2000, 2014),…

Noticing is often dependent on time-sensitivity and uses video or live observations. This paper explores loosening the time-sensitivity component and implementing self-narrative and inquiry approaches by having teachers write to explore noticing. This study explores narrative writing of beginning mathematics teachers using a noticing framework as…

Promoting positive student attitudes towards stochastics has become a core goal of statistics education reform, and we argue that this starts with the teachers during their teacher preparation program. Building on previous work assessing teachers' attitudes, we focus on how pre-service teacher attitudes vary across different dimensions, and how…

Mathematics teachers may at times take on the role of counselors to address the "math anxious" in their classrooms. Today math anxiety is real and is a factor in attracting young people to many STEM fields. By the time many young people reach middle school, they have developed certain dispositions toward mathematics. What strategies will…

In this article, I argue that the common practice across many school mathematics curricula of using a variety of different representations of number may diminish the coherence of mathematics for students. Instead, I advocate prioritising a single representation of number (the number line) and applying this repeatedly across diverse content areas.…

In mathematics education research, proofs are often conceptualized as sequences of mathematical assertions. We argue that this ignores proofs that contain instructions to perform mathematical actions, often in the form of imperatives, which are common both in mathematical practice and in undergraduate mathematics textbooks. We consider in detail a…

It is well known that students benefit from opportunities to interpret and create different representations (e.g., diagrams, graphs, tables, symbols) of mathematical ideas. Employing Marton's Variation theory as a lens, I argue for an expansion of the use of multiple representations in task design for graphs: Incorporate two different forms of the…

The process of constructing knowledge in mathematics education is critical in developing it as a discipline with an impact on the field of teaching, learning, and assessment based on theory and practice. How do mathematics educators perceive the processes of knowledge construction in mathematics education? It may have an implication in the methods…