This case study describes a Q methodology study which captured and analyzed the viewpoints of 45 UK teachers online. The teachers might liken their participation in the study to a "card sort" activity: their relative placement of statement cards revealed their opinions of mastery in mathematics. Factor analysis of the completed sorts…

This paper seeks to identify significant trends in mathematics curricula and teaching approaches in two education systems: the United States (a highly decentralised education system) and England (a highly centralised education system), with focus on 16-to-19-year-olds. The paper adopts a two-fold perspective: an historical overview, and comparison…

Understanding a Bayesian perspective demands comfort with conditional probability and with probabilities that appear to change as we acquire additional information. This paper suggests a simple context in conditional probability that helps develop the understanding students would need for a successful introduction to Bayesian reasoning.

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…

Based on data from a series of teaching experiments on standard tools of mathematical logic, this paper characterizes a range of student meanings for mathematical properties and logical connectives. Some observed meanings inhibited students' adoption of logical structure, while others greatly facilitated it. "Reasoning with predicates"…

This article provides results from a study examining the impact of a self-regulated strategy development (SRSD) intervention on the fraction calculations of three Grade 5 male students with or at-risk for emotional or behavioral disorders using a multiple-baseline across students, single-case design. The teacher-led SRSD Fractions intervention…

In our technological age, many technologies and real-world objects communicate with each other or partly merge. However, this combination of technologies and real-world objects has not yet found its way into everyday teaching practices in schools to any great extent. To investigate the possibilities of combining technologies and real-world objects…

This study examined the development of prospective teachers' (PTs) understanding of productive struggle using video episodes which PTs analyzed through the lens of professional teacher noticing. Our qualitative study included 66 PTs in four sections of a semester-long mathematics content course for prospective elementary and middle school teachers…

Fermi problems are useful for introducing modelling in primary school classrooms, although teachers' difficulties in problem solving may hinder their successful implementation. These difficulties are associated with the modelling process, but also with the estimation and measurement skills required by Fermi problems. In this work, a specific…

In 2020, Germany and Spain experienced lockdowns of their school systems. This resulted in a new challenge for learners and teachers: lessons moved from the classroom to the children's homes. Therefore, teachers had to set rules, implement procedures and make didactical-methodical decisions regarding how to handle this new situation. In this…

Using data from 82 classroom observations conducted in a large urban school district, we explore how kindergartners spend their time in general and across schools serving children from lower and higher income households. Consistent with prior research, we find that kindergartners spend the majority of instructional time on reading and mathematics,…

Students' contributions that are not yet mathematically complete, precise, or correct are crucial for learning through classroom discussions. We aim to support teacher candidates (TCs) to see students' ideas as evidence of sensemaking and to respond in ways that keep student thinking central to the discussion. Although approximations of practice…

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…

Teacher learning is a huge challenge in instructional change, but relatively little work has carefully examined the mechanisms by which teachers learn, in contrast to the extensive work on programs that help teachers learn and the high-leverage instructional practices that are strong predictors of student learning. Specifically, relatively little…

In this paper, we approach modelling mathematics dispositions from a different methodological perspective in order to shed more light into the complex interplay between teaching practices and students' learning outcomes. We draw on survey data from around 5000 students from Year 7-11 (age 11-16) from 40 Secondary schools in England. Our…