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Paper 1 suggests intuitively that as humans, we must continue to investigate physical Objects by our natural Geometry. At the same time, we may want to explore a Nongeometric tool to check some other aspects. The two positions presume two distinct scopes and two independent Logics, so they are not conflictual, and we should be able to form a single consistent picture (no-strange-things criterion). In Paper 2, we enter the technique of NBM more systematically. The text below comes from a compromise, as we want to make as clear as possible any assumption which hides into the Model. At the same time, we want it to remain a very straight and practical tool, so we formulate it in term of Rules, Procedures, and lists of instructions. [ABSTRACT FROM AUTHOR]

Dyslexia is a type of Specific Learning Disability (SLD) that affects the educational development of a student, as it is the reason of difficulties not only in writing or reading but also in other disciplines like Mathematics. Research has proven that Information and Communication Technologies (ICT) can have a positive effect to the educational development of a dyslexic student. In this paper, twenty 6 th -grade primary-school students were observed while using computers during exams - ten with Dyslexia and ten with no SLDs. All students were called to solve a digital test and a paper test that were including some basic mathematic operations. The researcher recorded and examined the differences between the results from the two tests. Descriptive and deductive statistical analysis showed that students had better results when examined via a computer compared to a traditional written examination. [ABSTRACT FROM AUTHOR]

Copyright of Hacettepe University Journal of Education is the property of Hacettepe University Journal of Education 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.)

The article explores curvature with paper models. It states that to study both Euclidean and non-Euclidean geometries discovered by Janos Bolyai, Nikolai Lobachevsky and Bernhard Riemann as curved surfaces, a concept of curvature dating to Carl Friendrich Gauss is used by differential geometers. It examines how the curvature of curves and surfaces is related to the angles of polygons or polygonal curves and solid angles at the vertices of polyhedra. Examples of paper models that use Descartes' version of curvature to explore hyperbolic and elliptic figures in a precise and accessible way are presented.

Copyright of Mathématiques & Sciences Humaines is the property of Editions du CNRS 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.)

This paper illustrates how years 1 and 2 students were guided to engage in data modelling and statistical reasoning through interdisciplinary mathematics and science investigations drawn from an Australian 3-year longitudinal study: Interdisciplinary Mathematics and Science Learning (https://imslearning.org/). The project developed learning sequences for 12 inquiry-based investigations involving 35 teachers and cohorts of between 25 and 70 students across years 1 through 6. The research used a design-based methodology to develop, implement, and refine a 4-stage pedagogical cycle based on students' problem posing, data generation, organisation, interpretation, and reasoning about data. Across the stages of the IMS cycle, students generated increasingly sophisticated representations of data and made decisions about whether these supported their explanations, claims about, and solutions to scientific problems. The teacher's role in supporting students' statistical reasoning was analysed across two learning sequences: Ecology in year 1 and Paper Helicopters in year 2 involving the same cohort of students. An explicit focus on data modelling and meta-representational practices enabled the year 1 students to form statistical ideas, such as distribution, sampling, and aggregation, and to construct a range of data representations. In year 2, students engaged in tasks that focused on ordering and aggregating data, measures of central tendency, inferential reasoning, and, in some cases, informal ideas of variability. The study explores how a representation-focused interdisciplinary pedagogy can support the development of data modelling and statistical thinking from an early age. [ABSTRACT FROM AUTHOR]

Mathematics plays a fundamental role in ecological research, yet its uses remain strikingly separate from advances in the environmental social sciences and humanities. In this paper, I work to address this impasse and outline the motivation and scope for an 'ecological mathematics', an approach to doing mathematics in environmental research which foregrounds relationship, embodiment and human difference. I begin by tracing the historical emergence of mathematics in ecology, noting how life processes have been conceptualised in a way which forces them to fit the ideals of mathematical models transplanted from the physical sciences. I then investigate the cultural factors shaping the evolution of mathematical thought, eliciting a malleability in how mathematical knowledge relates to the more-than-human world. This provides a place from which to rethink the role of abstraction in ecological thought, and develop mathematical methods grounded in ecological concepts. Drawing on ethnographic and perceptual accounts of space and time, I work with topological concepts from both mathematics and the social sciences to suggest a new correspondence between these subjects, elaborating a way of employing mathematical techniques which enliven, rather than deaden, the ecologies under study. The paper concludes with important philosophical clarifications to the approach of an ecological mathematics. [ABSTRACT FROM AUTHOR]

