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Our paper advocates the preparation of future mathematics teachers for the use of game-based learning and gamification technologies. For this purpose, we created a university course that is dedicated to familiarizing the students with basic concepts of game-based learning and gamification and to conveying direct experience with their use. We support the concept and activities in this course by the positive results of the research on the opinions of 115 students. We hope that the positive results and our description of the course will be an inspiration for the broader incorporation of game-based learning and gamification technologies into the training of future mathematics teachers. Limitations of our research are the research sample, we investigated students' reactions only at the author's home university. Therefore, in the future, the research could be done with a broader sample and studying more in detail the students' beliefs related to game-based learning and gamification before and after the course to get a better view of their development. [ABSTRACT FROM AUTHOR]

Northern Norway's population comprises many different cultural groups. According to the Norwegian Education Act, education must give students insight into and a firm foundation in history and culture. This paper aims to present a proposal for how to start working with the creation of local rural mathematics curricula for which Sámi culture in particular, and Northern Norwegian culture in general, is the basis and foundation. It examines three activities that are examples of intangible cultural heritage from different non-urban Northern Norwegian cultures: i) Sámi traditional measuring, ii) fishermen's traditional navigation at sea and iii) ruvden (a Sámi way of braiding). The activities are analysed with respect to the framework cultural symmetry, which was developed in research in Māori mathematics education. The analysis shows that the three activities are of great significance to local cultural reasoning to such an extent that they should be included in local rural mathematics education. Each of the three activities provides opportunities for developing a culture-based mathematics teaching that values the language and culture in which the activities are embedded. We conclude that cultural symmetry seems to function as a tool for developing a Sámi mathematics curriculum. [ABSTRACT FROM AUTHOR]

So far, many ways have been provided to solve Multiple-Criteria Decision-Making(MCDM)problems with interval numbers. Most of these methods rank the alternatives according to two criteria, that is, being close to the Positive Ideal Solution (PIS)and far away from the Negative Ideal Solution(NIS). In this paper, a method is presented for solving MCDM problems with interval numbers, such that being close to PIS and being away from NIS have the same effect in alternative ranking. In the proposed method, the first PIS and NIS are determined as interval numbers and distance of each alternative from PIS and NIS is calculated by extension of Euclidean distance. Then, a compromise index is de ned to rank the alternatives. Three numerical examples are given to compare the proposed method with other methods presented in the literature. [ABSTRACT FROM AUTHOR]

The research reported in this paper analyses teaching dilemmas experienced by four in-service teachers in the context of a reform-oriented teaching approach for primary mathematics called Developmental Education in Mathematics (DEM). The findings exemplify three teaching dilemmas: Whether to tell students how to solve a challenging task; what to do when students are bored with an important task; and trying to keep the pace of the lesson while supporting all students in the classroom. Importantly, the origins of these dilemmas were found to lie in internal tensions between the components of the DEM system, which the teachers had implemented. Finally, the implications for development of curricular material, implementation of reform-oriented teaching approaches, and the professional development of teachers are discussed. [ABSTRACT FROM AUTHOR]

Researchers have been paying attention to the convergence of technologies for it can result in improving human behaviour, including student's learning and teacher's instruction. The present paper intends to describe the different types of convergence of technologies in the classroom in general and the mathematics classroom in particular, focusing on the convergence of two types of them: convergence of the learner with the technological tools and convergence of the teacher with those tools. This focus is concerned with two instrumental frameworks: the instrumental genesis and the instrumental orchestration. The paper discusses the foundations of these two theoretical frameworks, the components of the frameworks and their educational uses as tools for analysing learners' and teachers' convergences with technological tools. Researchers assert that the two frameworks have contributed to the understanding of convergence of the learner and the teacher with technological tools, pointing, at the same time, at the need to extend these frameworks or combine them with other frameworks in order to understand the different aspects of this convergence. [ABSTRACT FROM AUTHOR]

