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Teachers' emotions while they teach and how these may play out in their students' experience of mathematics lessons is under-researched. Here, we present a proposition for the incorporation of a type of data not typically included in the study of teacher emotions while they teach: physiological data. Specifically, we present our use of a GSR (Galvanic Skin Response) sensor as a tool that offers approximate indications of how teacher emotions vary during lessons. We report from a study in which experienced secondary mathematics teachers were interviewed before and after observation and video recording of their lessons, during which they wore a GSR device. Episodes from the lessons--selected on the evidence provided by the video recordings, the observations, and the GSR sensor--were used to trigger teacher reflection in the postlesson interviews. A particular focus in the interviews was placed on the interplay between how the teachers' emotional intensity varied during the lesson and their teaching actions. The findings show that the use of the GSR sensor revealed aspects of this interplay not evidenced in the other data sources. The findings are presented using evidence from two participants. We propose that the use of GSR data in tandem with other types of data has the capacity to strengthen teacher reflection on how their emotional intensity may vary during a mathematics lesson and the impact of this variation on the lesson. The paper concludes with outlining the benefits for teacher education and professional development of using this unobtrusive yet insight-generating technology as an effective trigger for pedagogical reflection.

This research commentary argues for more research that attends to the processes of organizational change in mathematics departments. It outlines both the ways that research on organizational change can benefit scholarship in mathematics departments, and how mathematics education researchers are needed to develop theories of change that are contextualized to the teaching and learning of undergraduate mathematics. This commentary closes with a research agenda for moving this emergent field of study forward. This agenda involves applying change theories to historical, ongoing, and new change projects in mathematics departments, while simultaneously attending to issues of equity and social justice.

In this paper we present the results from a study in which 21 mathematics trainee teachers engage with two practice-based tasks in which classroom management interferes with mathematical learning. We investigate the trainees' considerations when they make decisions in classroom situations and how these tasks can trigger their reflections on the teaching and learning of mathematics. In our analysis we used the constructs of "Social" and "Sociomathematical norms" (Cobb & Yackel, 1996) and "Teaching Triad" (Jaworski, 1994). Results indicate commendable norms trainees aspire to establish in their classroom, such as peer respect, value of discussion and investigative mathematical learning. However, they often miss the opportunity to engage students with metacognitive discussions and mathematical challenge as they focus on behavioural issues or endorse dichotomous and simplistic views of mathematical learning. We credit these tasks with allowing insight into trainees' considerations and we propose their further implementation in teacher education programmes.

Non-mathematics specialists' competence and confidence in mathematics in their disciplines have been highlighted as in need of improvement. We report from a collaborative, developmental research project which explores the conjecture that greater integration of mathematics and biology in biology study programs, for example through engaging students with Mathematical Modeling (MM) activities, is one way to achieve this improvement. We examine the evolution of 12 first-semester biology students' mathematical discourse as they engage with such activities in four sessions which ran concurrently with their mandatory mathematics course and were taught by a mathematician with extensive experience with MM. The sessions involved brief introductions to different aspects of MM, followed by small-group work on tasks set in biological contexts. Our analyses use the "theory of commognition" to investigate the tensions between "ritualized and exploratory participation" in the students' MM activity. We focus particularly on a quintessential "routine" in MM, "assumption building": we trace attempts which start from ritualized engagement in the shape of "guesswork" and evolve into more productively exploratory formulations. We also identify signs of persistent "commognitive conflict" in the students' activity, both "intra-mathematical" (concerning what is meant by a "math task") and "extra-mathematical" (concerning what constitutes a plausible solution to the tasks in a biological sense). Our analyses show evidence of the fluid interplay between ritualized and exploratory engagement in the students' discursive activity and contribute towards what we see as a much needed distancing from operationalization of the commognitive constructs of ritual and exploration as an unhelpfully dichotomous binary.

