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When a classroom environment is designed to foster student sense-making and reasoning, resulting in collective argumentation, the teacher's support for collective argumentation requires adaptive teaching. This paper examines the teacher's adaptive support for argumentation during the teaching of mathematics in a digital environment that simulated a laboratory experiment. The teacher and twenty 15-year-old students engaged in multiple episodes of argumentation during the class. Adaptiveness of instruction is evidenced by the teacher's actions in support of collective argumentation both within and across episodes of argumentation. Within episodes, the kinds of questions and other supportive actions reveal the teacher's focus on adapting instruction with respect to the utterances, gestures, and observations of the students. Across episodes, the teacher's support for collective argumentation differed from the beginning of class to the end as evidenced by the number of questions asked in early episodes of argumentation and the preponderance of repeating actions later in the class session. • A teacher's micro-adaptations revealed by differences in support for argumentation. • Adaptive instruction apparent in responses to students' unexpected answers. • Purpose of arguments important to teacher's different supports for argumentation. [ABSTRACT FROM AUTHOR]

Although the notion of proof is important for all learners' mathematical experiences, there has been limited attention to what it might involve and look like to introduce students and prospective teachers to proof. In this paper we argue for the importance of having a coherent approach to introducing students and prospective teachers to proof, and we discuss the theoretical basis of a learning trajectory relevant to both groups. We also discuss an instructional sequence that aimed to promote the learning trajectory among English secondary students and U.S. prospective elementary teachers, drawing on data from two multi-year design experiments. The learning trajectory comprises two milestones: (1) seeing a need to learn about proof and (2) developing an operationally functional conceptualization of proof. The "need" in milestone 1 entails an aspect of epistemological justification applicable to both students and prospective teachers, and a further aspect of pedagogical justification applicable to prospective teachers. • It is unclear what it might involve and look like to introduce learners to proof. • A learning trajectory is proposed and its theoretical basis discussed. • The learning trajectory is applicable to both students and prospective teachers. • An instructional sequence was designed to promote the learning trajectory. • Data from two design experiments support the promise of the instructional sequence. [ABSTRACT FROM AUTHOR]

The Trends in International Mathematics and Science Study (TIMSS) is an influential mathematics and science assessment administered at fourth and eighth grades in around 60 countries across the world. Under current practices, TIMSS does not support claims about teachers unless the inference is drawn as a student characteristic ("Half of the eighth graders in the country have mathematics teachers with Master's degrees."). With this in mind, this paper proposes and tests through a simulation study two methods that would allow for teacher-centric inferences ("More than half of the eighth-grade mathematics teachers have Master's degrees.") if links between sampled teachers and the unsampled yet eligible classes were known. The first method posits that with such links inverse-probability weights could be calculated, and the second method, the Multiplicity-Adjusted Indirect Sampling (MAIS) approach, posits that teacher estimates could be obtained by adjusting downward the classroom weights based on these links. • Discusses teacher reporting in Trends in International Mathematics and Science Study. • One method creates and implements inverse-probability weights for teachers. • Another method reweights the class weights for each teacher. • A simulation study shows that both methods produce unbiased results. • Both methods would require collecting data on teachers' links to unsampled classes. [ABSTRACT FROM AUTHOR]

In this paper, we trace how mathematical models are made 'evidence enough' and 'useful for policy'. Working with the interview accounts of mathematical modellers and other scientists engaged in the UK Covid-19 response, we focus on two weeks in March 2020 prior to the announcement of an unprecedented national lockdown. A key thread in our analysis is how pandemics are made 'big'. We follow the work of one particular device, that of modelled 'doubling-time'. By following how modelled doubling-time entangles in its assemblage of evidence-making, we draw attention to multiple actors, including beyond models and metrics, which affect how evidence is performed in relation to the scale of epidemic and its policy response. We draw attention to: policy; Government scientific advice infrastructure; time; uncertainty; and leaps of faith. The 'bigness' of the pandemic, and its evidencing, is situated in social and affective practices, in which uncertainty and dis-ease are inseparable from calculus. This materialises modelling in policy as an 'uncomfortable science'. We argue that situational fit in-the-moment is at least as important as empirical fit when attending to what models perform in policy. • Pandemics are performed as crises of uncertain yet catastrophic potential. • Mathematical models are forms of scalar narrative affording epidemics their scale. • Models and projections are made useful as evidence in their situated policy events. • Calculations are given agency as affects in the evidencing of pandemics. • Modelling pandemics is a site of 'uncomfortable science' and 'dis-ease'. [ABSTRACT FROM AUTHOR]

