Search results for: philosophy of mathematics

Authors: Duygu Özdemir, Bilal Özçakır

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Usage of augmented reality in education helps students to make sense of the three-dimensional world of mathematics. In this study, it was aimed to develop activities about fractions for 5th-grade students by augmented reality and also aimed to assess these activities in terms of students’ understanding and views. Data obtained from 60 students in a private school in Marmaris, Turkey was obtained through classroom observations, students’ worksheets and semi-structured interviews during two weeks. Data analysis was conducted by using constant-comparative analysis which leads to meaningful categories of findings. Findings of this study indicated that usage of augmented reality is a facilitator to make concretize and provide real-life application for fractions. Moreover, students’ opinions about its usage were lead to categories as benefit for learning, enjoyment and creating awareness of usage of augmented reality in mathematics education. In general, this study could be a bridge to show the contributions of augmented reality applications to mathematics education and also highlights that augmented reality could be used with subjects like fractions rather than subjects only in geometry learning domain.

Keywords: augmented reality, mathematics, fractions, students

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Authors: Anne Tan, Kok-Sing Tang, Audrey Cooke

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Play has always been a prominent pedagogy in early childhood. However, there is growing evidence of success in students’ learning using explicit instruction, especially in literacy in the early years. There is also limited research using explicit instruction in early childhood mathematics, and play is usually prominently mentioned. This proposed research aims to investigate the possibilities and benefits of integrating guided play with explicit instruction in early childhood mathematics education. While play has traditionally been a prominent pedagogy in early childhood, there is growing evidence of success in student learning through explicit instruction, particularly in literacy. However, limited research exists on the integration of explicit instruction in early childhood mathematics, where play remains prominently mentioned. This study utilises a multiple case study methodology to gather data and provide immediate opportunities for curriculum improvement. The research will commence with semi-structured interviews to gain insights into educators' background knowledge. Highly structured observations will be conducted to record the frequency and manner in which guided play is integrated with specific elements of explicit instruction during mathematics teaching in early childhood. To enhance the observations, video recordings will be made using cameras with video settings and Microsoft Teams meeting recordings. In addition to interviews and observations, educators will maintain journals and use the Microsoft Teams platform for self-reflection on the integration of guided play and explicit instruction in their classroom practices and experiences. The study participants will include educators with early childhood degrees and students in years one and two. The primary goal of this research is to inform the benefits of integrating two high-impact pedagogies, guided play, and explicit instruction, for enhancing student learning outcomes in mathematics education. By exploring the integration of these pedagogical approaches, this study aims to contribute to the development of effective instructional strategies in early childhood mathematics education.

Keywords: early childhood, early childhood mathematics, early childhood numbers, guided play, play-based learning, explicit instruction

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Authors: Hugo T. Jorge, Richard T. Simanke

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Lacan’s work addresses overarching issues concerning the scientific intelligibility of the subject in its philosophical sense. Even though his reflection is not, strictly speaking, philosophy of science, it contains many traits that are typical of this branch of philosophy. However, the relation between Lacan’s early thought and the philosophy of science of the time is often disregarded or only incompletely accounted for in Lacanian scholarship. French philosopher of science Emile Meyerson was often implicitly or explicitly referred to in Lacan’s works, yet few publications can be found on their relationship. The objective of this paper is to contribute to the analysis of this relationship, indicating some of its possible implications. For this, the convergence between Meyerson’s doctrine of science and Lacan’s works between 1936 and 1953 is discussed, as well as the conditions under which Lacan’s reception of Meyerson’s ideas take place. In conclusion, it is argued that this convergence allows for the clarification of important issues in Lacan’s early work, such as the concept of imago, his views on the nature of truth, and his thesis of the anthropomorphism of natural sciences. Meyerson’s argument for the permanence of common sense within science makes Lacan’s claims on the anthropomorphism of natural sciences more understandable. Similarly, Meyerson’s views on the epistemological shortfall of the Principle of Identity sheds some light on Lacan’s 1936 critique of associationistic concepts of engram and truth and may be at the origins of his antirealist and anti-idealist stances. Meyerson’s Principle of Identity is also related to some aspects of Lacan’s concept of imago. The imago understood as the unconscious condition for the identity in time of family figures in childhood, would be an excellent expression of the Principle of Identity. In this sense, the Principle of Identity may be linked to the concept of imaginary as developed by Lacan in the 1950s. However, Lacan considerably distorts Meyerson’s views in his 1936 critique of Freud’s concept of libido. Finally, a possible relationship between Lacan’s late concept of the real and Meyerson’s concept of the irrational is suggested.

Keywords: imaginary, Lacan, Meyerson, philosophy of science, real

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Authors: Reyhan Tekin Sitrava

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Teachers should have robust and comprehensive content knowledge for effective mathematics teaching. It was explained that content knowledge includes knowing the facts, truths, and concepts; explaining the reasons behind these facts, truths and concepts, and making relationship between the concepts and other disciplines. By virtue of its importance, it will be significant to explore teachers and prospective teachers’ content knowledge related to variety of topics in mathematics. From this point of view, the purpose of this study was to investigate prospective mathematics teachers’ content knowledge. Particularly, it was aimed to reveal the prospective teachers’ knowledge regarding the definition of limit and derivate. To achieve the purpose and to get in-depth understanding, a qualitative case study method was used. The data was collected from 34 prospective mathematics teachers through a questionnaire containing 2 questions. The first question required the prospective teachers to define the limit and the second one required to define the derivative. The data was analyzed using content analysis method. Based on the analysis of the data, although half of the prospective teachers (50%) could write the definition of the limit, nine prospective teachers (26.5%) could not define limit. However, eight prospective teachers’ definition was regarded as partially correct. On the other hand, twenty-seven prospective teachers (79.5%) could define derivative, but seven of them (20.5%) defined it partially. According to the findings, most of the prospective teachers have robust content knowledge on limit and derivative. This result is important because definitions have a virtual role in learning and teaching of mathematics. More specifically, definition is starting point to understand the meaning of a concept. From this point of view, prospective teachers should know the definitions of the concepts to be able to teach them correctly to the students. In addition, they should have knowledge about the relationship between limit and derivative so that they can explain these concepts conceptually. Otherwise, students may memorize the rules of calculating the derivative and the limit. In conclusion, the present study showed that most of the prospective mathematics teachers had enough knowledge about the definition of derivative and limit. However, the rest of them should learn their definition conceptually. The examples of correct, partially correct, and incorrect definition of both concepts will be presented and discussed based on participants’ statements. This study has some implications for instructors. Instructors should be careful about whether students learn the definition of these concepts or not. In order to this, the instructors may give prospective teachers opportunities to discuss the definition of these concepts and the relationship between the concepts.