In this paper, we investigate adolescent students' ethical mathematics awareness as they reason through interview tasks that provoke them to make a decision based upon the results of data analytics. Drawing on multiple resources, including ethical principles from numerous STEM and business disciplines, we introduce an analytic framework for documenting the ethical mathematics awareness of adolescent students. Our findings indicate that 1) students justify their decision using a variety of ethical principles, and 2) half the students' decisions benefitted their hypothetical employer and half protected society. We conclude the paper with a discussion of implications for designing future instruction to support students' growth in ethical mathematics awareness. [ABSTRACT FROM AUTHOR]

The research described in this paper addresses the question of how school mathematics and mathematics teacher education can be reframed through critical and culturally responsive pedagogies. By analysing the perspectives offered through the research fields of Ethnomathematics (EM), Critical Mathematics (CM), Indigenous Education (IE), Language Diversity (LD) and Equity-based (E-b) approaches, the research works toward a new (disruptive) form of culturally responsive pedagogy (CRdP). As discussed here, CRdP is pedagogically informed by the EM-CM-IE-LD-E-b collective; it is theoretically informed by Nancy Fraser's three-dimensional approach to social justice and participatory parity; and it is methodologically informed by discourse analysis. That is, this paper explores the methodological innovation involved in operationalizing a form of discourse analysis which draws on Nancy Fraser's three-dimensional framework for social justice (distribution, recognition, and representation) to create a Fraser-framed lens through which to view scholarly texts in mathematics/teacher education. While the research is motivated by pedagogical concerns, and on tracing the dialogue between theory/methodology and practice/pedagogy, these concerns are located in the social, political, cultural, and economic insights that the pedagogic actions of CRdP offer to the fields of mathematics (and) teacher education. [ABSTRACT FROM AUTHOR]

Science teaching relies heavily on visual illustrations and visually organized assignments as methods of teaching and proving concepts like the Pythagorean theorem. As Visually Impaired Persons (VIPs) cannot see, they derive no benefit from the use of such illustrations alone. Often, material objects are used to help VIPs understand mathematical concepts by means of tactile and haptic perception. In this paper, I will show the practices employed in the pursuit of transforming a visually available material object into something of specific scientific relevance for tactile and haptic exploration. This article thus emphasizes the matter – in the original sense of materiality – of math. Based on video-recorded data, this paper provides an in-depth interactional analysis of a single case in which a VIP engages in a mathematics learning situation with an assistant. This research is based on and contributes to ethnomethodology and conversation analysis by critically examining how objects are used to teach VIPs in math classes. The research has implications for a broadened understanding of how learning mathematics is not just a matter of logics, verbal descriptions or the visual analysis of charts and diagrams, but can also inherently involve the tangible materiality of mathematical representations. [ABSTRACT FROM AUTHOR]

One essential goal of mathematics teaching is to develop the habit of mind and the ability to look for and recognize structures, to probe into and act upon structures, and to reason and justify in terms of general structures. Framed by the five practices for orchestrating productive mathematics discussions (Smith & Stein, 2011), this paper uses the Horse Rider problem as an example to illustrate how teachers can nurture student structural thinking through careful sequencing of mathematical tasks. [ABSTRACT FROM AUTHOR]

Language is organic, innate and ubiquitous. It is the skill that connects everything. Humans try to explore and express themselves through language. The nature and components of language have been humans' preoccupation for a long time. As a corollary, mathematics is also a medium through which humans try to make sense of their world and also express themselves. Humans have remained fascinated by the shapes in nature, and they constantly try to explore and express the world in mathematics. I think that both language and mathematics are inherent behaviors that humans possess and exhibit. As I tried to learn mathematics, I was inevitably struck by the features that overlap and run parallel in both the subjects - mathematics and language. This paper is more about my little understanding of both the subjects. [ABSTRACT FROM AUTHOR]

