Search results for: philosophy of mathematics

Authors: Mohini Mohamed, Nurul Huda Mas’od

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This study was aimed at designing and developing an assistive mathematical teaching aid (courseware) in helping dyslexic students in learning multiplication. Computers and multimedia interactive courseware has benefits students in terms of increase learner’s motivation and engage them to stay on task in classroom. Most disability student has short attention span thus with the advantage offered by multimedia interactive courseware allows them to retain the learning process for longer period as compared to traditional chalk and talk method. This study was conducted in a public school at a primary level with the help of three special education teachers and six dyslexic students as participants. Qualitative methodology using interview with special education teachers and observations in classes were conducted. The development of the multimedia interactive courseware in this study was divided to three processes which were analysis and design, development and evaluation. The courseware was evaluated by using User Acceptance Survey Form and interview. Feedbacks from teachers were used to alter, correct and develop the application for a better multimedia interactive courseware.

Keywords: disability students, dyslexia, mathematics teaching aid, multimedia interactive courseware

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Authors: Karen Koellner, Nanette Seago, Jennifer Jacobs, Helen Garnier

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Although studies of teacher professional development (PD) are prevalent, surprisingly most have only produced incremental shifts in teachers’ learning and their impact on students. There is a critical need to understand what teachers take up and use in their classroom practice after attending PD and why we often do not see greater changes in learning and practice. This paper is based on a mixed methods efficacy study of the Learning and Teaching Geometry (LTG) video-based mathematics professional development materials. The extent to which the materials produce a beneficial impact on teachers’ mathematics knowledge, classroom practices, and their students’ knowledge in the domain of geometry through a group-randomized experimental design are considered. Included is a close-up examination of a small group of teachers to better understand their interpretations of the workshops and their classroom uptake. The participants included 103 secondary mathematics teachers serving grades 6-12 from two US states in different regions. Randomization was conducted at the school level, with 23 schools and 49 teachers assigned to the treatment group and 18 schools and 54 teachers assigned to the comparison group. The case study examination included twelve treatment teachers. PD workshops for treatment teachers began in Summer 2016. Nine full days of professional development were offered to teachers, beginning with the one-week institute (Summer 2016) and four days of PD throughout the academic year. The same facilitator-led all of the workshops, after completing a facilitator preparation process that included a multi-faceted assessment of fidelity. The overall impact of the LTG PD program was assessed from multiple sources: two teacher content assessments, two PD embedded assessments, pre-post-post videotaped classroom observations, and student assessments. Additional data were collected from the case study teachers including additional videotaped classroom observations and interviews. Repeated measures ANOVA analyses were used to detect patterns of change in the treatment teachers’ content knowledge before and after completion of the LTG PD, relative to the comparison group. No significant effects were found across the two groups of teachers on the two teacher content assessments. Teachers were rated on the quality of their mathematics instruction captured in videotaped classroom observations using the Math in Common Observation Protocol. On average, teachers who attended the LTG PD intervention improved their ability to engage students in mathematical reasoning and to provide accurate, coherent, and well-justified mathematical content. In addition, the LTG PD intervention and instruction that engaged students in mathematical practices both positively and significantly predicted greater student knowledge gains. Teacher knowledge was not a significant predictor. Twelve treatment teachers self-selected to serve as case study teachers to provide additional videotapes in which they felt they were using something from the PD they learned and experienced. Project staff analyzed the videos, compared them to previous videos and interviewed the teachers regarding their uptake of the PD related to content knowledge, pedagogical knowledge and resources used. The full paper will include the case study of Ana to illustrate the factors involved in what teachers take up and use from participating in the LTG PD.