Keywords: content knowledge, derivative, limit, prospective mathematics teachers

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Authors: Mohd Iqbal Malik

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Ethical philosophy of Quran pinnacled virtue and economics as the part and parcel of human life. Human beings are to be imagined by the sign of morals. Soul and morality are both among the essences of human personality. Islam lays the foundation of ethics by installation of making a momentous variance between virtue and vice. It suggests for the distribution of wealth in-order to terminate accumulation of economic resources. Quran claims for the ambiguous pavement to attain virtue by saying, ‘Never will you attain the good (reward) until you spend (in the way of Allah) from that which you love. And whatever you spend indeed, Allah knows of it.’ The essence of Quran is to eliminate all the deep-seated approaches through which the wealth of nations is being accumulated within few hands. The paper will study the Quranic Philosophy Of Islamic Economic System. In recent times, to get out of the human resource development mystery of Muslims, Ismail Al-Raji Faruqi led the way in the so-called ‘Islamization’ of knowledge. Rahman and Faruqi formed opposite opinions on this project. Al-Faruqi thought of the Islamization of knowledge in terms of introducing Western learning into received Islamic values and vice versa. This proved to be a mere peripheral treatment of Islamic values in relation to Western knowledge. It is true that out of the programme of Islamization of knowledge arose Islamic universities in many Muslim countries. Yet the academic programmes of these universities were not founded upon a substantive understanding and application of the tawhidi epistemology.

Keywords: ethical philosophy, modern Islamic finance, knowledge of finance, Islamic banking

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Authors: Hilal Karakuş, Berrin Akman

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Preschool years are considered as critical years because of shaping the future lives of individuals. All of the knowledge, skills, and concepts are acquired during this period. Also, basis of academic skills is based on this period. As all of the developmental areas are the fastest in that period, the basis of mathematics education should be given in this period, too. Mathematics is seen as a difficult and abstract course by the most people. Therefore, the enjoyable side of mathematics should be presented in a concrete way in this period to avoid any bias of children for mathematics. This study is conducted to examine mathematics concept acquisition of children in terms of different variables. Screening model is used in this study which is carried out in a quantity way. The study group of this research consists of total 300 children, selected from each class randomly in groups of five, who are from public and private preschools in Çankaya, which is district of Ankara, in 2014-2015 academic year and attending children in the nursery classes and preschool institutions are connected to the Ministry of National Education. The study group of the research was determined by stage sampling method. The schools, which formed study group, are chosen by easy sampling method and the children are chosen by simple random method. Research data were collected with Bracken Basic Concept Scale–Revised Form and Child’s Personal Information Form generated by the researcher in order to get information about children and their families. Bracken Basic Concept Scale-Revised Form consists of 11 sub-dimensions (color, letter, number, size, shape, comparison, direction-location, and quantity, individual and social awareness, building- material) and 307 items. Subtests related to the mathematics were used in this research. In the “Child Individual Information Form” there are items containing demographic information as followings: age of children, gender of children, attending preschools educational intuitions for children, school attendance, mother’s and father’s education levels. At the result of the study, while it was found that children’s mathematics skills differ from age, state of attending any preschool educational intuitions , time of attending any preschool educational intuitions, level of education of their mothers and their fathers; it was found that it does not differ by the gender and type of school they attend.

Keywords: preschool education, preschool period children, mathematics education, mathematics concept acquisitions

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Authors: Nora Gavira Duron, Cinthya Moreda Gonzalez-Ortega, Reyna Susana Garcia Ruiz

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This paper objective is to analyze the mathematics performance in the Learning Evaluation National Plan (PLANEA for its Spanish initials: Plan Nacional para la Evaluación de los Aprendizajes), applied to Mexican students who are enrolled in the last elementary-school year over the 2017-2018 academic year. Such test was conducted nationwide in 3,573 schools, using a sample of 108,083 students, whose average in mathematics, on a scale of 0 to 100, was 45.6 points. 75% of the sample analyzed did not reach the sufficiency level (60 points). It should be noted that only 2% got a 90 or higher score result. The performance is analyzed while considering whether there are differences in gender, marginalization level, public or private school enrollment, parents’ academic background, and living-with-parents situation. Likewise, this variable impact (among other variables) on school performance by gender is evaluated, considering multivariate logistic (Logit) regression analysis. The results show there are no significant differences in mathematics performance regarding gender in elementary school; nevertheless, the impact exerted by mothers who studied at least high school is of great relevance for students, particularly for girls. Other determining variables are students’ resilience, their parents’ economic status, and the fact they attend private schools, strengthened by the mother's education.

