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In many countries, assessment and curriculum reforms came into being in recent decades. In Iran, an important educational assessment reform took place called Descriptive Assessment (DA). In this reform, the focus of student assessment was moved from a more summative approach of providing grades and deciding about promotion to the next grade to a more formative approach of providing descriptive feedback aimed at improving student learning. In this study, we evaluated how seven fourth-grade mathematics teachers used the principles of DA. Data were collected by a questionnaire on assessment practices and beliefs, lesson observations, and interviews. Although the teachers varied in how they assess their students, in general their assessment practice is by and large in line with the DA guidelines. Nevertheless, in some respects we found differences. When assessing their students, the teachers essentially do not check the students' strategies and when preparing the report cards, they still use final exams because they do not sufficiently trust the assessments methods suggested by DA. The guideline to use assessment results for adapting instruction is also not genuinely put into action. The article is concluded by discussing dilemmas the teachers may encounter when implementing DA.

The balance model is often used for teaching linear equation solving. Little research has investigated the influence of various representations of this model on students' learning outcomes. In this quasi-experimental study, we examined the effects of two learning environments with balance models on primary school students' reasoning related to solving linear equations. The sample comprised 212 fifth-graders. Students' algebraic reasoning was measured four times over the school year; students received lessons in between two of these measurements. Students in Intervention Condition 1 were taught linear equation solving in a learning environment with only pictorial representations of the balance model, while students in Intervention Condition 2 were taught in a learning environment with both physical and pictorial representations of the balance model, which allowed students to manipulate the model. Multi-group latent variable growth curve modelling revealed a significant improvement in algebraic reasoning after students' participation in either of the two intervention conditions, but no significant differences were found between intervention conditions. The findings suggest that the representation of the balance model did not differentially affect students' reasoning. However, analyzing students' reasoning qualitatively revealed that students who worked with the physical balance model more often used representations of the model or advanced algebraic strategies, suggesting that different representations of the balance model might play a different role in individual learning processes.

In this study, we explored the insights that Chinese primary mathematics teachers gained into their students' mathematical understanding from using classroom assessment techniques (CATs). CATs are short teacher-initiated targeted assessment activities proximate to the textbook, which teachers can use in their daily practice to make informed instructional decisions. Twenty-five third-grade teachers participated in a two-week program of implementing eight CATs focusing on the multiplication of two-digit numbers, and filled in feedback forms after using the CATs. When their responses described specific information about their students, emphasized the novelty of the gained information, or referred to a fitting instructional adaptation, and these reactions went together with references to the mathematics content of the CATs, the teachers' responses were considered as evidence of gained insights into their students' mathematics understanding. This was the case for three-quarters of the teachers, but the number of gained insights differed. Five teachers gained insights from five or more CATs, while 14 teachers did so only from three or fewer CATs, and six teachers showed no clear evidence of new insights at all. Despite the differences in levels of gained insights, all the teachers paid more attention to descriptions of students' performance than to possible instructional adaptations.

In a three-phase study, with a total of 40 third-grade teachers and their 830 students, teachers were supported to use classroom assessment techniques (CATs) to reveal their students' knowledge of number operations. In phase I, four teachers and 66 third-grade students participated in five monthly workshops in which CATs were co-designed and their use was discussed. In phase II, the first phase was replicated with four workshops with six different teachers and 148 third-grade students. In these two exploratory phases, we evaluated student achievement on a standardized national mathematics test in a pre-/posttest design and compared changes herein to changes in the national norm sample. In phase III, a control condition was added to the design to experimentally investigate the effect on student achievement with 30 teachers and 616 third-grade students. Teachers were randomly assigned to participate in 0, 1, 2, or 3 1-hour workshops. In all three phases, we found a significant increase in students' mathematics achievement scores on the standardized mathematics test. In phase III, the increase was significantly larger in the classes of teachers participating in three workshops than in classes with less workshops. Additionally, results from the analysis of classroom observations, feedback forms, and interviews indicate that teachers could easily integrate the CATs into their practice and could gather valuable information on their students. The results from the different phases of this study combined indicate that supporting teachers in their development and use of classroom assessment in mathematics may contribute to the improvement of students' mathematics achievement.