Keywords: geometry, mathematics professional development, pedagogical content knowledge, teacher learning

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Authors: Verónica Díaz Quezada

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The importance given to the development of the problem solving skill and the requirement to solve problems framed in mathematical or real life contexts, in practice, they are not evidence in relation to the teaching of proportional variations. This qualitative and descriptive study aims to (1) to improve problem solving ability of high school students in Chile, (ii) to elaborate and describe a didactic intervention strategy based on learning situations in proportional variations, focused on solving types of routine problems of various contexts and non-routine problems. For this purpose, participant observation was conducted, test of mathematics problems and an opinion questionnaire to thirty-six high school students. Through the results, the highest academic performance is evidenced in the routine problems of purely mathematical context, realistic, fantasy context, and non-routine problems, except in the routine problems of real context and compound proportionality problems. The results highlight the need to consider in the curriculum different types of problems in the teaching of mathematics that relate the discipline to everyday life situations

Keywords: algebra, high school, proportion variations, nonroutine problem solving, routine problem solving

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Authors: Muhammad Akram, Qamar Naseem, Imtiaz Ahmad

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The purpose of this study was to correlate students’ perceptions of teacher effectiveness with their academic achievement in English and Mathematics at the secondary level (grade 9th) based on five national professional standards for teacher evaluation in Pakistan (subject matter knowledge, instructional planning and strategies, assessment, learning environment, effective communication. A Students’ Perceptions of Teacher Effectiveness Questionnaire (SPTEQ) was developed by the researchers to collect data from 2009 students from forty public girls and boys high/ higher secondary schools in district Khanewal, Pakistan. The overall reliability of the SPTEQ was α=.86. The study found a significant positive relationship among all the five factors of teacher effectiveness construct. The study also showed significant, positive relationship between teacher effectiveness factors and students’ achievement in English and mathematics. No significant differences were found between male and female students’ perceptions about their English teacher effectiveness. The implications include students’ personal attachments with their teachers that might convince them to overrate their teachers.

Keywords: communication, students’ achievement, teacher effectiveness, teaching strategies, teaching strategies

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Authors: Thiago R. Pereira

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The philosophical hermeneutics is able to change the Brazilian Judiciary because of the understanding of the characteristics of the human being. It is impossible for humans, to be invested in the function of being a judge, making absolutely neutral decisions, but the philosophical hermeneutics can assist the judge making impartial decisions, based on the federal constitution. The normative legal positivism imagined a neutral judge, a judge able to try without any preconceived ideas, without allowing his/her background to influence him/her. When a judge arbitrates based on legal rules, the problem is smaller, but when there are no clear legal rules, and the judge must try based on principles, the risk of the decision is based on what they believe in. Solipsistically, this issue gains a huge dimension. Today, the Brazilian judiciary is independent, but there must be a greater knowledge of philosophy and the philosophy of law, partially because the bigger problem is the unpredictability of decisions made by the judiciary. Actually, when a lawsuit is filed, the result of this judgment is absolutely unpredictable. It is almost a gamble. There must be the slightest legal certainty and predictability of judicial decisions, so that people, with similar cases, may not receive opposite sentences. The relativism, since classical antiquity, believes in the possibility of multiple answers. Since the Greeks in in the sixth century before Christ, through the Germans in the eighteenth century, and even today, it has been established the constitution as the great law, the Groundnorm, and thus, the relativism of life can be greatly reduced when a hermeneut uses the Constitution as North interpretational, where all interpretation must act as the hermeneutic constitutional filter. For a current philosophy of law, that inside a legal system with a Federal Constitution, there is a single correct answer to a specific case. The challenge is how to find this right answer. The only answer to this question will be that we should use the constitutional principles. But in many cases, a collision between principles will take place, and to resolve this issue, the judge or the hermeneut will choose a solipsism way, using what they personally believe to be the right one. For obvious reasons, that conduct is not safe. Thus, a theory of decision is necessary to seek justice, and the hermeneutic philosophy and the linguistic turn will be necessary for one to find the right answer. In order to help this difficult mission, it will be necessary to use philosophical hermeneutics in order to find the right answer, which is the constitutionally most appropriate response. The constitutionally appropriate response will not always be the answer that individuals agree to, but we must put aside our preferences and defend the answer that the Constitution gives us. Therefore, the hermeneutics applied to Law, in search constitutionally appropriate response, should be the safest way to avoid judicial individual decisions. The aim of this paper is to present the science of law starting from the linguistic turn, the philosophical hermeneutics, moving away from legal positivism. The methodology used in this paper is qualitative, academic and theoretical, philosophical hermeneutics with the mission to conduct research proposing a new way of thinking about the science of law. The research sought to demonstrate the difficulty of the Brazilian courts to depart from the secular influence of legal positivism. Moreover, the research sought to demonstrate the need to think science of law within a contemporary perspective, where the linguistic turn, philosophical hermeneutics, will be the surest way to conduct the science of law in the present century.