Nearly 30 years after the end of apartheid in South Africa, the education system has yet to provide learners with an adequate school experience. With school closures during the pandemic, the urgency to provide a quality education in the townships became even more dire. In collaboration with the leadership of Charles Duna Primary School in Gqeberha, South Africa, Partnerships for Educational Excellence and Research (PEER) International reestablished a partnership to design a flexible implementation of methods and curricula to build numeracy repertoires. Professional development efforts leverage evidence-based best teaching and learning strategies included in the Morningside Model of Generative Instruction (Johnson et al., 2020). Weekly videoconferences target the development of basic computation skill acquisition and math problem solving skills. The dramatically different environment and available resources in township schools is a prevailing consideration in this transfer of instructional technology. Our project started early in 2022 and continues with optimism and determination. The purpose of this paper is to describe our constructional approach (Goldiamond, 1974/2002 Behavior and Social Issues, 11(2), 108-197) when invited to improve classroom conditions for teachers and learners. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the links between prospective elementary teachers' (PTs') ability to notice student mathematical thinking, their mathematical knowledge for teaching (MKT) and their ability to decompose learning goals into component conceptual parts (Morris et al., 2009). Previously, researchers have proposed theoretical connections between MKT and teachers' professional noticing, but empirical support for these relationships has been limited. Results of this mixed-methods study indicate that PTs who scored higher on an MKT assessment outperformed their peers in terms of attending to student thinking but had similar performance in terms of interpreting that thinking. However, PTs who were able to conceptually unpack a learning goal into subconstructs performed higher-quality interpretations of student thinking. We hypothesize that the skill of decomposing learning goals may allow PTs to apply their mathematics knowledge to successfully interpret student work. These results have implications for understanding how noticing and MKT may develop in relation with each other. [ABSTRACT FROM AUTHOR]

The exploration of children's drawings as mathematical representations is a current focus in early years mathematics education research. This paper presents a qualitative analysis of 72 kindergarten to Grade 3 (5 to 8 years old) children's drawings produced during problem-solving tasks centred on multiplicative strategies. Existing frameworks for the developmental sequence of mathematical drawings and the progression of children's strategies for multiplicative situations were an interpretive lens through which to analyse the drawings. Children used pictographic and iconic drawing types to represent the "story" in the problem and the multiplicative strategies employed to solve the tasks. Exploration of the children's drawings suggested that as children's drawings become more structural, schematic in nature, it may be easier for children to show their understanding of the structural elements of multiplicative relationships. Results revealed that structural elements of multiplicative relationships were more easily seen in iconic representations; however, both pictographic and iconic drawings were useful to observe counting, additive, and multiplicative strategies when mathematical elements of the problem were visible. Additional representations attached to the drawings (e.g. numerical) were needed to confirm children's strategies when their drawings lacked structure. These findings have implications for how young children's drawings are interpreted by classroom teachers. The interpretation of these drawings suggested that some children may not yet realise how their drawings in mathematics need to shift from illustrations of the problem's story context to representing mathematical ideas and processes — which requires intentional teaching of the purpose of drawings for mathematical contexts. [ABSTRACT FROM AUTHOR]

Copyright of Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales is the property of Academia Colombiana de Ciencias Exactas, Fisicas y Naturales 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.)

Assessments constitute a fundamental and inevitable component of any educational journey. Manual effort required for the evaluation of these assessments is very high. Automation of the evaluation process and grading helps in making the review process more efficient, objective, and scalable, thereby reducing the workload of human reviewers. Automating the grading process for multiple-choice and short-answer assessments is relatively straightforward, but it poses significant challenges when applied to the evaluation of formal languages, particularly in the context of mathematical assessments. In this paper a model that automatically evaluates and grades the Quadratic Equation problems is presented. The study is conducted using a manually curated dataset comprising 1200 solutions to various quadratic equation problems. Embeddings of the quadratic solutions are generated using Google's T5 Model. These embeddings are then used to train different traditional and ensembled machine learning models along with complex Deep learning models like LSTM and Bi LSTM. An in-depth analysis of the fine-tuned T5 model's performance, evaluating its effectiveness in comparison with the pretrained T5 model in automatic grading of quadratic equation problems has been explored. Fine-tuning significantly contributes to the reduction of error by 70% and a noticeable increase in the R2 value to 97%. [ABSTRACT FROM AUTHOR]

