It is commonplace in the educational literature on mathematical practice to argue for a general conclusion from isolated quotations from famous mathematicians. In this paper, we supply a critique of this mode of inference. We review empirical results that show the diversity and instability of mathematicians' opinions on mathematical practice.…

Larry Lesser is a Professor in the Department of Mathematical Sciences at The University of Texas at El Paso. He is also a UTEP Distinguished Teaching Professor whose awards include a 2016 Minnie Stevens Piper Professor Award, the 2012 International Sun Conference Scholarship of Teaching and Learning Award, a 2011 UT System Regents' Outstanding…

In this paper, I wish to reply to the questions posed by Gascón & Nicolás (2017) about the (possibly) prescriptive nature of the research results in didactics of mathematics: To what extent, how, under which conditions can (or must), didactics set value judgments and normative prescriptions in order to provide criteria about how to organize…

In their commentary, "Toward a Framework for Research Linking Equitable Teaching with the Standards for Mathematical Practice," Bartell et al. (2017) provide a stepping-stone into the challenge of clarifying the interface between equity and standards setting in mathematics education by devising a framework that relates the "Common…

In this commentary, the authors explore how mathematics education research and the decisions mathematics education researchers (MERs) make to include (or not) an equity lens are not just choices; rather, they are political acts. MERs must take a hard look at themselves as human beings shaped by the political landscape of their different histories…

In this response paper to Hoyles' contribution "Transforming the mathematical practices of learners and teachers through digital technology" (EJ1200112) focuses on three points. First, more knowledge is needed on why teaching and learning practices should transform, into what will they transform, and by what or by whom will they be…

The secondary-school mathematics curriculum is narrow in scope and technical in character; this is quite different from the nature of the discipline itself. As a result, it offers little inspiration to both students and teachers, and provides students with poor preparation for university mathematics courses and indeed for life. Over the past…

In this commentary, I draw exclusively on the ten papers in this issue of "ZDM" focused on "Mathematical Tasks and the Student." These papers represent various cultural and theoretical stances and when reading them I was looking for common themes across some or all the papers. Based on my readings, I argue that (a) each task…

Sternberg (2017) summarizes the history of identification of giftedness in the 20th century and presents a case for the shortcomings of measures such as IQ for problem-solving skills required in the 21st century. The Active Concerned Citizenship and Ethical Leadership (ACCEL) model is proposed to replace the outdated construct of IQ, particularly…

To an unreconstructed cognitivist with experience of developing General Certificate of Secondary Education (GCSE) examinations and national tests in mathematics, the three papers which provide the core of this special issue (Morgan & Sfard; Morgan, Morgan & Tang) provided a refreshing opportunity to consider examination items from a…

When it comes to improving student achievement in mathematics, a core belief is that curriculum materials are of the utmost importance. However, the link between a curriculum program and student learning is affected by the ways in which teachers use resources to design learning experiences. In the first half of this commentary, I raise questions…

This paper comments on the theoretical formulations and usage of the construct of teacher noticing in a selection of the papers in this special issue of "ZDM Mathematics Education." The analysis of how the notion of teacher noticing is used in the papers suggests that it draws attention to several interdependencies involved that have not…

The NCTM Research Committee identifies key influences on mathematics education that are largely outside the domain of the academic world in which most mathematics education researchers live. The groups that are identified--including the media, companies and foundations, and other academic domains--affect the public's perception of mathematics and…

Mathematics education has benefited from qualitative methodological approaches over the past 40 years across diverse topics. Although the number, type, and quality of qualitative research studies in mathematics education has changed, little is known about how a collective body of qualitative research findings contributes to our understanding of a…

When the author returned to teaching after several years in graduate school, she came armed with knowledge and visions of a student-centered classroom. Her experiences in a doctoral program taught her much about effective mathematics instruction and rekindled her desire to teach. However, a student-centered classroom reflected a major shift in…