Keywords: hermeneutic, right answer, solipsism, Brazilian judiciary

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Authors: Marie-Josée Morneau

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A literacy-based approach, centred on the use of the language of instruction as a cognitive tool, can increase the L2 communication skills of French immersion students. Academic subject areas such as science and mathematics offer an authentic language learning context where students can become more proficient speakers while using specific vocabulary and language structures to learn, interact and communicate their reasoning, when provided the opportunities and guidance to do so. In this Canadian quasi-experimental study, the effects of teaching specific language elements during mathematic classes through literacy-based activities in Early French Immersion programming were compared between two Grade 7/8 groups: the experimental group, which received literacy-based teaching for a 6-week period, and the control group, which received regular teaching instruction. The results showed that the participants from the experimental group made more progress in their mathematical communication skills, which suggests that targeting L2 language as a cognitive tool can be beneficial to immersion learners who learn mathematic concepts and remind us that all L2 teachers are language teachers.

Keywords: mathematics, French immersion, literacy-based, oral communication, L2

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Authors: Haofei Li

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To support academic growth and foster love of learning, MathMates has been introduced for grade 6-8 students at Andrew Hamilton public school in 2022. The program is targeted at students from diverse backgrounds, particularly those underperforming in Pennsylvania System of School Assessment (PSSA) exams. Then, this study aims to evaluate the efficacy of MathMates by comparing student performance on the PSSA test, before and after the intervention. Through a randomized control trial, the study will collect associated costs using the ingredients method and measure the effectiveness for cost-effectiveness analysis. Text messages will be sent to parents/guardians as a reminder of the program and to encourage student participation. The findings of this study will provide valuable insights for funding organizations seeking to understand the impact and costs of math tutoring interventions on student academic achievement, which also emphasizes the importance of the collaborative efforts between higher education and local public schools.

Keywords: mathematics education, mathematics tutoring, college-community initiative, middle schools, Philadelphia public schools, after-school program, PSSA

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Authors: Santiago Moll Lopez, Erica Vega Fleitas, Dolors Rosello Ferragud, Luis Manuel Sanchez Ruiz, Jose Antonio Moraño Fernandez

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Game-based learning (GBL) is becoming popular in education. Learning through games offers students a motivating experience related to the social aspect of games. Among the significant positive outcomes are promoting positive emotions and collaboration, improving the assimilation of concepts, and creating an attractive and dynamic environment standout. This work presents a study of the design and implementation of games created with RPG Maker MZ software with a Sci-Fi storytelling environment for developing specific and transversal skills in a Mathematics subject at the Beng in Aerospace Engineering. Games were applied during regular classes and as a part of a Flip-Teaching methodology to increase the motivation and the assimilation of mathematical concepts in an engaging way. The key features of the games were the introduction of avatar design and the promotion of collaboration among students. Students' opinions and grades obtained in the activities and exams showed increased motivation and a significant improvement in their performance compared with other groups or past students' performances.

Keywords: game-based learning, rol games, mathematics, science fiction

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Authors: Wajeeh Daher, Nimer Baya'a

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High Order Thinking Skills (HOTS) are suggested today as essential for the cognitive development of students and as preparing them for real life skills. Teachers are encouraged to use HOTS activities in the classroom to help their students develop higher order skills and deep thinking. So it is essential to prepare pre-service teachers to write and use HOTS activities for their students. This paper describes a model for integrating HOTS activities with GeoGebra in pre-service teachers’ preparation. This model describes four aspects of HOTS activities and working with them: Activity components, preparation procedure, strategies and processes used in writing a HOTS activity and types of the HOTS activities. In addition, the paper describes the pre-service teachers' difficulties in preparing and working with HOTS activities, as well as their perceptions regarding the use of these activities and GeoGebra in the mathematics classroom. The paper also describes the contribution of a HOTS activity to pupils' learning of mathematics, where this HOTS activity was prepared and taught by one pre-service teacher.