Current liquid chromatography-tandem mass spectrometry (LC-MS/MS) applications for circulating androgen measurements are technically diverse. Previously, variable results have been reported for testosterone. Data are scarce for androstenedione and absent for dehydroepiandrosterone sulfate (DHEAS). We assessed the agreement of androstenedione, DHEAS and testosterone LC-MS/MS measurements among nine European centers and explored benefits of calibration system unification. Androgens were measured twice by laboratory-specific procedures in 78 patient samples and in EQA materials. Results were obtained by in-house and external calibration. Intra- and inter-laboratory performances were valued. Intra-laboratory CVs ranged between 4.2–13.2 % for androstenedione, 1.6–10.8 % for DHEAS, and 4.3–8.7 % and 2.6–7.1 % for female and male testosterone, respectively. Bias and trueness in EQA materials were within ±20 %. Median inter-laboratory CV with in-house vs. external calibration were 12.0 vs. 9.6 % for androstenedione (p<0.001), 7.2 vs. 4.9 % for DHEAS (p<0.001), 6.4 vs. 7.6 % for female testosterone (p<0.001) and 6.8 and 7.4 % for male testosterone (p=0.111). Median bias vs. all laboratory median with in-house and external calibration were −13.3 to 20.5 % and −4.9 to 18.7 % for androstenedione, −10.9 to 4.8 % and −3.4 to 3.5 % for DHEAS, −2.7 to 6.5 % and −11.3 to 6.6 % for testosterone in females, and −7.0 to 8.5 % and −7.5 to 11.8 % for testosterone in males, respectively. Methods showed high intra-laboratory precision but variable bias and trueness. Inter-laboratory agreement was remarkably good. Calibration system unification improved agreement in androstenedione and DHEAS, but not in testosterone measurements. Multiple components, such as commutability of calibrators and EQA materials and internal standard choices, likely contribute to inter-laboratory variability. [ABSTRACT FROM AUTHOR]

We examine teachers' use of resources as they prepare to teach the topic of numerical series of real numbers, in order to identify how their "personal relationship" with mathematical content--and its teaching--interacts with their use of a commonly used textbook. We describe this interplay between textbook and personal relationship, a term coined in the Anthropological Theory of the Didactic (ATD, Chevallard, 2003), in terms of "documentation work" ("resources," "aims," "rules of action," "operational invariants"), a key construct from the documentational approach (DA, Gueudet & Trouche, in "Educational Studies in Mathematics," 71, 199-218, 2009). We do so in the case of five post-secondary teachers who use the same textbook as a main resource for teaching the topic. Documentational analysis of interviews with the teachers led to the identification of their aims and rules of action (the "what" and "how" of their resource use as they organise their teaching of the topic) as well as the operational invariants (the "why" for this organisation of their teaching). We describe the teachers' documentation work in two sets of aims/rules of action: scaffolding mathematical content (series as a stepping stone to learning about Taylor polynomials and Maclaurin series), and organising student learning about series through drill exercises, visualisation, examples, and applications. Our bridging (networking) of theoretical constructs originating in one theoretical framework (personal relationship, ATD) with the constructs of a different, yet compatible, framework (documentation work, DA) aims to enrich the latter (teachers' documentation work) with the individual agency (teachers' personal relationships with the topic) provided by the former.

We explore the transition from school to university through a commognitive (Sfard 2008) analysis of twenty-two students' examination scripts from the end of year examination of a first year, year-long module on Sets, Numbers, Proofs and Probability in a UK mathematics department. Our analysis of the scripts relies on a preliminary analysis of the tasks and the lecturers' (also exam setters') assessment practices, and focuses on manifestations of unresolved commognitive conflict in students' engagement with the tasks. Here we note four such manifestations concerning the students' identification of and consistent work with: the appropriate numerical context of the examination tasks; the visual mediators and the rules of school algebra and Set Theory discourses; the visual mediators of the Probability and Set Theory discourses; and, with the visual mediators and rules of the Probability Theory discourse. Our analysis suggests that, despite lecturers' attempts to assist students towards a smooth transition to the different discourses of university mathematics, students' errors at the final examination reveal unresolved commognitive conflicts. A pedagogical implication of our analysis is that a more explicit and systematic presentation of the distinctive differences between these discourses, along with facilitation of the flexible moves between them, is needed.