In this paper, we address the weighted multi-objective re-entrant owshop scheduling problem considering release dates in order to minimize makespan, total completion time, total tardiness, maximum idle time, and number of tardy jobs. Each job is taken into account with deterministic processing times, and release dates. The flow-shop comprised of two workshops in whose jobs are entered to the main workshop and after the first part of the processing, they are transferred to the second workshop and after this stage, the jobs are returned to the main workshop for the last part of the processing. We model the problem by a new mixed integer programming based on formulating sum of idle time as a new concept. Moreover, a hybrid evolutionary algorithm is proposed based on some dispatching rules, ant colony optimization, and genetic algorithm. The performance of the proposed algorithm on some test instances is compared to the mixed integer linear programming model as well as the state-of-the-art algorithms called genetic algorithm, tabu search, bio-geography based optimization, and artificial bee colony. The computational experiments show that our proposed approach outperforms other algorithms and the results indicate efficiency and capability of the proposed algorithm in comparison with the traditional algorithms. [ABSTRACT FROM AUTHOR]

This paper reports on the development and use of a Blueprint for Rural Mathematics (herein referred to as the Blueprint) in a study of middle-primary mathematics teaching. The study presented a counter-narrative to the deficit discourse around rural education outcomes through an emic perspective of middle-primary mathematics on the Yorke Peninsula, a rural district in southern Australia. This study defined 'rural' as a sociological and geographical phenomenon. It takes a sociological stance acknowledging the situatedness of the rural and the social and cultural uniqueness of the people and their communities. Geographically, the rural locations in this study were those distanced from, and outside the commuting zone of, large urban areas and major cities. This study claimed that rural schools of Yorke Peninsula are unresearched, undertheorised and underestimated in their teaching of mathematics. Hence, very little was known about the experiences of the Yorke Peninsula teachers or the pedagogical practices they employed in their mathematics teaching. Yorke Peninsula people have an identity of deficit imposed on them with no opportunity to negotiate it. In understanding and addressing the accuracy of this pervasive negative framing, this study investigated Yorke Peninsula teachers of mathematics. It concluded that the rural social space, the identity of its members, and teacher pedagogy are essential considerations in mathematics teaching. The Blueprint provides a framework to explore these key components of rural education. [ABSTRACT FROM AUTHOR]

Purpose: The paper aims to examine the casual role of higher-order thinking skills as a mediator in the relationship between students' strength in mathematics and achievement in electrical and electronic engineering education. Design/Methodology/Approach: The study adopted a quantitative research design where random cluster sampling was used to select a total of 488 final-year students from four technical universities in Ghana. Mathematics achievement tests were used to gather data on students' higher-order thinking skills and competence in five areas of mathematics. Also, their examination results were collected from their respective universities. Mediation analysis was done using AMOS 26. Finding: The study revealed that the positive effect of students' strengths in the five selected mathematics topics on their performance in electrical and electronic engineering education is mediated by their higher-order thinking skills. Conclusion: The research concludes that there is a partial mediation in the relationship between students' strength in mathematics and achievement in electrical and electronic engineering education by higher-order thinking skills. Research Limitations: It is recommended that further researchers carry out similar research with more mathematics indicators to explain more variations in achievement in electrical and electronic engineering education. Practical Implication: Engineering mathematics curriculum developers should stress the need for mathematics, especially algebra, for the development of higher-order thinking skills to facilitate problem-solving in electrical and electronic engineering education and practice. Contribution to Literature: This study highlights the relationship between the understanding of the concepts of specific mathematics topics, higher-order thinking skills, and achievement in electrical and electronic engineering education. [ABSTRACT FROM AUTHOR]

This paper aims to raise awareness about a potential harmful consequence of teaching adaptations due to the Covid-19 pandemic and advanced AI-powered chat bots in the context of large language models. As video lectures might undermine pluralism in mathematics, we argue that such developments could be harmful for mathematical practice and society at large. We argue that the mathematical undergraduate curriculum should not be too hard codified and formalized via an abuse of online teaching tools. In order to show why a plurality of research practices constitutes a great resource for mathematical progress, we will discuss a historical situation regarding the developments of the Tripos in Cambridge. We will also discuss analogies with economics and ideas on mathematical pluralism and productive ambiguity. Finally, we suggest that pluralism in education may be desirable in other fields too. [ABSTRACT FROM AUTHOR]