Keywords: high order thinking skills, HOTS activities, pre-service teachers, professional development

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Authors: Nodi Islam

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This paper critically reads Rumi’s poems in The Masnavi (Book One) and the philosophy of master-disciple relationship, as reflected as a medium to attain the higher consciousness in the poems which is considered as spiritual by the Sufi practitioners. This paper further applies the concept of collective consciousness introduced by Durkheim, which stands for a set of beliefs, ideas, moral attitudes that operate as a unifying force in a certain society, in reading Rumi’s poems. According to Sufi philosophy, in order to reach to the beloved who is the Higher Being, a lover has to be a disciple of a master and dedicate himself completely even if it means to give up the earthly desires. When the process is completed, he achieves the divinity which is the utmost happiness to be one with the beloved. As this process is considered spiritual by the Sufi practitioners, this paper suggests that, apart from being spiritual, this is a reflection of collective consciousness also. This process plays a part to construct the collectivity as a means to create masters and disciples. Collective consciousness operates in this particular belief system of Sufis who tend to follow this phenomenon as a rule of obedience and accepts the rule because this is how their particular community proceeds on. This paper offers a view of Rumi’s poems which reflect such relationship and tends to offer a general discussion on the hegemonic approach of the Sufi society especially of the Mevlevi order. Finally, this paper offers a constructive representation of Mevlevi society based upon the idea of spirituality which could be an outcome of psychological and social issues and practices.

Keywords: collective consciousness, divinity, master-disciple relationship, Mevlevi order

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Authors: Richard Harrison

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Developing competency in mathematics and related critical thinking skills is essential to the education of undergraduate students of Science, Technology, Engineering and Mathematics (STEM). Recently, the HE sector has been impacted by a seemingly widening disconnect between the mathematical competency of incoming first-year STEM students and their entrance qualification tariffs. Despite relatively high grades in A-Level Mathematics, students may initially lack fundamental skills in key areas such as algebraic manipulation and have limited capacity to apply problem solving strategies. Compounded by compensatory measures applied to entrance qualifications during the pandemic, there has been an associated decline in student performance on introductory university mathematics modules. In the UK, a number of online resources have been developed to help scaffold the transition to university mathematics. However, in general, these do not offer a structured learning journey focused on individual developmental needs, nor do they offer an experience coherent with the teaching and learning characteristics of the destination institution. In order to address some of these issues, a bespoke framework has been designed and implemented on our VLE in the Faculty of Engineering & Physical Sciences (FEPS) at the University of Surrey. Called the FEPS Maths Support Framework, it was conceived to scaffold the mathematical development of individuals prior to entering the university and during the early stages of their transition to undergraduate studies. More than 90% of our incoming STEM students voluntarily participate in the process. Students complete a set of initial diagnostic questions in the late summer. Based on their performance and feedback on these questions, they are subsequently guided to self-select specific mathematical topic areas for review using our proprietary resources. This further assists students in preparing for discipline related diagnostic tests. The framework helps to identify students who are mathematically weak and facilitates early intervention to support students according to their specific developmental needs. This paper presents a summary of results from a rich data set captured from the framework over a 3-year period. Quantitative data provides evidence that students have engaged and developed during the process. This is further supported by process evaluation feedback from the students. Ranked performance data associated with seven key mathematical topic areas and eight engineering and science discipline areas reveals interesting patterns which can be used to identify more generic relative capabilities of the discipline area cohorts. In turn, this facilitates evidence based management of the mathematical development of the new cohort, informing any associated adjustments to teaching and learning at a more holistic level. Evidence is presented establishing our framework as an effective early intervention strategy for addressing the sector-wide issue of supporting the mathematical development of STEM students transitioning to HE

Keywords: competency, development, intervention, scaffolding

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Authors: Bhaddiya Tanchangya