Keywords: multivariate regression analysis, academic performance, learning evaluation, mathematics result per gender

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Authors: Irokanulo I. Emmanuel

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The idea of ‘Oshinowoism’ is a representational school, which is a concept based on pure and rustic energy in painting. It is described as any painting that depicts the actions of significant through simple illusions. The idea is never to replicate a photographic resemblance with paint but to create an affinity between what one sees and what one artistically intends to create as a representation of that which one beholds in society as an illusion of reality, not as a reality in itself, but as subjective analysis of reality. The disciples of ‘Oshinowoism’ pursue their art from a representational point of view, creating material realities within feels of colours, forms and space, not trying to confuse the art as a substitute for reality nor reality as a substitute for art, but giving each its space and materialism to exist. The depictions of Oshinowo are the constant reminders or perhaps interpretations of those developments that emerged in contemporary African societies because of neocolonialism. This essay has three objectives. First, it examines the misconception around the development of this thought. Secondly, it contextualizes the later contemporary development of painting as art and craft in present-day Lagos, and third, it constructs the misconception and misconstruction of the concept of ‘Oshinowoism’ and offers a correct ideology of this thought with the body of Oshinowo’s work to give the existence to this philosophy. This study looks at the students of Kolade Oshinowo, especially those students who share similar elements and an affinity with the master painting skills, as a way of reconstructing and addressing the misconception in his style. The early works of Olaku, Edosa, and Lara Ige Jacks are plausible evidence of the existential essence of Oshinowo’s artistic philosophy. To this end, therefore, this study would explore the quality of their pictorial techniques and skills in painting as a way of preserving their master’s philosophy.

Keywords: Oshinowoism, colour scheme, drawing, philosophy, representations

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Authors: Eliana Bergamin

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This philosophical inquiry, influenced by the seminal works of Annemarie Mol and Jeannette Pols, critically examines the transformative impact of artificial intelligence (AI) on emotional caregiving practices within virtual healthcare. Rooted in the traditions of philosophy of care, philosophy of emotions, and applied philosophy, this study seeks to unravel nuanced shifts in the moral and emotional fabric of healthcare mediated by AI-powered technologies. Departing from traditional empirical studies, the approach embraces the foundational principles of care ethics and phenomenology, offering a focused exploration of the ethical and existential dimensions of AI-mediated emotional caregiving. At its core, this research addresses the introduction of AI-powered technologies mediating emotional and care practices in the healthcare sector. By drawing on Mol and Pols' insights, the study offers a focused exploration of the ethical and existential dimensions of AI-mediated emotional caregiving. Anchored in ethnographic research within a pioneering private healthcare company in the Netherlands, this critical philosophical inquiry provides a unique lens into the dynamics of AI-mediated emotional practices. The study employs in-depth, semi-structured interviews with virtual caregivers and care receivers alongside ongoing ethnographic observations spanning approximately two and a half months. Delving into the lived experiences of those at the forefront of this technological evolution, the research aims to unravel subtle shifts in the emotional and moral landscape of healthcare, critically examining the implications of AI in reshaping the philosophy of care and human connection in virtual healthcare. Inspired by Mol and Pols' relational approach, the study prioritizes the lived experiences of individuals within the virtual healthcare landscape, offering a deeper understanding of the intertwining of technology, emotions, and the philosophy of care. In the realm of philosophy of care, the research elucidates how virtual tools, particularly those driven by AI, mediate emotions such as empathy, sympathy, and compassion—the bedrock of caregiving. Focusing on emotional nuances, the study contributes to the broader discourse on the ethics of care in the context of technological mediation. In the philosophy of emotions, the investigation examines how the introduction of AI alters the phenomenology of emotional experiences in caregiving. Exploring the interplay between human emotions and machine-mediated interactions, the nuanced analysis discerns implications for both caregivers and caretakers, contributing to the evolving understanding of emotional practices in a technologically mediated healthcare environment. Within applied philosophy, the study transcends empirical observations, positioning itself as a reflective exploration of the moral implications of AI in healthcare. The findings are intended to inform ethical considerations and policy formulations, bridging the gap between technological advancements and the enduring values of caregiving. In conclusion, this focused philosophical inquiry aims to provide a foundational understanding of the evolving landscape of virtual healthcare, drawing on the works of Mol and Pols to illuminate the essence of human connection, care, and empathy amid technological advancements.

Keywords: applied philosophy, artificial intelligence, healthcare, philosophy of care, philosophy of emotions

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Authors: Chandrabati Chakraborty

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The progressive emergence, in the course of the evolution of life, mind and personality, requires us to assume a creative Principle operating timeless Reality in the temporal. The difference between Western philosophy and that of India, concerns the origin and the purpose of the philosophical enquiry. While the former wonders at the external world, the latter is awareness of perennial suffering associated with human existence. The present world suffers from a basic form of rootlessness,reflecting many psychological, philosophical studies. Alienation,a major theme of human condition in the contemporary epoch has emerged as natural consequences of existential predicament. As Edmund Fuller also observes that individuals suffer not only from famine, ruin or even war but also from devastating inner problems, which are that of estrangement, hopelessness and utter despair. This existentialism is thus considered by Jean Wahl as the “Philosophies of existence”.The post world war scenario well analyses the chaos,annihilation,frustration and anguished estrangement. In such conditions when the West cries out , “What is there?I know first of all that I am.But who am I?.....I am sepeated.What I am seperated from I cannot name it. But I am seperated.”(Dostoevsky:The Confession), Vedantic philosophy looks upon the Pilgrim’s Progress of Humanity as being essentially one,operationg squarely within the bounds of reality, reflecting a basic human experience, outbraving indecorous dictims that have failed to give due honour to human beings,echoing for centuries the Sanskrit slokas with ultimate certitude: II Esa Atma samaha plusina samo masakena samo nagena sama ebhis tribhir lokaih.....sama nena sarvena II (The Atman (Divine Soul) is the same in the ant, the same in the gnat, the same in the elephant, the same in these three worlds....the same in the whole Universe). The present paper aims at a comparative study of cultural and philosophical expression taking into view extensive illustrations from Western Philosophers and The Vedantic,Upanishadic lores of Indian philosophy.