In response to urgent calls for teaching that is culturally affirming, scholars have developed a myriad of images of culturally sustaining (and related) pedagogies (CSPs). However, for maths teachers, CSPs remain elusive, in part because these images are typically content-neutral and their applicability to practice opaque. In this paper, I synthesize research to help conceptualize and clarify what CSPs may look like specifically in mathematics classrooms. I offer a framework for CSPs in mathematics comprised of four dimensions: (1) anti-assimilationism, (2) strengths-based teaching, (3) power and justice, and (4) affirming identities. [ABSTRACT FROM AUTHOR]

Copyright of MAT-KOL (Banja Luka), Matematicki Kolokvijum is the property of Scientific Society of Mathematicians Banja Luka and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this research paper, we will analyze the mathematics curriculum for the II class of high school, comparing the learning outcomes according to Bloom's (Benjamin Bloom) taxonomy and the lesson fund according to educational outcomes, evaluation criteria, forms of monitoring and checking, as well as the application of van Hiele's (Dina van Hiele-Geldof and Pierre van Hiele) theories about learning geometry. [ABSTRACT FROM AUTHOR]

The importance of computational thinking (CT) as a 21st-century skill for future generations has been a key consideration in the reforms of many national and regional educational systems. Much attention has been paid to integrating CT into the traditional subject classrooms. This paper describes a scoping review of learning tools for integrating CT and mathematics in current empirical studies published from 2015 to 2021. The review showed that most of the studies implemented CT-intensive Math-connected integration. Five major types of CT tools had been identified, i.e., digital tangibles, apps and games, programming languages, formative or summative assessments, and other technological tools. In many instances, the tools also provide functions of assessment of CT skills. The most assessed CT competencies were including algorithms and algorithmic thinking, abstraction, testing and debugging, loops, and sequences. Geometry and Measurement was the most assessed mathematics topic. Our scoping review is beneficial in the investigation of the literature on CT and mathematics education, as well as guides those who are interested in developing curriculum, programs, or assessments that involve the integration of CT and mathematics. [ABSTRACT FROM AUTHOR]

With the shift to next generation digital assessments, increased attention has focused on Technology-Enhanced Assessments and Items (TEIs). This study evaluated the feasibility of a high-fidelity digital assessment item response format, which allows students to solve mathematics questions on a tablet using a digital pen. This digital ink approach allows students to hand write their responses while showing their work in a digital format. Responses obtained using the digital pen were compared to both paper- and type-written response formats in a repeated measures design. Results showed that students liked the digital pen format and preferred it to the type-written format, but continued to rank the paper format as their first preference. Statistical comparisons showed no significant differences in student performance across response modalities, but means fell in the predicted order favoring digital pen over keyboard for the digital response formats. Results are discussed in light of software usability, technical issues during data collection, and statistical power for detecting effects in the study. [ABSTRACT FROM AUTHOR]

Airy and Bessel functions are one of the most popular and important special functions in various branches of physics, mathematics, and engineering. An observation to their behavior for the real argument suggest that they are related. This relation was studied earlier, but were accompanied by a number of assumptions, approximations, and sometimes even misconceptions. This motivated us to develop a fresh and transparent method to establish these relations. As the continuation of our study of the two papers published in resonance already, here we have used the general asymptotic series and the convergent series of these functions and thereby developed two new methods which throw light on the subtle interrelationships between these functions. Numerical evidences of our claims are provided for better clarity and understanding. [ABSTRACT FROM AUTHOR]