In [Anal. Math. Phys., 8 (2018), 77-83], we have obtained two main theorems dealing with the | N ¯ , p n | k summability factors of infinite series and trigonometric Fourier series. In this paper, we have generalized these theorems for the | N ¯ , p n ; θ n | k summability methods. We have also obtained some new and known results for certain absolute summability methods. [ABSTRACT FROM AUTHOR]

This study examined the mediating roles of mathematics anxiety and learning interest between problematic smartphone use and mathematics achievement. After two-stage stratified sampling, 30,601 Chinese fourth-graders participated by completing a paper-based test on mathematics achievement and an online questionnaire that included questions on demographic information as well as the problematic smartphone use, mathematics anxiety, and mathematics learning interest scales. The results showed that (1) smartphone use was more problematic among boys than among girls, and students with a low SES tended to be more problematic smartphone users, (2) problematic smartphone use was negatively correlated with mathematics achievement, (3) mathematics anxiety and learning interest partially mediated the relationship between problematic smartphone use and mathematics achievement, and (4) the relationship between problematic smartphone use and mathematics achievement was serially mediated by mathematics anxiety and then mathematics learning interest. The implications of this study and suggestions for future research are discussed. • This study examines the relation between PSU by pupils and math achievement. • The mediating roles of math anxiety and learning interest are also investigated. • PSU was negatively correlated with mathematics achievement. • Math anxiety and learning interest played partially mediating roles respectively. • Math anxiety and then learning interest also played serially mediating roles. [ABSTRACT FROM AUTHOR]

This paper tests whether barely obtaining a pass score in at least one of two midterm tests has an effect on subsequent achievement in a Math course. To estimate the effect, we created a novel dataset by linking administrative and survey data on students at a medium size Spanish university and used a regression discontinuity design in which the cutoff is 5, i.e., the pass score in the national grading system. Although obtaining a score just equal to or barely greater than 5 in midterm tests has no immediate consequence for students, it may have a psychological effect by acting as a (de)motivating signal to study and pass the course, with the sign of the effect being unclear ex-ante. We find that obtaining a pass score in at least one midterm has a positive effect on the final exam score. The result seems to be explained by higher students' motivation when jointly accounting for their effort. Overall, our results suggest that partly unexplored psychological mechanisms may help us deepen our understanding of the determinants of achievement in higher education. [ABSTRACT FROM AUTHOR]

In Proposition 1 in the above paper μ 3 ≤ μ 2 should be replaced by μ 3 ≥ μ 2 . [ABSTRACT FROM AUTHOR]

• Novice facilitators' changes in practices in two different countries are examined. • Despite the different contexts, changes in practices are found to be similar. • Practices are linked to facilitators' resources, orientations, goals and identity. • Managing mathematics teachers' PD discussions can be learned and developed. • Recommendations for supporting novice facilitators of are presented. Novice facilitators of professional development (PD) programs for mathematics teachers often face challenges in leading productive discussions and achieving the goals of these programs. Although research in this area is gradually accumulating, not much is known about how novice facilitators address these challenges and change their practices accordingly. This paper presents case studies of two novice facilitators of PD programs in two different countries. The analyses look at their work over one year, to illustrate the changes in their practices while managing discussions. The results show that although the facilitators operated in different contexts, their practices and their processes of change resembled, suggesting that these processes are not idiosyncratic. We argue that novice facilitators' changes in practices correspond to changes in their resources, orientations, goals, and identities and that PD program teams can support these changes. [ABSTRACT FROM AUTHOR]