Keywords: existentialism, Vedanta, philosophy, absurdism

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Authors: Mary Ann Cristine R. Olgado

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Diversity in the classroom might make it difficult to promote individualized learning, but differentiated instruction that caters to students' various learning preferences may prove to be beneficial. Hence, this study examined the effectiveness of Hybrid-Differentiated Mathematics Instruction (HDMI) in improving the students’ academic performance in Mathematics. It employed the quasi-experimental research design by using a comparative analysis of the two variables: the experimental and control groups. The learning styles of the students were identified using the Grasha-Riechmann Student Learning Style Scale (GRSLSS), which served as the basis for designing differentiated action plans in Mathematics. In addition, adapted survey questionnaires, pre-tests, and post-tests were used to gather information and were analyzed using descriptive and correlational statistics to find the relationship between variables. The experimental group received differentiated instruction for a month, while the control group received traditional teaching instruction. The study found that Hybrid-Differentiated Mathematics Instruction (HDMI) improved the academic performance of Grade 11-TVL students, with the experimental group performing better than the control group. This program has effectively tailored the teaching methods to meet the diverse learning needs of the students, fostering and enhancing a deeper understanding of mathematical concepts in Statistics & Probability, both within and beyond the classroom.

Keywords: differentiated instruction, hybrid, learning styles, academic performance

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Authors: Norzaliza Md. Nor, Sh-Hussain Salleh, Mahyar Hamedi, Hadrina Hussain, Wahab Abdul Rahman

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Motivational factor is mainly the students’ desire to involve in learning process. However, it also depends on the goal towards their involvement or non-involvement in academic activity. Even though, the students’ motivation might be in the same level, but the basis of their motivation may differ. In this study, it focuses on the intrinsic motivational factor which student enjoy learning or feeling of accomplishment the activity or study for its own sake. The intrinsic motivational factor of students in learning mathematics and science has found as difficult to be achieved because it depends on students’ interest. In the Program for International Student Assessment (PISA) for mathematics and science, Malaysia is ranked as third lowest. The main problem in Malaysian educational system, students tend to have extrinsic motivation which they have to score in exam in order to achieve a good result and enrolled as university students. The use of electroencephalogram (EEG) signals has found to be scarce especially to identify the students’ intrinsic motivational factor in learning science and mathematics. In this research study, we are identifying the correlation between precursor emotion and its dynamic emotion to verify the intrinsic motivational factor of students in learning mathematics and science. The 2-D Affective Space Model (ASM) was used in this research in order to identify the relationship of precursor emotion and its dynamic emotion based on the four basic emotions, happy, calm, fear and sad. These four basic emotions are required to be used as reference stimuli. Then, in order to capture the brain waves, EEG device was used, while Mel Frequency Cepstral Coefficient (MFCC) was adopted to be used for extracting the features before it will be feed to Multilayer Perceptron (MLP) to classify the valence and arousal axes for the ASM. The results show that the precursor emotion had an influence the dynamic emotions and it identifies that most students have no interest in mathematics and science according to the negative emotion (sad and fear) appear in the EEG signals. We hope that these results can help us further relate the behavior and intrinsic motivational factor of students towards learning of mathematics and science.

Keywords: EEG, MLP, MFCC, intrinsic motivational factor

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Authors: M. Rodionov, Z. Dedovets

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The level and type of student academic motivation are the key factors in their development and determine the effectiveness of their education. Improving motivation is very important with regard to courses on middle school mathematics. This article examines the general position regarding the practice of academic motivation. It also examines the particular features of mathematical problem solving in a school setting.

Keywords: teaching strategy, mathematics, motivation, student

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Authors: Marie-Josee Lavallee

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Adorno’s reputation as an abstract and pessimistic thinker who indulged in a critic of capitalist society and culture without bothering himself with opening prospects for change, and who has no interest in political activism, recently begun to be questioned. This paper, which has a twofold objective, will push revisionist readings a step further by putting forward the thesis that revolutionary praxis has been an enduring concern for Adorno, surfacing throughout his entire work. On the other hand, it will hold that his understanding of the relationships between theory and praxis, which will be explained by referring to Ernst Bloch’s distinction between the warm and cold currents of Marxism, can help to interpret the paralysis of revolutionary practice in our own time under a new light. Philosophy and its tasks have been an enduring topic of Adorno’s work from the 1930s to Negativ Dialektik. The writings in which he develops these ideas stand among his most obscure and abstract so that their strong ties to the political have remained mainly overlooked. Adorno’s undertaking of criticizing and ‘redeeming’ philosophy and metaphysics is inseparable from a care for retrieving the capacity to act in the world and to change it. Philosophical problems are immanent to sociological problems, and vice versa, he underlines in his Metaphysik. Begriff and Problem. The issue of truth cannot be severed from the contingent context of a given idea. As a critical undertaking extracting its contents from reality, which is what philosophy should be from Adorno's perspective, the latter has the potential to fully reveal the reification of the individual and consciousness resulting from capitalist economic and cultural domination, thus opening the way to resistance and revolutionary change. While this project, according to his usual method, is sketched mainly in negative terms, it also exhibits positive contours which depict a socialist society. Only in the latter could human suffering end, and mutilated individuals experiment with reconciliation in an authentic way. That Adorno’s continuous plea for philosophy’s self-critic and renewal hides an enduring concern for revolutionary praxis emerges clearly from a careful philosophical analysis of his writings on philosophy and a selection of his sociological work, coupled with references to his correspondences. This study points to the necessity of a serious re-evaluation of Adorno’s relationship to the political, which will impact on the interpretation of his whole oeuvre, is much needed. In the second place, Adorno's dialectical conception of theory and praxis is enlightening for our own time, since it suggests that we are experiencing a phase of creative latency rather an insurmountable impasse.