In this study we investigated the structure of quantitative competence of kindergartners by testing a hypothesized four-factor model of quantitative competence consisting of the components counting, subitizing, additive reasoning and multiplicative reasoning. Data were collected from kindergartners in the Netherlands (n = 334) and in Cyprus (n = 304). A confirmatory factor analysis showed that the four-factor structure fitted the empirical data from the Netherlands. For the Cyprus data a one-factor structure was found to have a more adequate fit. Regarding the effect of country on performance, a comparison at item level showed that the kindergartners in the Netherlands outperformed those in Cyprus in the majority of quantitative competence items. Analyses of variance revealed for each country a significant effect of kindergarten year on performance, with children in K2 (second kindergarten year) outperforming those in K1 (first kindergarten year). A statistical implicative analysis at item level revealed that in both countries the relevant implicative chain, showing what successful solving of an item implies for correct solving of another item, reflects by and large the sequential steps mostly followed in teaching kindergartners early number. This sequence starts with counting and subitizing, then continues with additive reasoning and finally multiplicative reasoning. These implicative chains also clearly show that the development of early quantitative competence is not linear. There are many parallel processes and cross-connections between the components of quantitative competence.

This paper reports an overview of contemporary research on early childhood mathematics teaching and learning presented at recent mathematics education research conferences and papers included in the special issue (2020--4) of "ZDM Mathematics Education." The research covers the broad spectrum of educational research focusing on different content and methods in teaching and learning mathematics among the youngest children in the educational systems. Particular focus in this paper is directed to what lessons can be drawn from teaching interventions in early childhood, what facilitates children's mathematical learning and development, and what mathematical key concepts can be observed in children. Together, these themes offer a coherent view of the complexity of researching mathematical teaching and learning in early childhood, but the research also brings this field forward by adding new knowledge that extends our understanding of aspects of mathematics education and research in this area, in the dynamic context of early childhood. This knowledge is important for future research and for the development of educational practices.

Reasoning about graphical representations representing dynamic data (e.g., distance changing over time), including interpreting, creating, changing, combining, and comparing graphs, can be considered a domain-specific operationalization of the general twenty-first century skills of creative, critical thinking and solving problems. This paper addresses the issue of how these 21st century skills of interpreting and creating graphs can be supported in a six-lesson teaching sequence about graphing motion. In this teaching sequence, we focused on the potential of an embodied learning environment to facilitate the development of primary school students' reasoning about motion graphs by having primary school students (9-11 years) 'walk' graphs in front of a motion sensor to generate distance-time graphs. We asked: "How does students' reasoning about graphing motion develop over a six-lesson teaching sequence within an embodied learning environment?" Based on the collected data, we examined changes in students' level of reasoning on graph interpretation and graph construction tasks using a repeated measurement design. Additionally, we present two teaching episodes showing instances of how perceptual-motor experiences during the lessons aided students' reasoning about graphical representations of motion. Results show that students went from iconic understanding towards understanding in which they reasoned based on one or two variables when interpreting and constructing graphical representations of motion events. At these higher levels of reasoning these students showed understanding of modelling motion in line with the intended 21st century skills of generating, refining, and evaluating graphs.

Abstract Background Muscle relaxants are routinely used during anesthesia to facilitate endotracheal intubation and to optimize surgical conditions. However, controversy remains about the required depth of neuromuscular block (NMB) needed for optimal surgical working conditions and how this relates to other outcomes. For instance, a deep neuromuscular block yields superior surgical working conditions compared to a standard NMB in laparoscopic surgery, however, a robust association to other (safety) outcomes has not yet been established. Methods Trial design: an international multicenter randomized controlled double-blind strategy trial. Trial population: 922 patients planned for elective, laparoscopic or robotic, abdominal surgery. Intervention: Patients will be randomized to a deep NMB (post-tetanic count 1–2 twitches) or standard care (single-dose muscle relaxant administration at induction and repeated only if warranted by surgical team). Main trial endpoints: Primary endpoint is the difference in incidence of intraoperative adverse events during laparoscopic surgery graded according to ClassIntra® classification (i.e., ClassIntra® grade ≥ 2) between both groups. Secondary endpoints include the surgical working conditions, 30-day postoperative complications, and patients’ quality of recovery. Discussion This trial was designed to analyze the effect of deep neuromuscular block compared to standard neuromuscular block on intra- and postoperative adverse events in patients undergoing laparoscopic surgery. Trial registration ClinicalTrials.gov NCT04124757 (EURO-RELAX); registration URL: https://clinicaltrials.gov/ct2/show/NCT04124757 , registered on October 11th, 2019.

Embodied learning environments have a substantial share in teaching interventions and research for enhancing learning in science, technology, engineering, and mathematics (STEM) education. In these learning environments, students' bodily experiences are an essential part of the learning activities and hence, of the learning. In this systematic review, we focused on embodied learning environments supporting students' understanding of graphing change in the context of modeling motion. Our goal was to deepen the theoretical understanding of what aspects of these embodied learning environments are important for teaching and learning. We specified four embodied configurations by juxtaposing embodied learning environments on the degree of "bodily involvement" (own and others/objects' motion) and "immediacy" (immediate and non-immediate) resulting in four classes of embodied learning environments. Our review included 44 articles (comprising 62 learning environments) and uncovered eight mediating factors, as described by the authors of the reviewed articles: "real-world context," "multimodality," "linking motion to graph," "multiple representations," "semiotics," "student control," "attention capturing," and "cognitive conflict." Different combinations of mediating factors were identified in each class of embodied learning environments. Additionally, we found that learning environments making use of students' own motion immediately linked to its representation were most effective in terms of learning outcomes. Implications of this review for future research and the design of embodied learning environments are discussed.