This paper examines the relationship between early childhood music and maths. The emphasis is on children as intuitive pattern makers as they explore, categorise and imagine their worlds. We argue for the careful listening of childhood languages and reason that music and maths are expressive languages that young children use to investigate and experiment. This concept is based on Malaguzzi’s idea of the hundred languages of children. Children’s explorations of patterns, whether music, maths or other media will follow the principle of symmetry. We observe the intersectionality of language/s. Data are drawn from video and teaching materials prepared for early childhood teachers in-service training in Australia. Framing the discussion with Vygotskian and developmental theories we identify the patterns a child makes in a music discovery video and categorise the child’s actions to combine both musical and mathematical concepts within the one action. The aim of the research is to revisit early childhood curriculum and pedagogy, rethinking sources of knowledge and the value of treating arts and sciences as being of equal importance as children discover and define their worlds. [ABSTRACT FROM AUTHOR]

Written answers to open-ended questions can have a higher long-term effect on learning than multiple-choice questions. However, it is critical that teachers immediately review the answers, and ask to redo those that are incoherent. This can be a difficult task and can be time-consuming for teachers. A possible solution is to automate the detection of incoherent answers. One option is to automate the review with Large Language Models (LLM). They have a powerful discursive ability that can be used to explain decisions. In this paper, we analyze the responses of fourth graders in mathematics using three LLMs: GPT-3, BLOOM, and YOU. We used them with zero, one, two, three and four shots. We compared their performance with the results of various classifiers trained with Machine Learning (ML). We found that LLMs perform worse than MLs in detecting incoherent answers. The difficulty seems to reside in recursive questions that contain both questions and answers, and in responses from students with typical fourth-grader misspellings. Upon closer examination, we have found that the ChatGPT model faces the same challenges. [ABSTRACT FROM AUTHOR]

Due to rapid immigration, many children worldwide are learning mathematics in a second or additional language. This language diversity can be challenging for both teachers and students and carries profound implications for mathematics educators. Research shows that teachers use various ways to support English Language Learners. Research on multilingualism in mathematics classrooms has often focused on qualitative research. This meta-analysis aims to explore the statistically effective successful teaching practices from the studies using quantitative or mixed-method research approaches and aims to inform the research field in a cumulative manner. The specific research question that guided this meta-analysis is: What is the evidence regarding successful teaching of mathematics for Year 1–10 English Language Learners from 2009–2019 in countries where curricula are delivered predominantly in English? Four successful intervention categories were identified: Dual Language Programmes, Curriculum integration, Teacher Professional Development, and Cognitively Focused Interventions. The paper concludes with recommendations for practice and further research in this area. [ABSTRACT FROM AUTHOR]

Using the probit analysis technique, mathematical algorithm and MATLAB computer program have been implemented in this paper to calculate both the Log-Dose (LD) and the Effective-Dose (ED) for any given percent. The probit analysis uses a successive weighted simple linear regression of experimental or row data. The kind of row data obtained from the bioassays should be generally in percent response (mortality or affected) at the corresponding doses (or concentrations). The response should be always in binomial form (e.g. death/no death) and the relationship between the response and the various doses or concentrations is always sigmoid or non-linear. The probit analysis here acts as a transformation from sigmoid or non-linear relationship to linear one and then uses a successive weighted simple linear regression on the linear relationship of the observed data. It is necessarily to note that, the probit analysis always assumes that the relationship between number responding (not proportion response) and dose (or concentration) should be normally distributed. Two simple examples are explained in this paper to prove the validity and the consistency of both the proposed mathematical methodology and the concerning computer program. [ABSTRACT FROM AUTHOR]

The recent axiomization of Origami has led to numerous breakthroughs in both mathematics and in understanding of the ancient art of paper folding. We propose a puzzle whose solution demonstrates the power of mathematical origami. This puzzle is accessible to the geometry student and could be used as supplemental geometry instruction as an extension of traditional compass and straight edge constructions. Detailed images and photos are provided to guide the audience through the puzzle's solution. [ABSTRACT FROM AUTHOR]

Steganography is used to hide the occurrence of communication. Discovering and rendering useless such covert message is an art of steganalysis. The importance of techniques that can reliably detect the presence of secret messages in images is increasing as images can hide a large amount of malicious code that could be activated by a small Trojan horse type of virus and also for tracking criminal activities over Internet. This paper presents an improved blind steganalysis technique. The proposed algorithm reduces the initial-bias, and estimates the LSB embedding message ratios by constructing equations with the statistics of difference image histogram. Experimental results show that this algorithm is more accurate and reliable than the conventional difference image histogram method. It outperforms other powerful steganalysis approaches for embedded ratio greater than 40% and comparable with RS steganalysis technique for shorter hidden message length. [ABSTRACT FROM AUTHOR]