• We weight the complete multipartite graphs. • We compute the resistance distances of the vertex-weighted complete multipartite graphs. • We generalize the Gervacio's result on the resistance distances of the complete multipartite graphs. Let G be a vertex-weighted complete multipartite graph with vertex set V and edge set E , and vertex-weighted function ω : V → R +. This results in an edge-weighted network graph in which the weight (resistance) of every edge (u , v) ∈ E equals ω (u) ω (v). Gervacio (Discrete Appl. Math. 203 (2016) 53–61) derived the formula to compute the resistance distances between two vertices of the complete multipartite graph where each vertex has a weight of 1. In this paper, we generalize the Gervacio's result and obtain the formula to compute the resistance distance between any two vertices in the vertex-weighted complete multipartite network graph. [ABSTRACT FROM AUTHOR]

• A fast contact detection algorithm (FCDA) for ice-ship interaction (ISI) is proposed • The MPI parallelization for 2-D Peridynamic (PD) theory is first introduced • The newly developed ice-ship interaction (ISI) model is effective in predicting ice damage and crack propagation in the icebreaking process • The developed ice-ship interaction (ISI) model is applied to investigate icebreaking effectiveness for two different bow shapes The bow shape is the most critical factor to determine the icebreaking performance of an icebreaker. Mechanism study on the icebreaking process for different bow types is necessary for the initial design of the icebreaker hull form. This paper proposed an ice-ship interaction model based on the meshfree method, Peridynamics, in which the geometric mathematics concept is embedded to detect the contact between material points and ship hull. Furthermore, a fast contact detection algorithm based on Massage Passing Interface (MPI) solver is built to improve the computational efficiency of the developed numerical method. Two typical icebreaker bows, the conventional bow and the unconventional bow, breaking the level ice with constant speed is numerically studied by the above model. The results of the conventional icebreaker bow are compared with the experimental results, which verifies the simulation accuracy of the model developed in the present work. Afterwards, the icebreaking modes and icebreaking loads of two different shapes of icebreaker bows are compared and analysed. The results show that the developed ice-ship interaction model effectively predicts differences of icebreaking processes between different icebreakers, such as ice damage pattern, ice loads, and channel, despite their common point in domain bending failure mode. Moreover, this research significantly improves computational efficiency and provides theoretical guidance for designing the icebreaker bow. [ABSTRACT FROM AUTHOR]

This paper examines the impact of stricter high school math requirements on the likelihood of completing a degree in STEM fields. Exploiting cross-state variation in the timing of math reforms, I find that stricter math curriculum requirements significantly increased the proportion of the college-educated population earning a STEM degree. Within STEM, the increases in degree completion are concentrated in math and science while there is little discernible impact in technology and engineering. Further analysis suggests that high school graduation, college attendance, and overall degree completion are largely unaffected by the implementation of math reforms. Instead, stricter math curriculum requirements appear to have shifted some students away from non-STEM fields into STEM fields. [ABSTRACT FROM AUTHOR]

The main aim of the study is analyzing of pupils' knowledge in mathematics by adaptive neuro fuzzy inference system (ANFIS) after implementation of distance learning application or e-learning (electronic learning). Since a large number of faculties and other institutions are increasingly using e-learning, it can be stated that for this purpose the Modular object-oriented dynamic learning environment (Moodle) learning management system (LMS) is mostly used. This paper deals with the analysis of distance learning and the application of Moodle LMS in higher education institutions, taking into account the impact of such education on the quality of teaching and the acquisition of knowledge by students, and the methods teachers use in Serbia. The ANFIS is used to determine which factors are the most important for pupils' performance in mathematics. The results show that the main influence on the pupils' performance is their prior knowledge. The prior knowledge is more effective when it is combined with education software in the lectures of mathematics in elementary school. In secondary school, the prior knowledge is more effective if it is combined with motivation for learning mathematics. [ABSTRACT FROM AUTHOR]

This paper discusses, from a mathematician's point of view, the thesis formulated by Israel Gelfand, one of the greatest mathematicians of the 20th century, and one of the pioneers of mathematical biology, about the unreasonable ineffectiveness of mathematics in biology as compared with the obvious success of mathematics in physics. The author discusses the limitations of the mainstream mathematics of today when it is used in biology. He suggests that some emerging directions in mathematics have potential to enhance the role of mathematics in biology. [ABSTRACT FROM AUTHOR]