This paper reports a systematic literature review of the balance model, an often-used aid to teach linear equations. The purpose of the review was to report "why" such a model is used, "what" types of models are used, and "when" they are used. In total, 34 peer-reviewed journal articles were analyzed, resulting in a comprehensive overview of described rationales for using the balance model, its appearances, situations in which it was used, and the gained learning outcomes. Some trends appeared about how rationales, appearances, situations, and learning outcomes are related. However, a clear pattern could not be identified. Our study shows that this seemingly simple model actually is a rather complex didactic tool of which in-depth knowledge is lacking. Further systematic research is needed for making informed instructional decisions on when and how balance models can be used effectively for teaching linear equation solving.

Introduction: To avoid general anesthesia (GA) and improve postoperative pain management for subcutaneous implantable cardioverter-defibrillator (S-ICD) implantation there is a growing interest for alternative methods. We describe the first experience in the Netherlands of S-ICD implantation under Ultrasound-guided Serratus Anterior Plane Block (US-SAPB). Methods: US-SAPB was performed 1 hour before S-ICD implantation. The two-incision technique was used and a pocket beneath the latissimus dorsi muscle was surgically created. Lidocaine was used to provide anesthesia of the skin. Sedation during defibrillation testing (DFT) was induced by intravenous Propofol. Periprocedural pain experience was monitored using the Numerical Rating Scale for Pain (NRS-Pain). The results were compared with a control group of patients undergoing S-ICD implantation under GA. Results: Forty consecutive patients (29 Male/11 Female, median age 59 years (range 34–84 years), median body mass index 26 (range 17–41) underwent S-ICD implantation; Twenty patients under US-SAPB and twenty under GA. Median procedure time was 42 min. (range 28–60 min.) with no differences between both groups. In both groups implantations went successful and defibrillation was accomplished using 65 J. US-SAPB was successful in 19 of the 20 patients and GA was successful in all cases. Median NRS-Pain in the US-SAPB group was 2 (range 2–6) and in the GA group 4 (range 2–6). In the US-SAPB group 5 patients required additional opioids postoperatively compared to 10 patients in the GA group. Conclusions: S-ICD implantation under US-SAPB is feasible, safe and reduces the need for postoperative opioids significantly. S-ICD implantation under US-SAPB seems a good alternative for GA.

Abstract Background There is increasing evidence for the use of lower insufflation pressures during laparoscopic surgery. Deep neuromuscular blockade allows for a safe reduction in intra-abdominal pressure without compromising the quality of the surgical field. While there is considerable evidence to support superior surgical conditions during deep neuromuscular blockade, there is only a limited amount of studies investigating patient outcomes. Moreover, results are not always consistent between studies and vary between different types of laparoscopic surgery. This study will investigate the effect of low-pressure pneumoperitoneum facilitated by deep NMB on quality of recovery after laparoscopic colorectal surgery. Methods The RECOVER study is a multicenter double-blinded randomized controlled trial consisting of 204 patients who will be randomized in a 1:1 fashion to group A, low-pressure pneumoperitoneum (8 mmHg) facilitated by deep neuromuscular blockade (post tetanic count of 1–2), or group B, normal-pressure pneumoperitoneum (12 mmHg) with moderate neuromuscular blockade (train-of-four response of 1–2). The primary outcome is quality of recovery on postoperative day 1, quantified by the Quality of Recovery-40 questionnaire. Discussion Few studies have investigated the effect of lower insufflation pressures facilitated by deep neuromuscular blockade on patient outcomes after laparoscopic colorectal procedures. This study will identify whether low pressure pneumoperitoneum and deep neuromuscular blockade will enhance recovery after colorectal laparoscopic surgery and, moreover, if this could be a valuable addition to the Enhanced Recovery After Surgery guidelines. Trial registration EudraCT 2018-001485-42 . Registered on April 9, 2018. Clinicaltrials.gov NCT03608436 . Registered on July 30, 2018.