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This article discusses the Four Noble Truths, the foundational teachings of Buddhism, and their significance to Buddhist philosophy. The Four Noble Truths are the Noble Truth of Suffering, the Noble Truth of the Cause of Suffering, the Noble Truth of the End of Suffering, and the Noble Truth of the Path Leading to the End of Suffering. The first truth, the Noble Truth of Suffering, explains that suffering or dukkha is an inherent part of existence, including emotional, physical, and existential forms of suffering, including the Five Aggregates, which refer to the five components that make up a sentient being's experience of existence, as they are all conditioned, interdependent, subject to the Three Characteristics of Existence: impermanence, unsatisfactoriness and emptiness. The second truth, the Noble Truth of the Cause of Suffering, states that craving or attachment to the sensory experiences of the Five Aggregates leads to suffering and identifies three types of craving: craving for sensual pleasures, craving for existence, and craving for non-existence. Through the doctrine of Dependent Origination (Paṭiccasamuppāda), the Buddha graphically shows how the entire process of suffering arises and ceases. The third truth, the Noble Truth of the End of Suffering, asserts that there is a way to end suffering and attain a state of liberation called Nibbāna that marks the end of the cycle of birth and death by removing that very craving towards the sensory experiences by cultivating the Noble Eightfold Path. The fourth truth, the Noble Truth of the Path Leading to the End of Suffering, describes the Noble Eightfold Path, a set of guidelines to develop insight and wisdom to overcome craving and attachment and attain liberation from suffering. The article emphasizes that the Four Noble Truths are universal, applicable to all people regardless of culture, background, or beliefs, and form the foundation of Buddhist philosophy and practice.

Keywords: four noble truths, impermanence, suffering, not-self-ness, interconnectedness, emptiness, morality, concentration, wisdom, nirvana, happiness

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Authors: Zawahir Siddique

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The paper explores the philosophical, spiritual, and mystical dimensions of the glorified journey of Hajira and Bilal. The black Ethiopian slave Hajira’s skirt was chosen to cover the first house of God on earth. Hajira was chosen by God as the embodiment of love and submission. The philosophy behind her migration with her child Ismail and wandering between Safa and Marwa in search of water that eventually gushed forth from the feet of Ismail and how God gifted Hajira, Ismail, and the entire humanity with Zamzam needs to be explored. Every year over two million pilgrims assemble and circumambulate around the Holy Kabah during Hajj, and every day, millions of Muslims pray, riveting their faith around Kabah. The significance and mysticism of the central figure of Hajira deserve due attention. Several eras later, the most blessed personality of humanity, Prophet Muhammad, elevated another Ethiopian Slave to the highest honor in the first Mosque of the Prophet of Islam in Medina. The purity of his heart and spiritually captivating voice of Bilal was preferred over his pre-Islamic social status. When the companions of the Prophet questioned the diction and pronunciation of 'SHEEN' by Bilal owing to his African origin, the Prophet immediately corrected them, justifying the purity of Bilal’s heart mattered more and hence Bilal’s 'SEEN' was heard as 'SHEEN' by God Almighty. The journey of Bilal to Islam and his pious and devoted contributions to Islam in the light of spirituality, mysticism, and social reforms are also explored further in this paper.

Keywords: philosophy, spirituality, mysticism, Hajira, Bilal

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Authors: Aida Nurul Safitri, Rosita Sari

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Physics is science, which in its learning there are some product such as theory, fact, concept, law and formula. So that to understand physics lesson students not only need a theory or concept but also mathematical calculation to solve physics problem through formula or equation. This is can be taken from mathematics lesson which obtained by students. This research is to know the influence of mathematics learning outcomes towards physics ability in Senior High School through authentic assessment system. Based on the researches have been discussed, is obtained that mathematic lesson have an important role in physics learning but it according to one aspect only, namely cognitive aspect. In Indonesia, curriculum of 2013 reinforces displacement in the assessment, from assessment through test (measuring the competence of knowledge based on the result) toward authentic assessment (measuring the competence of attitudes, skills, and knowledge based on the process and results). In other researches are mentioned that authentic assessment system give positive responses for students to improve their motivation and increase the physics learning in the school.

Keywords: authentic assessment, curriculum of 2013, mathematic, physics

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Authors: Ayoub Kafyulilo, Petra Fisser, Joke Voogt

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This study was conducted to assess the continuation of the use of technology in science and mathematics teaching of the pre-service and in-service teachers who attended the professional development programme. It also assessed professional development, personal, institutional, and technological factors contributing to the continuous use of technology in teaching. The study involved 42 teachers, thirteen pre-service teachers, and twenty-nine in-service teachers. A mixed-method research approach was used to collect data for this study. Findings showed that the continuous use of technology in teaching after the termination of the professional development arrangement was high among the pre-service teachers, and differed for the in-service teachers. The regression model showed that knowledge and skills, access to technology and ease of use were strong predictors (R2 = 55.3%) of the teachers’ continuous use of technology after the professional development arrangement. The professional development factor did not have a direct effect on the continuous use of technology, rather had an influence on personal factors (knowledge and skills). In turn, the personal factors had influence on the institutional factors (access to technology) and technological factors (ease of use), which together had an effect on the teachers’ continuous use of technology in teaching.