Keywords: Frankfurt school, philosophy and revolution, revolutionary praxis, Theodor W. Adorno

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Authors: Aleksandar Savanović

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In this paper we will analyze the relationship between the neo-liberal concept of property rights and redistribution policy. This issue is back in the focus of interest due to the crisis 2008. The crisis has reaffirmed the influence of the state on the free-market processes. The interference of the state with property relations re-opened a classical question: is it legitimate to redistribute resources of a man in favor of another man with taxes? The dominant view is that the neoliberal philosophy of natural rights is incompatible with redistributive measures. In principle, this view can be accepted. However, when we look into the details of the theory of natural rights proposed by some coryphaei of neoliberal philosophy, such as Hayek, Nozick, Buchanan and Rothbard, we can see that it is not such an unequivocal view.

Keywords: economic neoliberalism, natural law, property, redistribution

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Authors: Asadullah Sheikh, Kerry Barnett, Paul Ayres

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Despite significant progress in access, equity and public examination success, poor student performance in mathematics in secondary schools has become a major concern in Bangladesh. A substantial body of research has emphasised the important contribution of teaching practices to student achievement. However, this has not been investigated in Bangladesh. Therefore, the study sought to find out the effectiveness of mathematics teaching practices as a means of improving secondary school mathematics in Dhaka Municipality City (DMC) area, Bangladesh. The purpose of this study was twofold, first, to identify the 20 highest performing secondary schools in mathematics in DMC, and second, to investigate the teaching practices of mathematics teachers in these schools. A two-phase mixed method approach was adopted. In the first phase, secondary source data were obtained from the Board of Intermediate and Secondary Education (BISE), Dhaka and value-added measures used to identify the 20 highest performing secondary schools in mathematics. In the second phase, a concurrent mixed method design, where qualitative methods were embedded within a dominant quantitative approach was utilised. A purposive sampling strategy was used to select fifteen teachers from the 20 highest performing secondary schools. The main sources of data were classroom teaching observations, and teacher interviews. The data from teacher observations were analysed with descriptive and nonparametric statistics. The interview data were analysed qualitatively. The main findings showed teachers adopt a direct teaching approach which incorporates orientation, structuring, modelling, practice, questioning and teacher-student interaction that creates an individualistic learning environment. The variation in developmental levels of teaching skill indicate that teachers do not necessarily use the qualitative (i.e., focus, stage, quality and differentiation) aspects of teaching behaviours effectively. This is the first study to investigate teaching behaviours of effective secondary mathematics teachers within Dhaka, Bangladesh. It contributes in an international dimension to the field of educational effectiveness and raise questions about existing constructivist approaches. Further, it contributes to important insights about teaching behaviours that can be used to inform the development of evidence-based policy and practice on quality teaching in Bangladesh.

Keywords: effective teaching, mathematics, secondary schools, student achievement, value-added measures

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Authors: Theresa Marie Miller, Ma. Nympha Joaquin

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The aim of this study was to check the predictive power of social-oriented and individual-oriented achievement motivation on student engagement and collaborative problem-solving skills in mathematics. A sample of 277 fourth year high school students from the Philippines were selected. Surveys and videos of collaborative problem solving activity were used to collect data from respondents. The mathematics teachers of the participants were interviewed to provide qualitative support on the data. Systemaitc correlation and regression analysis were employed. Results of the study showed that achievement motivations−SOAM and IOAM− linearly predicted student engagement but was not significantly associated to the collaborative problem-solving skills in mathematics. Student engagement correlated positively with collaborative problem-solving skills in mathematics. The results contribute to theorizing about the predictive power of achievement motivations, SOAM and IOAM on the realm of academic behaviors and outcomes as well as extend the understanding of collaborative problem-solving skills of 21st century learners.

Keywords: achievement motivation, collaborative problem-solving skills, individual-oriented achievement motivation, social-oriented achievement motivation, student engagement

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Authors: Tripti Watwe

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Music or art of any country is its national heritage and represents the cultural personality of that region. Noble Laureate Rabindranath Tagore through his international educational endeavour called ‘Visva-Bharati’ established this concept that music can very much be a part of the mainstream education of a country because the purpose of both music and education is to bring in transformation in an individual. An individual with musical veins is more focused and meditative towards his or her goal in life. That is why in Tagore’s Visva-Bharati, one can observe even the brightest brains from various fields of economics, science, social sciences or literature equally verbal and efficient in Rabindra songs which the poet created under his own name.Tagore established this phenomenon that music if made a part of education and life, brings in profound transformation in the character and over-all personality of a person giving better and responsible citizens to a nation. It is expected that this hypothesis that music and education can be a nectarine combination can be established and proved with the help of various recorded observations containing Tagore’s educational philosophy, his experiments in his own institution ‘Visva-Bharati’ and through recorded research materials which have been gathered during the author’s field work in Visva-Bharati.

Keywords: Rabindranath Tagore, Visva-Bharati, education, music, philosophy

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Authors: Ali Taher Othman Ali

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The aim of this research is to provide a draft proposal for the professional development of mathematics teachers in accordance with the orientation of science, technology, engineering and mathematics which is known by the abbreviation STEM, as a modern and contemporary orientation in the teaching and learning of mathematics and in order to achieve the objective of the research, the researcher used the theoretical descriptive method through the induction of the literature of education and the previous studies and experiments related to the topic. The researcher concluded by providing the proposal according to five basic axes, the first axe: professional development as a system, and its requirements include: development of educational systems, and allocate sufficient budgets to support the requirements of teaching STEM, identifying mechanisms for incentives and rewards for teachers attending professional development programs based on STEM; the second: development of in-depth knowledge content and its requirements include: basic sciences content development for STEM, linking the scientific understanding of teachers with real-world issues and problems, to provide the necessary resources to expand teachers' knowledge in this area; the third: the necessary pedagogical skills of teachers in the field of STEM, and its requirements include: identification of the required training and development needs and the mechanism of determining these needs, the types of professional development programs and the mechanism of designing it, the mechanisms and places of execution, evaluation and follow-up; the fourth: professional development strategies and mechanisms in the field of STEM, and its requirements include: using a variety of strategies to enable teachers to design and transfer effective educational experiences which reflect their scientific mastery in the fields of STEM, provide learning opportunities, and developing the skills of procedural research to generate new knowledge about the STEM; the fifth: to support professional development in the area of STEM, and its requirements include: support leadership within the school, provide a clear and appropriate opportunities for professional development for teachers within the school through professional learning communities, building partnerships between the Ministry of education and the local and international community institutions. The proposal includes other factors that should be considered when implementing professional development programs for mathematics teachers in the field of STEM.

