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Performance outcomes in mathematics in South African primary schools have reached alarming proportions. This paper seeks to delve deep into the challenges contributing to mathematics underperformance and gain insights from the perspectives of the departmental heads regarding the strategies they deploy in improving performance in their schools. In examining this phenomenon, we conducted semi-structured interviews that targeted departmental heads in primary schools in the Province of Limpopo, South Africa. In addition, quality management theory was used as a lens to frame the study theoretically. The study results demonstrate that departmental heads employ differentiated strategies to mitigate the pertinent challenges facing mathematics performance in primary schools. Amongst the key strategies departmental heads deploy include the following: Collaborative workshops and subject meetings, departmental heads initiated continuous professional development opportunities, provision of resources for teaching mathematics, control and monitoring as accounting measures, and confronting teacher insubordination. This paper is of significant value as it adds to new knowledge in managing and teaching mathematics in primary schools. [ABSTRACT FROM AUTHOR]

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]

Research has shown the importance of helping students, especially those with mild-to-moderate learning disabilities, to offload information during problem-solving. When students can get their thoughts onto paper, number line strategies can help them develop a firm foundation in mathematical problem-solving while understanding the relationships between mathematical operations. These strategies are helpful for the development of addition, subtraction, multiplication, division, and later, fractional mathematics. In this article, we describe the progression of number lines as a supportive strategy for elementary students and those with developmental delays in mathematics to improve mathematical understanding. This strategy is based on students being able to show their work and think about what they have written on paper or how they have used manipulatives. [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]

The work focuses on the comparison of basic strategies in the teaching of mathematics. The first option is to use a calculator and ICT in order to solve more complex tasks and not waste time on algorithmically simple tasks. The second option is to solve all tasks with a paper-and-pencil strategy, while the number of tasks will be lower due to the fact that we need time for numerical calculation. Pupils of the 7th grade of elementary school were compared with pupils up to two grades higher in order to find out the differences between their performances. Pupils of the 7th grade do not use calculators during the math classes and thus have to cope with each task without help. Pupils of higher grades have been using calculators for numerically more challenging tasks for the last two years. Results of the nonmetric multidimensional scaling showed that the 7th grade pupils have the different position on the one-dimensional scale than the pupils of higher grades.43T [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]

Emphasis on STEM education has gained the attention of activists to promote gender equality in the education field in the last few years. The objectives of the present research paper are: Why is there a need to address gender inequalities in STEM education in Pakistan? The second objective of the research is to highlight the obstacles that restrict women's access to STEM education in Pakistan. This research is qualitative in nature and based on the interviews of students enrolled in the faculty of humanities at the BS level in AIOU. Research gives directions to policymakers on how to increase women's enrollment in science, technology, engineering, and mathematics (STEM). [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]

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]

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]

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 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]

The paper compares the accuracy of reconstruction using different wavelets, and the authors also use fast and discrete Fourier transforms together to calculate the forward and inverse continuous wavelet transform in the frequency domain. Due to the use of calculations in the frequency domain, it becomes possible to perform decomposition, reconstruction, image filtering, and other transformations with high performance and precision. For multiscale signal analysis, a wavelet with a rectangular amplitude-frequency response has been constructed, which allows for an increase in the accuracy of decomposition and reconstruction compared to the Mallat algorithm presented in Matlab computer mathematics. At the same time, the time of multiscale analysis is reduced several times compared to the Mallat algorithm. [ABSTRACT FROM AUTHOR]

The triumph of scientific materialism in the Seventeenth Century not only bifurcated nature into matter and mind and primary and secondary qualities, as Alfred North Whitehead pointed out in Science and the Modern World. It divided science and the humanities. The core of science is the effort to comprehend the cosmos through mathematics. The core of the humanities is the effort to comprehend history and human nature through narratives. The life sciences can be seen as the zone in which the conflict between these two very different ways of comprehending the world collide. Evolutionary theory as defended by Schelling developed out of natural history, but efforts have been made to formulate neo-Darwinism through mathematical models. However, it is impossible to eliminate stories from biology. As Stuart Kauffman argued, mathematical models attempt to pre-state all possibilities, but in evolution there can be adjacent possibles that can be embraced by organisms but cannot be pre-stated. To account for such actions it is necessary to tell stories. Mathematics provides analytic precision allowing long chains of deductions, but tends to deny temporal becoming and cannot do justice to the openness of the future, while narratives focus on processes and events, but lack exactitude that would provide precise deductions and predictions. In advancing mathematics adequate to life, Robert Rosen argued that living beings as anticipatory systems must have models of themselves, and strove to develop a form of mathematics able to model life itself. It has been convincingly argued that narratives are central to human self-creation and they are lived out before being explicitly told. Their models of themselves are first and foremost, stories or narratives. If this is the case, might not living beings as biological entities be characterized by proto-stories or narratives in their models of themselves? Biosemiotics, largely inspired by C.S. Peirce, provides a bridge between mathematical and narrative comprehension, conceiving them as different forms of semiosis. The study of life through biosemiotics could reveal how mathematics and narratives can be understood in relation to each other. This could then have implications for how we understand science and the humanities and their relationship to each other. In this paper I will examine work in theoretical biology that might advance these efforts. [ABSTRACT FROM AUTHOR]

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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]

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]

Future experts, decision-makers, stakeholders and future citizens – they all go to school, which could be a place to prepare students to facing post-normal problems in their future roles. While the literature on mathematics and science education shows increased interest in post-normal science to critically understand contemporary problems, mathematics is still generally taught as a neutral subject with either correct or wrong answers. In this paper, I lean on post-normal science literature and the slowly growing literature on ethics and mathematics education to develop a framework for identifying how mathematics education can prepare students for ethical aspects of post-normal problems. Three areas of ethics associated with post-normal problems are explored through concepts from ethics and mathematics education: ethical perspectives of the problem, ethical perspectives embedded in knowledge, and ethics in interpersonal care in discussions and care for students' self-esteem in participatory processes. This framework is used to analyse and discuss three classroom projects to provide examples of what these areas may contain. The projects partly align with post-normal science, and are about clothing and sustainability, traffic safety, and argumentation related to open an offshore area to oil exploitation. The ethical areas are discussed in terms of ethical awareness and democratic practices. • Three teaching and learning situations with 13–15-year-olds are analysed. • Ecological, societal and individual stakes of problems were addressed. • Ethics embedded in knowledge production could be more explicit. • Care for participants and their self-appreciation is key is extended peer-reviews. • Mathematics class is suitable for addressing ethics of post-normal problems. [ABSTRACT FROM AUTHOR]