Mathematics education is seen as a right for all children, and important to ensure a prosperous future. However, in Australia and other nations, rural students and students from low socioeconomic backgrounds both perform less well in mathematics and are less likely to pursue advanced mathematics. This paper presents a case study of a low socioeconomic status, rural government school that has high engagement and achievement in senior mathematics, despite its setting. The study uses a conceptual framework informed by Appreciative Inquiry and the theory of Practice Architectures to explore the activities and facilitatory elements that have likely contributed to the school's mathematics success. Rather than being attributed to one or two key programmes, the school's mathematics success seemed associated with a collection of whole-school factors. Setting high expectations while providing proactive learning support, differentiating instruction, emphasising the value of mathematics, linking mathematics to careers, and building mathematics teacher capacity were all associated with the school's higher than expected mathematics performance. Rather than hindering the school's mathematics programme, its small size and rural context were used to enable practices that contributed to mathematics success. [ABSTRACT FROM AUTHOR]

Integral Calculus II is a second-year undergraduate course offered by the Department of Pure and Applied Mathematics at Maseno University. It is one of the 20 foundational courses with a high enrolment of about 800 students drawn from the school of Mathematics, Education, Science, and Business. Because of the large number of enrollments in these foundational courses, and the small number of teaching staff, instructors face challenges in providing immediate personalized feedback that can guide learning. Systems for Teaching and Assessment which use Computer Algebra Kernerl, STACK, a computer-aided assessment plug-in that provides a sophisticated assessment in mathematics-related disciplines, was used to deploy Continuous Assessment Tests (CAT) in the course for 370 students. This paper reports on the findings of the course based on a comparison between student test scores in STACK and in the final course exam. [ABSTRACT FROM AUTHOR]

Understanding the students' perception of STACK tasks is vital for optimizing the students' learning. Questionnaires are a common method to learn about their experiences, but they are time-consuming for teachers and students. Plus, they are usually answered with a certain delay after students have completed the task. To solve these problems, we developed STACKrate, a JavaScript-based tool that allows teachers to easily integrate a collection of evaluation questions directly into STACK questions. Thus, the evaluation is done directly after the students completed their work on the tasks. The tool uses a star rating principle and is designed to be intuitive and easy to use for students. In this paper, we describe the features and benefits of STACKrate and tell about the use of the tool in a course at Ruhr-Universität Bochum, Germany. We then discuss the added value of STACKrate in evaluation over the use of questionnaires alone. [ABSTRACT FROM AUTHOR]

Students' mathematics learning ability should always be assessed, predicted and given appropriate interventions. However, due to lack of exposure and knowledge to mechanisms of neuroscience and Adaptive neuro-fuzzy inference system (ANFIS), both elements are not optimally applied in educational measurement and evaluation settings. Therefore, based on the findings of neuroscience through the AGES model and the ANFIS formulation as well as the mathematics learning model, this paper will discuss the development of a conceptual model for predicting students' neuroscience mechanistic. The significance of this model is to reveal students' mathematical learning ability and analyze the causes of weaknesses or attributes that affect learning. [ABSTRACT FROM AUTHOR]

This practice paper provides a detailed scaffolded layout of how to embed computational thinking concepts into a project-based math methods course. Parallel to completing a project in which the in-service teachers design solutions for math struggles of their P-12 students, the graduate students reflect on their problem-solving activities using computational thinking (CT) terms. This application of CT as a metacognitive reflection tool is new to the field of CT in teacher education. The mechanisms by which this is carried out are think alouds and digital powerups. This paper represents the first study on teachers engaging with CT concepts and co-constructing meaning of these concepts in their own project-based activity in a math methods course. The research questions and data to be gathered are mentioned as the research portion of this study is in progress. However, the model of CT-integration using reflection mechanisms is valuable to teacher educators and course designers and is easily replicable. [ABSTRACT FROM AUTHOR]

Fifty years ago, a small one and a half page paper without a single reference was published in the leading journal Nature. The paper laid out the most general mathematical formulation of natural selection that would work for all kinds of selection processes and under any form of inheritance (not just biological evolution and Mendelian genes), although the paper discussed the issue in a genetical framework. Written by a maverick American expatriate in England, with no prior background of studying evolution or genetics, the paper had initially been turned down by the editor of Nature as too difficult to understand. Largely ignored by the evolutionary biology community till the 1990s, the Price Equation is now widely recognized as an extremely useful conceptualization, permitting the incorporation of non-genetic inheritance into evolutionary models, serving to clarify the relationship between kin-selection and group-selection, unifying varied approaches used in the past to model evolutionary change, and forming the foundation of multi-level selection theory. [ABSTRACT FROM AUTHOR]