This study investigated Chinese primary school mathematics teachers' views on assessment in an effort to determine their assessment profiles. A large-scale questionnaire survey with 1101 teachers from 12 Chinese provinces and regions was carried out. The teachers reported to use assessment on a daily or weekly basis for different purposes. They recognized the importance of assessing different types of skills and knowledge and considered assessment useful for improving teaching and learning. To determine teachers' assessment profiles, we used several latent variable modeling techniques. With exploratory factor analyses, we identified eight factors in the teachers' responses: general instructional decision-making assessment purposes [1], specific instructional decision-making assessment purposes [2], assessment methods [3], diversity of assessment problem format [4], importance of assessing skills and knowledge [5], importance of assessing extra-curricular skills [6], Perceived usefulness [7], and acceptance of assessment [8]. When these factors were used to interpret the results of a latent class analysis, three distinct assessment profiles could be distinguished. One fifth of the teachers were in the "Enthusiastic assessors" profile. These teachers not only reported to use assessment frequently [3, 4] and purposefully [1, 2], but also highly endorsed its importance [5, 6] and usefulness [7, 8]. Around half of the teachers were in the "Mainstream assessors" profile; these teachers scored close to the mean on all factors. The remaining teachers held the relatively negative views on assessment and were therefore in the "Unenthusiastic assessors" profile. This profile characterization sheds light on Chinese primary school mathematics teachers' assessment culture.

In the Netherlands, mathematics textbooks are a decisive influence on the enacted curriculum. About a decade ago, Dutch primary school mathematics textbooks provided hardly any opportunities to learn problem solving. In this study we investigated whether this provision has changed. In order to do so, we carried out a textbook analysis in which we established to what degree current textbooks provide non-routine problem-solving tasks for which students do not immediately have a particular solution strategy at their disposal. We also analyzed to what degree textbooks provide 'gray-area' tasks, which are not really non-routine problems, but are also not straightforwardly solvable. In addition, we inventoried other ways in which present textbooks facilitate the opportunity to learn problem solving. Finally, we researched how inclusive these textbooks are with respect to offering opportunities to learn problem solving for students with varying mathematical abilities. The results of our study show that the opportunities that the currently most widely used Dutch textbooks offer to learn problem solving are very limited, and these opportunities are mainly offered in materials meant for more able students. In this regard, Dutch mainstream textbooks have not changed compared to the situation a decade ago. A textbook that is the Dutch edition of a Singapore mathematics textbook stands out in offering the highest number of problem-solving tasks, and in offering these in the materials meant for all students. However, in the ways this textbook facilitates the opportunity to learn problem solving, sometimes a tension occurs concerning the creative character of genuine problem solving.

This article discusses students' perceptions as a source for understanding education. It addresses what didactically experienced children, called "didactikids", taught us about the empty number line as a didactical model for teaching whole number calculations. The article mainly reports on a student consultancy study carried out in the Netherlands. The findings are similar to what was revealed in an Australian study. Both studies explain what can go wrong when the number line is applied rigidly and wrongly implemented. (Contains 3 footnotes and 14 figures.)

Abstract This paper reports a systematic literature review of the balance model, an often-used aid to teach linear equations. The purpose of the review was to report why such a model is used, what types of models are used, and when they are used. In total, 34 peer-reviewed journal articles were analyzed, resulting in a comprehensive overview of described rationales for using the balance model, its appearances, situations in which it was used, and the gained learning outcomes. Some trends appeared about how rationales, appearances, situations, and learning outcomes are related. However, a clear pattern could not be identified. Our study shows that this seemingly simple model actually is a rather complex didactic tool of which in-depth knowledge is lacking. Further systematic research is needed for making informed instructional decisions on when and how balance models can be used effectively for teaching linear equation solving.

The importance of laying a foundation for algebraic reasoning at a young age is increasingly being emphasized. In this article, the authors report on an activity that elicits in a natural way algebraic strategies that in a later stage of learning algebra are crucial for solving equations. The activity brings about the students' spontaneous use of symbolic notations. It also makes students' reasoning visible both to themselves and to their teacher and helps build students' conceptual understanding and foster productive classroom discussion. This activity involves the work of students aged 11-12, using a hanging mobile as a balance model representing an equation with unknowns.

ABSTRACT: In this study, we aimed to gain further knowledge about Brazilian primary school teachers' assessment practices and beliefs in mathematics education. For this, we carried out an analysis of curriculum documents and reviewed recent research literature on assessment in Brazil, permitting us to answer the following research question: How are the mathematics assessment practices and teachers' beliefs, as revealed in recent research, and how are these related to the conceptualization of assessment in Brazilian mathematics curriculum documents? We found that teachers' assessment practices, as described in the reviewed research between 2010 and 2017, did, in general, not reflect the conceptualization of assessment in the curriculum documents. Furthermore, despite that the beliefs of most teachers on assessment reflected it to be a process to improve teaching and learning, their mathematics assessment practices did not favor assessment for learning. Still, they were mostly used as an instrument to determine students' classification. We recommend a public policy in which teachers are offered opportunities for professional development, focusing on formative assessment in mathematics education.