Keywords: technology, professional development, teachers, science and mathematics

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Authors: Linto Francis Kallukulangara

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Although the Catholic and Reformed traditions share a common baptismal heritage, they differe considerably in their epistemic stance on whether a believer can legitimatly subscribe to a proposition of Christian Revelation without any evidence. Catholic tradition, which is essentially rooted in the internalist epistemology, posits that a theistic belief must be substantiated by a rational ground that is cognitively accessible to the believer. In contrast, Reformed thinkers have historically maintained a non-evidentialist stance, which has received strong criticism, including allegations of irrationality. However, recent developments in analytic philosophy, particularly the rise of externalist epistemology, have revitalized the non-evidentialist position within the Reformed tradition. The intellectual allure of this movement has led many contemporary thinkers to argue that the Catholic internalist/evidentialist position has not only been significantly challenged but has also been largely silenced by this externalism-based Reformed epistemological stance. Consequently, they argue that the non-cogntive Reformed currect has established itself as the dominant, or perhaps the only, epistemological position in the philosophy of religion. This paper counters the prevailing narrative, arguing that despite the ostensible challenge posed by Reformed non-evidentialism, a synthesis is possible. By analyzing various Reformed epistemological movements within the contemporary anaytic tradtion, we demonstrate that externalist-based Reformed epistemology does not fundamentally undermine Catholic evidentialism. Instead, it offers a new and more promising framework for a Christian epistemology that sythesizes elements from both traditions, offering a more comprehensive and nuanced understing of the justification of religion belief, incoperating both internalist and externalist perspective.

Keywords: reformed and catholic epistemology, evidentialism, non-evidentialism, internalism, externalism

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Authors: Zeite Shumneiyang Koireng

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Liberation is the act of liberating or the state of being liberated. Indian philosophy, in general, understands liberation as moksa, which etymological is derived from the Sanskrit root muc+ktin meaning to loose, set free, to let go, discharge, release, liberate, deliver, etc. According to Indian schools of thought, moksa is the highest value on realizing which nothing remains to be realized. It is the cessation of birth and death, all kinds of pain and at the same time, it is the realization of one’s own self. Sankara’s Advaita philosophy is based on the following propositions: Brahman is the only Reality; the world has apparent reality, and the soul is not different from Brahman. According to Sankara, Brahman is the basis on which the world form appears; it is the sustaining ground of all various modification. It is the highest self and the self of all reveals himself by dividing himself [ as it was in the form of various objects] in multiple ways. The whole world is the manifestation of the Supreme Being. Brahman modifying itself into the Atman or internal self of all things is the world. Since Brahman is the Upadhana karana of the world, the sruti speaks of the world as the modification of Brahman into the Atman of the effect. Contemplation as the fulfillment of man finds a radical foundation in Aquinas teaching concerning the natural end or as he also referred to it, natural desire. The third book of the Summa Contra Gentiles begins the study of happiness with a consideration of natural desire. According to him, all creatures, even those devoid of understanding are ordered to God as an ultimate end. Intrinsically, a part of every nature is a tendency or inclination, originating in the natural form and tendency toward the end for which the possessor of nature exists. It is the study of the nature and finality of inclination that Aquinas establishes through an argument of induction man’s Contemplation of God as the fulfillment of his nature. The present paper is attempted to critically approach two important, seminal and originated thought, representing Indian and Western traditions which mark on the thinking of their respective times. Both these thoughts- Advaitic concept of Liberation in the Indian tradition and the concept of Contemplation in Thomas Aquinas’ Summa Contra Gentiles’- confront directly the question of the ultimate meaning of human existence. According to Sankara, it is knowledge and knowledge alone which is the means of moksa and the highest knowledge is moksa itself. Liberation in Sankara Vedanta is attained as a process of purification of self, which gradually and increasingly turns into purer and purer intentional construction. Man’s inner natural tendency for Aquinas is towards knowledge. The human subject is driven to know more and more about reality and in particular about the highest reality. Contemplation of this highest reality is fulfillment in the philosophy of Aquinas. Rather, Contemplation is the perfect activity in man’s present state of existence.