In the recent years, as technology grew, so did the chatbot technology. More and more companies and people are using and reaping the benefits from them. This paper shows how a chatbot for mathematical tasks, named mathbot, was developed. The chatbot uses mathematical exercises from the "Schulapps" of the LearningLab of Graz, University of Technology and combines them with textual questions to provide a useful utility for practicing. It is shown that such a chatbot could be useful for pupils and teachers by evaluating a test run in an elementary school. [ABSTRACT FROM AUTHOR]

In multi-agent systems, norm enforcement is a mechanism for steering the behavior of individual agents in order to achieve desired system-level objectives. Due to the dynamics of multi-agent systems, however, it is hard to design norms that guarantee the achievement of the objectives in every operating context. Also, these objectives may change over time, thereby making previously defined norms ineffective. In this paper, we investigate the use of system execution data to automatically synthesise and revise conditional prohibitions with deadlines, a type of norms aimed at prohibiting agents from exhibiting certain patterns of behaviors. We propose DDNR (Data-Driven Norm Revision), a data-driven approach to norm revision that synthesises revised norms with respect to a data set of traces describing the behavior of the agents in the system. We evaluate DDNR using a state-of-the-art, off-the-shelf urban traffic simulator. The results show that DDNR synthesises revised norms that are significantly more accurate than the original norms in distinguishing adequate and inadequate behaviors for the achievement of the system-level objectives. [ABSTRACT FROM AUTHOR]

The LM-cut heuristic, both alone and as part of the operator counting framework, represents one of the most successful heuristics for classical planning. In this paper, we generalize LM-cut and its use in operator counting to optimal numeric planning with simple conditions and simple numeric effects, i.e., linear expressions over numeric state variables and actions that increase or decrease such variables by constant quantities. We introduce a variant of hmaxhbd (a previously proposed numeric hmax heuristic) based on the delete-relaxed version of such planning tasks and show that, although inadmissible by itself, our variant yields a numeric version of the classical LM-cut heuristic which is admissible. We classify the three existing families of heuristics for this class of numeric planning tasks and introduce the LM-cut family, proving dominance or incomparability between all pairs of existing max and LM-cut heuristics for numeric planning with simple conditions. Our extensive empirical evaluation shows that the new LM-cut heuristic, both on its own and as part of the operator counting framework, is the state-of-the-art for this class of numeric planning problem. [ABSTRACT FROM AUTHOR]

Copyright of Paradigma is the property of Universidad Pedagogica Experimental Libertador and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Paradigma is the property of Universidad Pedagogica Experimental Libertador and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Spatial reasoning, recognised as playing a critical role across STEM disciplines, is gaining prominence in mathematics education, not only as fundamental to mathematics, but also as embodied mathematical activity. In this paper, we discuss spatial reasoning and its embodiment in mathematics. We then present a systematic review of the topics as researched and related to deaf and general education from 2010 to 2019. Publication trends during the ten years reveal similarities and differences across both fields. Based on the findings, we share insights, prospects, and provocations for promoting spatial reasoning in mathematics with an emphasis on research and pedagogy for deaf education. [ABSTRACT FROM AUTHOR]