In this paper, we propose an enriched and extended application of Harel and Sowder's proof schemes taxonomy that can be used as a diagnostic tool for characterizing secondary students' emergent learning of proof and proving. We illustrate this application in the analysis of data collected from 85 Year 9 (age 14-15) secondary students. We capture these students' first encounters with proof and proving in an educational context (mixed ability, state schools in Greece) where mathematical proof is explicitly present in algebra and geometry lessons and where proving skills are typically expected, and rewarded, in key national examinations. We analyze student written responses to six questions, soon after the students had been introduced to proof and we identify evidence of six of the seven proof schemes proposed by Harel and Sowder as well as a further eight combinations of the six. We observed these combinations often within the response of the same student and to the same item. Here, we illustrate the eight combinations and we claim that a dynamic use of the proof schemes taxonomy that encompasses sole and combined proof schemes is a potent theoretical and pedagogical tool for mapping students' multi-faceted and evolving competence in, and appreciation for, proof and proving.

This paper is a commentary on the classroom interventions on the teaching and learning of proof reported in the seven empirical papers in this special issue. The seven papers show potential to enhance student learning in an area of mathematics that is not only notoriously difficult for students to learn and for teachers to teach, but also critically important to knowing and doing mathematics. Although the seven papers, and the intervention studies they report, vary in many ways--student population, content domain, goals and duration of the intervention, and theoretical perspectives, to name a few--they all provide valuable insight into ways in which classroom experiences might be designed to positively influence students' learning to prove. In our commentary, we highlight the contributions and promise of the interventions in terms of whether and how they present capacity to change the classroom culture, the curriculum, or instruction. In doing so, we distinguish between works that aim to enhance students' preparedness for, and competence in, proof and proving and works that explicitly foster appreciation for the need and importance of proof and proving. Finally, we also discuss briefly the interventions along three dimensions: how amenable to scaling up, how practicable for curricular integration, and how capable of producing long-lasting effects these interventions are.

Simple Summary: Cancer patients frequently experience pain, impacting their quality of life. Unfortunately, pain management in those referred for radiotherapy (RT) is often insufficient, with limited research in this area. This study aimed to assess the adequacy and effectiveness of pain management and identify factors affecting them in cancer patients referred for RT. We observed 1042 cancer outpatients and found that 42.9% did not receive adequate pain management. Specifically, 72% of patients referred for palliative RT and 75% of those referred for curative RT experienced inadequate or ineffective analgesic therapy. Patients undergoing palliative RT, those with poorer general health, those with cancer-related pain, and those treated in Northern Italy had higher odds of receiving adequate pain management. Our findings highlight the need for educational and organizational strategies to address this issue and suggest that early palliative RT referral can improve pain management and treatment outcomes for cancer patients. Background: Pain is a prevalent symptom among cancer patients, and its management is crucial for improving their quality of life. However, pain management in cancer patients referred to radiotherapy (RT) departments is often inadequate, and limited research has been conducted on this specific population. This study aimed to assess the adequacy and effectiveness of pain management when patients are referred for RT. Moreover, we explored potential predictors of adequate pain management. Methods: This observational, prospective, multicenter cohort study included cancer patients aged 18 years or older who were referred to RT departments. A pain management assessment was conducted using the Pain Management Index (PMI), calculated by subtracting the pain score from the analgesic score (PMI < 0 indicated inadequate pain management). Univariate and multivariate analyses were performed to identify predictors of adequate pain management. Results: A total of 1042 cancer outpatients were included in the study. The analysis revealed that 42.9% of patients with pain did not receive adequate pain management based on PMI values. Among patients with pain or taking analgesics and referred to palliative or curative RT, 72% and 75% had inadequate or ineffective analgesic therapy, respectively. The odds of receiving adequate pain management (PMI ≥ 0) were higher in patients undergoing palliative RT (OR 2.52; p < 0.001), with worse ECOG-PS scores of 2, 3 and 4 (OR 1.63, 2.23, 5.31, respectively; p: 0.017, 0.002, 0.009, respectively) compared to a score of 1 for those with cancer-related pain (OR 0.38; p < 0.001), and treated in northern Italy compared to central and southern of Italy (OR 0.25, 0.42, respectively; p < 0.001). Conclusions: In this study, a substantial proportion of cancer patients referred to RT departments did not receive adequate pain management. Educational and organizational strategies are necessary to address the inadequate pain management observed in this population. Moreover, increasing the attention paid to non-cancer pain and an earlier referral of patients for palliative RT in the course of the disease may improve pain response and treatment outcomes. [ABSTRACT FROM AUTHOR]