Keywords: professional development, mathematics teachers, the orientation of science, technology, engineering and mathematics (STEM)

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Authors: Juanita Morris

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The purpose of this study will examine the mediating relationships between the theories of intelligence, mathematics anxiety, gender stereotype threat, meta-cognition and math performance through the use of eye tracking technology, affecting student perception and problem-solving abilities. The participants will consist of (N=80) female graduate students. Test administered were the Abbreviated Math Anxiety Scale, Tobii Eye Tracking software, gender stereotype threat through Google images, and they will be asked to describe their problem-solving approach allowed to measure metacognition. Participants will be administered mathematics problems while having gender stereotype threat shown to them through online images while being directed to look at the eye tracking software Tobii. We will explore this by asking ‘Is mathematics anxiety associated with the theories of intelligence and gender stereotype threat and how does metacognition and math performance place a role in mediating those perspectives?’. It is hypothesized that math-anxious students are more likely affected by the gender stereotype threat and that may play a role in their performance? Furthermore, we also want to explore whether math anxious students are more likely to be an entity theorist than incremental theorist and whether those who are math anxious will be more likely to be fixated on variables associated with coefficients? Path analysis and independent samples t-test will be used to generate results for this study. We hope to conclude that both the theories of intelligence and metacognition mediate the relationship between mathematics anxiety and gender stereotype threat.

Keywords: math anxiety, emotions, affective domains fo learning, cognitive underlinings

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Authors: Ezeamagu M.U, Madu B.C

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This study was designed to investigate the efficacy of 5Es constructivist-based instructional model on students’ retention in primary Mathematics. 5Es stands for Engagement, Exploration, Explanation, Elaboration and Evaluation. The study adopted the pre test post test non-equivalent control group quasi-experimental research design. The sample size for the study was one hundred and thirty four pupils (134), seventy six male (76) and fifty eight female (58) from two primary schools in Nsukka education zone. Two intact classes in each of the sampled schools comprising all the primary four pupils were used. Each of the schools was given the opportunity of being assigned randomly to either experimental or control group. The Experimental group was taught using 5Es model while the control group was taught using the conventional method. Two research questions were formulated to guide the study and three hypotheses were tested at p ≤ 0. 05. A Fraction Achievement Test (FAT) of ten (10) questions were used to obtain data on pupils’ retention. Research questions were answered using mean and standard deviation while hypotheses were tested using analysis of covariance (ANCOVA). The result revealed that the 5Es model was more effective than the conventional method of teaching in enhancing pupils’ performance and retention in mathematics, secondly there is no significant difference in the mean retention scores of male and female students taught using 5Es instructional model. Based on the findings, it was recommended among other things, that the 5Es instructional model should be adopted in the teaching of mathematics in primary level of the educational system. Seminar, workshops and conferences should be mounted by professional bodies, federal and state ministries of education on the use of 5Es model. This will enable the mathematics educator, serving teachers, students and all to benefit from the approach.

Keywords: constructivist, education, mathematics, primary, retention

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Authors: Early Sol A. Gadong, Lourdes C. Zamora, Jonny B. Pornel, Aurora Fe C. Bautista

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Various research has shown that writing allows students to engage in metacognition and provides them with a venue to communicate their disposition towards what they are learning. However, few studies have explored students’ feelings about the incorporation of such writing activities in their mathematics classes. Through reflection sheets, group discussions, and interviews, this mixed-methods study explored students’ perceptions and insights on supplementary writing activities in their Elementary Algebra class. Findings revealed that while students generally have a positive regard for writing activities, they have conflicting views about how writing activities can help them in their learning. A big majority contend that writing activities can enhance the learning of mathematical content and attitudes towards mathematics if they allow students to explore and synthesize what they have learned and reflected on their emotional disposition towards mathematics. Also, gender does not appear to play a significant role in students’ reactions to writing activities.

Keywords: writing in math, metacognition, affective factors in learning, elementary algebra classroom

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Authors: Ali Rashash Alzahrani, Elizabeth Stojanovski

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Data on various aspects of education are collected at the institutional and government level regularly. In Australia, for example, students at various levels of schooling undertake examinations in numeracy and literacy as part of NAPLAN testing, enabling longitudinal assessment of such data as well as comparisons between schools and states within Australia. Another source of educational data collected internationally is via the PISA study which collects data from several countries when students are approximately 15 years of age and enables comparisons in the performance of science, mathematics and English between countries as well as ranking of countries based on performance in these standardised tests. As well as student and school outcomes based on the tests taken as part of the PISA study, there is a wealth of other data collected in the study including parental demographics data and data related to teaching strategies used by educators. Overall, an abundance of educational data is available which has the potential to be used to help improve educational attainment and teaching of content in order to improve learning outcomes. A multivariate assessment of such data enables multiple variables to be considered simultaneously and will be used in the present study to help develop profiles of students based on performance in mathematics using data obtained from the PISA study.