Keywords: liberation, Brahman, contemplation, fulfillment

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Authors: Mário Ernesto Sitoe, Orlando Zacarias

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University education is influenced by several factors that range from the adoption of strategies to strengthen the whole process to the academic performance improvement of the students themselves. This work uses data mining techniques to develop a predictive model to identify students with a tendency to evasion and retention. To this end, a database of real students’ data from the Department of University Admission (DAU) and the Department of Mathematics and Informatics (DMI) was used. The data comprised 388 undergraduate students admitted in the years 2009 to 2014. The Weka tool was used for model building, using three different techniques, namely: K-nearest neighbor, random forest, and logistic regression. To allow for training on multiple train-test splits, a cross-validation approach was employed with a varying number of folds. To reduce bias variance and improve the performance of the models, ensemble methods of Bagging and Stacking were used. After comparing the results obtained by the three classifiers, Logistic Regression using Bagging with seven folds obtained the best performance, showing results above 90% in all evaluated metrics: accuracy, rate of true positives, and precision. Retention is the most common tendency.

Keywords: evasion and retention, cross-validation, bagging, stacking

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Authors: Jane Larkin

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Combining elements of philosophy, science, and creative writing, this investigation explores how a philosophically structured science-fiction novel can challenge the theory of linearity and singularity of time through the ‘many worlds’ theory. This concept is addressed through the creation of a research exegesis and accompanying creative artefact, designed to be read in conjunction with each other in an explorative, interwoven manner. Research undertaken into scientific concepts, such as the ‘many worlds’ interpretation of quantum mechanics and diverse philosophers and their ideologies on time, is embodied in an original science-fiction narrative titled, It Goes On. The five frames that make up the creative artefact are enhanced not only by five leading philosophers and their philosophies on time but by an appreciation of the research, which comes first in the paper. Research into traditional approaches to storytelling is creatively and innovatively inverted in several ways, thus challenging the singularity and linearity of time. Further nonconventional approaches to literary techniques include an abstract narrator, embodied by time, a concept, and a figure in the text, whose voice and vantage point in relation to death furthers the unreliability of the notion of time. These further challenge individuals’ understanding of complex scientific and philosophical views in a variety of ways. The science-fiction genre is essential when considering the speculative nature of It Goes On, which deals with parallel realities and is a fantastical exploration of human ingenuity in plausible futures. Therefore, this paper documents the research-led methodology used to create It Goes On, the application of the ‘many worlds’ theory within a framed narrative, and the many innovative techniques used to contribute new knowledge in a variety of fields.

