The COVID-19 pandemic revealed that many countries have failed to provide the general population with the cognitive tools to thoroughly understand and cope with a global health crisis. While scientists and leaders worldwide have struggled to discover ways to contain the spread of the virus, this difficult task has become overwhelming due to the…

Teaching students to reason with data is not a totally new enterprise. A small but insistent statistics education community has been studying the process for decades. This commentary provides an introduction to some major themes of that research, in order to provide common ground for conversations between learning sciences researchers and those…

Recently, Lima lamented on the 'time-consuming and tiresome' pedagogical nature of repeated integration by parts, throwing down the challenge of providing a pencil-and-paper solution to a related problem in a few seconds. Lima put forth a simple formula as an alternative. In this work, I offer a response to Lima's challenge and his formula.…

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…

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.…

This paper will provide several examples of science and mathematics integration: navigation/map-reading, ecology/ecosystems/population growth, and chemistry/molecular structures. This paper underscores integrating STEM subjects with problem-based learning with technology such as video/computer simulations/programming/coding and the dynamic free…

This paper is about the role and the potential of the history of mathematics in mathematics education. We report a discussion that we had about theoretical issues in this context, particularly about the notion of Otherness as developed by the French philosopher Emmanuel Levinas. The focus is on the reading of historical texts, both in the context…

In this position paper we highlight language as a perennial factor contributing to compromised meaning-making in multilingual primary school mathematics classrooms. We note use of the term 'translanguaging' in discussions around mitigating this meaning-making challenge. The paper argues that, while much work remains to be done towards clarifying…

Beginning a teaching career and working to prepare and support beginning teachers is a roller-coaster of successes and puzzling moments. In this article, author Cassandra (Cassie) Seiboldt shares how she learned to manage her first years of teaching by purposefully planning through anticipating student thinking and solutions, and the positive…

These four chapters describe studies of using models for integer addition and subtraction. The models draw principally on the two grounding metaphors of object collection and motion along a path. A strength of all chapters is detailed analysis of how the models are and can be implemented and how they influence student's learning. Together the…

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…

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…

This is a methodological critique of research by the Best Practice in Grouping Students (BPGS) project claiming teacher bias in allocating students to first-year secondary school mathematics teaching sets ("British Educational Research Journal," 45(4), 873-897 [EJ1223692]). The research assumes that bias could be shown by non-random…

How can middle school mathematics teachers navigate their roles as authorities in managing classroom democracies while providing their students with opportunities to exercise their rights? The concept of complementarity (Vithal, 1999) acknowledges that a teacher's authority is not always in conflict with students' rights or agency, but instead a…

Students who are identified as having a disability, according to the Individuals with Disabilities Education Act (IDEA), are guaranteed a Free Appropriate Public Education (FAPE) that provides them access to the general curriculum (IDEA Regulations, 34 C.F.R. § 300.39 [a][3]liil). NCTM and CEC believe that for students with disabilities,…