Keywords: cluster analysis, education, mathematics, profiles

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Authors: Emmanuel Iyamuremye, Irenee Ndayambaje

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This study investigated the influence of Concrete Pictorial Abstract (CPA) teaching approach on mathematics achievement based on a sample of eighth-grade students (N = 10,345) from the Rwandan Lower Secondary School quasi-experimental study with pre-test and post-test control group of 2019 (RLSQES19). Key aspects studied included mathematics concept understanding and mathematics concept retention and how these are influenced by teacher's teaching approach. Specifically, the study aimed to a.) investigate students' concept understanding and concept retention in mathematics when exposed to CPA approach and to those exposed to non-CPA approach before and after the intervention, and b.) ascertain the significant difference between the performance of the students exposed to CPA approach and those exposed to non-CPA approach in terms of post-test scores and retention test scores. Two groups (control and experimental) undergone pre-test, post-test, and retention test. The assignment of control and experimental group among senior two classes from 10 schools was done randomly. The materials used to determine the performance of the students is a teacher-made test. Descriptive statistics and ANCOVA were used for the analysis of the study. For determining the improvement in concept understanding of mathematics, Hakes methods of calculating gain were used to analyze the pre-test and post test score. The level of performance of the two groups in the pre-test is below average level. During the post-test and retention test, the performance of students in non-CPA group is on average level, and students in CPA group are on above average level. Hakes methods of calculating gain revealed higher significant performance in the post-test and retention test of CPA group of students than non-CPA group of students.

Keywords: concept understanding, concept retention, performance, teaching approach

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Authors: Carol Okigbo

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Mathematical problem solving has long been accorded an important place in mathematics curricula at every education level in both advanced and emerging economies. Its classroom approaches have varied, such as teaching for problem-solving, teaching about problem-solving, and teaching mathematics through problem-solving. It requires engaging in tasks for which the solution methods are not eminent, making sense of problems and persevering in solving them by exhibiting processes, strategies, appropriate attitude, and adequate exposure. Teachers play important roles in helping students acquire competency in problem-solving; thus, they are expected to be good problem-solvers and have proper conceptions of problem-solving. Studies show that teachers’ conceptions influence their decisions about what to teach and how to teach. Therefore, how teachers view their roles in teaching problem-solving will depend on their pedagogical conceptions of problem-solving. If teaching problem-solving is a major component of secondary school mathematics instruction, as recommended by researchers and mathematics educators, then it is necessary to establish teachers’ conceptions, what they do, and how they approach problem-solving. This study is designed to determine secondary school teachers’ conceptions regarding mathematical problem solving, its current situation, how teachers’ conceptions relate to their demographics, as well as the interaction patterns in the mathematics classroom. There have been many studies of mathematics problem solving, some of which addressed teachers’ conceptions using single-method approaches, thereby presenting only limited views of this important phenomenon. To address the problem more holistically, this study adopted an integrated mixed methods approach which involved a quantitative survey, qualitative analysis of open-ended responses, and ethnographic observations of teachers in class. Data for the analysis came from a random sample of 327 secondary school mathematics teachers in two Nigerian states - Anambra State and Enugu State who completed a 45-item questionnaire. Ten of the items elicited demographic information, 11 items were open-ended questions, and 25 items were Likert-type questions. Of the 327 teachers who responded to the questionnaires, 37 were randomly selected and observed in their classes. Data analysis using ANOVA, t-tests, chi-square tests, and open coding showed that the teachers had different conceptions about problem-solving, which fall into three main themes: practice on exercises and word application problems, a process of solving mathematical problems, and a way of teaching mathematics. Teachers reported that no period is set aside for problem-solving; typically, teachers solve problems on the board, teach problem-solving strategies, and allow students time to struggle with problems on their own. The result shows a significant difference between male and female teachers’ conception of problems solving, a significant relationship among teachers’ conceptions and academic qualifications, and teachers who have spent ten years or more teaching mathematics were significantly different from the group with seven to nine years of experience in terms of their conceptions of problem-solving.

Keywords: conceptions, education, mathematics, problem solving, teacher

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Authors: Ayşegül Çabuk, Mine Işıksal

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Mathematics is a sense-making activity so that it requires meaningful learning. Hence based on this idea, meaningful mathematical connections are necessary to learn mathematics. At that point, the major question has become that which educational methods can provide opportunities to provide mathematical connections and to understand mathematics. The amalgam of reasoning and proof can be the one of the methods that creates opportunities to learn mathematics in a meaningful way. However, even if reasoning and proof should be included from prekindergarten to grade 12, studies in literature generally include secondary school students and pre-service mathematics teachers. With the light of the idea that the amalgam of reasoning and proof has significant effect on middle school students' mathematical learning, this study aims to investigate middle grade students' tendencies while reasoning the correctness of statements related to numbers. The sample included 272 middle grade students, specifically 69 of them were sixth grade students (25.4%), 101 of them were seventh grade students (37.1%) and 102 of them were eighth grade students (37.5%). Data was gathered through an achievement test including 2 essay types of problems about algebra. The answers of two items were analyzed both quantitatively and qualitatively in terms of students' solutions strategies while reasoning the correctness of the statements. Similar on the findings in the literature, most of the students, in all grade levels, used numerical examples to judge the statements. Moreover the results also showed that the majority of these students appear to believe that providing one or more selected examples is sufficient to show the correctness of the statement. Hence based on the findings of the study, even students in earlier ages have proving and reasoning abilities their reasoning's generally based on the empirical evidences. Therefore, it is suggested that examples and example-based reasoning can be a fundamental role on to generate systematical reasoning and proof insight in earlier ages.

Keywords: reasoning, mathematics learning, middle grade students

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Authors: Zahid Ullah, Atlas Khan

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In today's data-driven world, the role of mathematics in bridging the gap between theory and applications is becoming increasingly vital. This abstract highlights the significance of mathematics as a powerful tool for analyzing, interpreting, and extracting meaningful insights from vast amounts of data. By integrating mathematical principles with real-world applications, researchers can unlock the full potential of data-driven decision-making processes. This abstract delves into the various ways mathematics acts as a bridge connecting theoretical frameworks to practical applications. It explores the utilization of mathematical models, algorithms, and statistical techniques to uncover hidden patterns, trends, and correlations within complex datasets. Furthermore, it investigates the role of mathematics in enhancing predictive modeling, optimization, and risk assessment methodologies for improved decision-making in diverse fields such as finance, healthcare, engineering, and social sciences. The abstract also emphasizes the need for interdisciplinary collaboration between mathematicians, statisticians, computer scientists, and domain experts to tackle the challenges posed by the data-driven landscape. By fostering synergies between these disciplines, novel approaches can be developed to address complex problems and make data-driven insights accessible and actionable. Moreover, this abstract underscores the importance of robust mathematical foundations for ensuring the reliability and validity of data analysis. Rigorous mathematical frameworks not only provide a solid basis for understanding and interpreting results but also contribute to the development of innovative methodologies and techniques. In summary, this abstract advocates for the pivotal role of mathematics in bridging theory and applications in a data-driven world. By harnessing mathematical principles, researchers can unlock the transformative potential of data analysis, paving the way for evidence-based decision-making, optimized processes, and innovative solutions to the challenges of our rapidly evolving society.