Artificial intelligence (AI) has permeated all human activities, bringing about significant changes and creating new scientific and ethical challenges. The field of education could not be an exception to this development. OpenAI's unveiling of ChatGPT, their large language model (LLM), has sparked significant interest in the potential applications of this technology in education. This paper aims to contribute to the ongoing discussion on the role of AI in education and its potential implications for the future of learning by exploring how LLMs could be utilized in the teaching of mathematics in higher education and how they compare to the currently widely used computer algebra systems (CAS) and other mathematical tools. It argues that these innovative tools have the potential to provide functional and pedagogical opportunities that may influence changes in curriculum and assessment approaches. [ABSTRACT FROM AUTHOR]

Distance learning is very challenging for both teachers and students. Technology can help educators in combined teaching, which means combining traditional educational methods with active learning. The Halomda educational platform provides improving students' active learning due to better students' engagement. This enhances students' performance as well as the ability to solve mathematics problems. In this paper, we share our experience of how using the Halomda system for combined teaching in the "differential equations" course significantly improves student learning outcomes. [ABSTRACT FROM AUTHOR]

Groupwork provides opportunities to learn important communication and collaboration skills, but how can we ensure all students are participating equitably while also engaging with the academic content when working in groups? Group-worthy tasks provide participation structures needed for students to engage with the content as well as develop and practice such social skills. This paper describes how to revise or design a task to be group-worthy in the mathematics classroom, using an example task we modified from the National Council of Teacher of Mathematics. [ABSTRACT FROM AUTHOR]

Understanding children's attitudes towards mathematics provides insights into their lived mathematical experience and engagement. Despite the considerable amount of research into students' attitudes toward mathematics, limited research has been conducted into young children's attitudes toward mathematics (YCATM). Within this limited research, investigating YCATM has certain challenges. From a methodological perspective, limitations exist regarding the type of research techniques that can be employed to study the nuances of the issue. The foci of this paper are to present and evaluate a methodological approach that used children's drawings (N = 106) and interview responses as the primary sources of data. Findings indicate that the strategy of "Draw yourself doing mathematics", when used with other research methods, generated rich attitudinal data in the form of personal stories about YCATM. [ABSTRACT FROM AUTHOR]

In the process of autonomous vehicle motion planning and to create comfort for vehicle occupants, factors that must be considered are the vehicle's safety features and the road's slipperiness and smoothness. In this paper, we build a mathematical model based on the combination of a genetic algorithm and a neural network to offer lane‐change solutions of autonomous vehicles, focusing on human vehicle control skills. Traditional moving planning methods often use vehicle kinematic and dynamic constraints when creating lane‐change trajectories for autonomous vehicles. When comparing this generated trajectory with a man‐generated moving trajectory, however, there is in fact a significant difference. Therefore, to draw the optimal factors from the actual driver's lane‐change operations, the solution in this paper builds the training data set for the moving planning process with lane change operation by humans with optimal elements. The simulation results are performed in a MATLAB simulation environment to demonstrate that the proposed solution operates effectively with optimal points such as operator maneuvers and improved comfort for passengers as well as creating a smooth and slippery lane‐change trajectory. [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.)

This paper reports on a large clinical study with 193 children (Grades 3-6) who interacted with 12 digital math games during clinical interviews. Children completed a pretest interacted with the digital math games, completed a posttest, and answered questions about their interactions with the games. During the interviews, researchers used two video perspectives to capture children's interactions and onscreen gestures. Mixed methods were employed to analyze pretest and posttest data and to examine how the design features in each digital game afforded learning opportunities for children. The resuits showed that children exhibited different levels of awareness of the design features. some features helped or hindered different children, and children who were able to connect the digital games with the mathematics in the games exhibited higher learning gains. [ABSTRACT FROM AUTHOR]

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]

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]

This paper reports on a design oriented study conducted in close collaboration between two researchers and three preschool teachers. Within this study, a play-based interview script was designed in accordance with theoretically driven principles. Based on this script, the preschool teachers conducted interviews with children from three preschools five times over four semesters. The focus of this paper is methodological, aiming to show how sensitive divergence in these play-based interviews lead to a strengthened research quality. Of importance is that this quality improving divergence would not have been realized without the close collaboration between researchers and preschool teachers. [ABSTRACT FROM AUTHOR]

Copyright of Educacao e Pesquisa is the property of Faculdade de Educacao da Universidade de Sao Paulo 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.)

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]

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]

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]

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]