Mathematical structure is central to the interconnectedness of numerical, spatial or logical relationships, but it is not known how well teachers understand this concept or implement it in pedagogical practice. In this paper, we examine three junior secondary mathematics teachers' understanding of mathematical structure and observe whether they apply it in their teaching. Case study data comprised teacher interviews and mathematics lesson observations. Analysis of interviews and teacher-directed communication (utterances) in lessons utilised an emergent framework for categorising mathematical structure: connections to other learning (C), recognising patterns (R), identifying similarities and differences (I) and generalising and reasoning (G). Findings from the interviews indicated that teachers supported the development of mathematical structure, but the interview responses were not generally reinforced by their utterances in mathematics lesson observations. Analysis of teacher utterances revealed superficial understanding and use of mathematical structure although there was some evidence of CRIG components in the teacher-directed communication for individual cases. [ABSTRACT FROM AUTHOR]

In the present paper we would like to share our technology enhanced, interactive and student centric approach applied during our long-lived experience in teaching mathematics and informatics in higher education institutions. Our goal is to develop active-engagement student-centered environment instead of the traditional instructor-centered environment. Our teaching is based on cooperative learning, flipped learning, guided discovery, laboratory approach, simulations and investigations. It is oriented to the application of modern technologies and involves research elements. [ABSTRACT FROM AUTHOR]

In recent decades, plural logic has established itself as a well-respected member of the extensions of first-order classical logic. In the present paper, I draw attention to the fact that among the examples that are commonly given in order to motivate the need for this new logical system, there are some in which the elements of the plurality in question are internally singularized (e.g. 'Whitehead and Russell wrote Principia Mathematica'), while in others they are not (e.g. 'Some philosophers wrote Principia Mathematica'). Then, building on previous work, I point to a subsystem of plural logic in which inferences concerning examples of the first type can be adequately dealt with. I notice that such a subsystem (here called 'discrete plural logic') is in reality a mere variant of first-order logic as standardly formulated, and highlight the fact that it is axiomatizable while full plural logic is not. Finally, I urge that greater attention be paid to discrete plural logic and that discrete plurals are not used in order to motivate the introduction of full-fledged plural logic--or, at least, not without remarking that they can also be adequately dealt with in a considerably simpler system. [ABSTRACT FROM AUTHOR]

The choice of mobile applications (apps) for learning has been heavily relied on customer and teacher reviews, designers' descriptions, and alignment with existing learning and human-computer interaction theories. There is limited empirical evidence to advise on the educational value of mobile apps as these are used by children. Understanding the impact of mobile apps on young children's learning is timely given the lack of evidence-based recommendations that could guide parents and teachers in selecting apps for their children. In this paper, we present the results of a series of Randomised Control Trials (RCTs) with 376 children aged 5 to 6 years old who interacted with two maths apps in three schools in the UK. Pre/post-test comparisons revealed learning gains in both the control and intervention groups, suggesting that the selected applications are equally good to standard maths practice. Implications for the selection and use of mobile apps are discussed. [ABSTRACT FROM AUTHOR]

Factors affecting academic achievement were widely analyzed and compared. This paper studies the effect of some context variables, including Gender, Age and School Resources (namely, General School Resources index ?GSR? and Resources for Mathematics Instruction ?RMI?) on the performance in Mathematics of the Moroccan?s fourth-grade students that participated on the TIMSS 2019 survey. The data collection method uses secondary data from this survey. Two statistical software packages are used (R Core Team, 2017 and SPSS 20) to treat data and apply multilevel modeling. The results of this modeling show that the variance explained at the school level is 39.41 [ABSTRACT FROM AUTHOR]

We provide a detailed description of a purposefully sampled tutoring session during which a student with a learning disability displayed common tendencies we have seen in our work on algebra teaching. The student struggled with solving equations in general and especially with distribution and knowing how to distribute terms and what steps to take in the correct order. The tutor responded by helping the student offload information, gesturing while speaking with the student, and asking questions strategically to both support and challenge the student to think critically. The purpose of this paper is to provide, through a case study, an accessible description for teachers and researchers of how students with learning disabilities interact with algebra and how teachers can support and challenge these students in this context. [ABSTRACT FROM AUTHOR]