Keywords: mathematics, bridging theory and applications, data-driven world, mathematical models

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Authors: Ahmet Erdoğan, Şahin Kesici, Mustafa Baloğlu

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Information technologies have lead to changes in the areas of communication, learning, and teaching. Besides offering many opportunities to the learners, these technologies have changed the teaching methods and beliefs of teachers. What the Technological Pedagogical Content Knowledge (TPACK) means to the teachers is considerably important to integrate technology successfully into teaching processes. It is necessary to understand how to plan and apply teacher training programs in order to balance students’ pedagogical and technological knowledge. Because of many inefficient teacher training programs, teachers have difficulties in relating technology, pedagogy and content knowledge each other. While providing an efficient training supported with technology, understanding the three main components (technology, pedagogy and content knowledge) and their relationship are very crucial. The purpose of this study is to determine whether motivational beliefs and self-regulated learning strategies are significant predictors of mathematics teacher candidates' TPACK perceptions. A hundred seventy five Turkish mathematics teachers candidates responded to the Motivated Strategies for Learning Questionnaire (MSLQ) and the Technological Pedagogical And Content Knowledge (TPACK) Scale. Of the group, 129 (73.7%) were women and 46 (26.3%) were men. Participants' ages ranged from 20 to 31 years with a mean of 23.04 years (SD = 2.001). In this study, a multiple linear regression analysis was used. In multiple linear regression analysis, the relationship between the predictor variables, mathematics teacher candidates' motivational beliefs, and self-regulated learning strategies, and the dependent variable, TPACK perceptions, were tested. It was determined that self-efficacy for learning and performance and intrinsic goal orientation are significant predictors of mathematics teacher candidates' TPACK perceptions. Additionally, mathematics teacher candidates' critical thinking, metacognitive self-regulation, organisation, time and study environment management, and help-seeking were found to be significant predictors for their TPACK perceptions.

Keywords: candidate mathematics teachers, motivational beliefs, self-regulated learning strategies, technological and pedagogical knowledge, content knowledge

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Authors: Siriwan Chatmaneerungcharoen

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An emerging body of ‘21st century skills’-such as adaptability, complex communication skills, technology skills and the ability to solve non-routine problems--are valuable across a wide range of jobs in the national economy. Within the Thai context, a focus on the Philosophy of Sufficiency Economy is integrated into Science Education. Thai science education has advocated infusing 21st century skills and Philosophy of Sufficiency Economy into the school curriculum and several educational levels have launched such efforts. Therefore, developing science teachers to have proper knowledge is the most important factor to success of the goals. The purposes of this study were to develop 40 Cooperative Science teachers’ Technological Pedagogical Content Knowledge (TPACK) and to develop Professional Development Model integrated with Co-teaching Model and Coaching System (Co-TPACK). TPACK is essential to career development for teachers. Forty volunteer In-service teachers who were science cooperative teachers participated in this study for 2 years. Data sources throughout the research project consisted of teacher refection, classroom observations, Semi-structure interviews, Situation interview, questionnaires and document analysis. Interpretivist framework was used to analyze the data. Findings indicate that at the beginning, the teachers understood only the meaning of Philosophy of Sufficiency Economy but they did not know how to integrate the Philosophy of Sufficiency Economy into their science classrooms. Mostly, they preferred to use lecture based teaching and experimental teaching styles. While the Co- TPACK was progressing, the teachers had blended their teaching styles and learning evaluation methods. Co-TPACK consists of 3 cycles (Student Teachers’ Preparation Cycle, Cooperative Science Teachers Cycle, Collaboration cycle (Co-teaching, Co-planning, and Co-Evaluating and Coaching System)).The Co-TPACK enhances the 40 cooperative science teachers, student teachers and university supervisor to exchange their knowledge and experience on teaching science. There are many channels that they used for communication including online. They have used more Phuket context-integrated lessons, technology-integrated teaching and Learning that can explicit Philosophy of Sufficiency Economy. Their sustained development is shown in their lesson plans and teaching practices.

Keywords: technological pedagogical content knowledge, philosophy of sufficiency economy, professional development, coaching system

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Authors: Sisay Tamrat Ayalew

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This paper explores the concept of humanism as a guiding philosophy in education, specifically focusing on Ethiopian Higher Education Institutions (EHEIs). It highlights the perceived lack of humanistic elements within the educational system and the resulting intellectual and moral decay among students. The aim of this study is to critically reflect on the essence of humanism and its relevance to Ethiopian higher education. By examining the philosophy and practice of humanism, the paper seeks to evaluate the existing state of EHEIs in relation to this educational approach. The methodology employed in this research is qualitative. The study relies primarily on literature review and analysis of policy documents to gain insights into the subject matter. A hermeneutic approach is utilized to interpret the realities observed in various contexts. The key finding of this paper is that Ethiopian higher education institutions lack humanistic elements in their educational practices. This deficiency contributes to the overall moral and intellectual decay among students. The study accentuates that humanism is not merely an optional extra but an essential tool for creating a clean academic environment and fostering the holistic development of students.

Keywords: humanism, higher education, human dignity, intellectual decadence, moral sickness

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