Keywords: time, many-worlds theory, Heideggerian philosophy, framed narrative

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Authors: C.Ardil

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Open Science translates the understanding and application of various theories and practices in open science philosophy, systems, paradigms and epistemology. Open Science originates with the premise that universal scientific knowledge is a product of a collective scholarly and social collaboration involving all stakeholders and knowledge belongs to the global society. Scientific outputs generated by public research are a public good that should be available to all at no cost and without barriers or restrictions. Open Science has the potential to increase the quality, impact and benefits of science and to accelerate advancement of knowledge by making it more reliable, more efficient and accurate, better understandable by society and responsive to societal challenges, and has the potential to enable growth and innovation through reuse of scientific results by all stakeholders at all levels of society, and ultimately contribute to growth and competitiveness of global society. Open Science is a global movement to improve accessibility to and reusability of research practices and outputs. In its broadest definition, it encompasses open access to publications, open research data and methods, open source, open educational resources, open evaluation, and citizen science. The implementation of open science provides an excellent opportunity to renegotiate the social roles and responsibilities of publicly funded research and to rethink the science system as a whole. Open Science is the practice of science in such a way that others can collaborate and contribute, where research data, lab notes and other research processes are freely available, under terms that enable reuse, redistribution and reproduction of the research and its underlying data and methods. Open Science represents a novel systematic approach to the scientific process, shifting from the standard practices of publishing research results in scientific publications towards sharing and using all available knowledge at an earlier stage in the research process, based on cooperative work and diffusing scholarly knowledge with no barriers and restrictions. Open Science refers to efforts to make the primary outputs of publicly funded research results (publications and the research data) publicly accessible in digital format with no limitations. Open Science is about extending the principles of openness to the whole research cycle, fostering, sharing and collaboration as early as possible, thus entailing a systemic change to the way science and research is done. Open Science is the ongoing transition in how open research is carried out, disseminated, deployed, and transformed to make scholarly research more open, global, collaborative, creative and closer to society. Open Science involves various movements aiming to remove the barriers for sharing any kind of output, resources, methods or tools, at any stage of the research process. Open Science embraces open access to publications, research data, source software, collaboration, peer review, notebooks, educational resources, monographs, citizen science, or research crowdfunding. The recognition and adoption of open science practices, including open science policies that increase open access to scientific literature and encourage data and code sharing, is increasing in the open science philosophy. Revolutionary open science policies are motivated by ethical, moral or utilitarian arguments, such as the right to access digital research literature for open source research or science data accumulation, research indicators, transparency in the field of academic practice, and reproducibility. Open science philosophy is adopted primarily to demonstrate the benefits of open science practices. Researchers use open science applications for their own advantage in order to get more offers, increase citations, attract media attention, potential collaborators, career opportunities, donations and funding opportunities. In open science philosophy, open data findings are evidence that open science practices provide significant benefits to researchers in scientific research creation, collaboration, communication, and evaluation according to more traditional closed science practices. Open science considers concerns such as the rigor of peer review, common research facts such as financing and career development, and the sacrifice of author rights. Therefore, researchers are recommended to implement open science research within the framework of existing academic evaluation and incentives. As a result, open science research issues are addressed in the areas of publishing, financing, collaboration, resource management and sharing, career development, discussion of open science questions and conclusions.

Keywords: Open Science, Open Science Philosophy, Open Science Research, Open Science Data

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Authors: Sarah Lister, Pauline Palmer

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Research findings presented within this paper form part of a larger scale collaboration between academics at Manchester Metropolitan University and a technology company. The overarching aims of this project focus on developing a series of game-based resources to promote the teaching of aspects of mathematics through a second language (L2) in primary schools. This study explores the potential of game-based learning (GBL) as a dynamic way to engage and motivate learners, making learning fun and purposeful. The research examines the capacity of GBL resources to provide a meaningful and purposeful context for CLIL. GBL is a powerful learning environment and acts as an effective vehicle to promote the learning of mathematics through an L2. The fun element of GBL can minimise stress and anxiety associated with mathematics and L2 learning that can create barriers. GBL provides one of the few safe domains where it is acceptable for learners to fail. Games can provide a life-enhancing experience for learners, revolutionizing the routinized ways of learning through fusing learning and play. This study argues that playing games requires learners to think creatively to solve mathematical problems, using the L2 in order to progress, which can be associated with the development of higher-order thinking skills and independent learning. GBL requires learners to engage appropriate cognitive processes with increased speed of processing, sensitivity to environmental inputs, or flexibility in allocating cognitive and perceptual resources. At surface level, GBL resources provide opportunities for learners to learn to do things. Games that fuse subject content and appropriate learning objectives have the potential to make learning academic subjects more learner-centered, promote learner autonomy, easier, more enjoyable, more stimulating and engaging and therefore, more effective. Data includes observations of the children playing the games and follow up group interviews. Given that learning as a cognitive event cannot be directly observed or measured. A Cognitive Discourse Functions (CDF) construct was used to frame the research, to map the development of learners’ conceptual understanding in an L2 context and as a framework to observe the discursive interactions that occur learner to learner and between learner and teacher. Cognitively, the children were required to engage with mathematical content, concepts and language to make decisions quickly, to engage with the gameplay to reason, solve and overcome problems and learn through experimentation. The visual elements of the games supported the learning of new concepts. Children recognised the value of the games to consolidate their mathematical thinking and develop their understanding of new ideas. The games afforded them time to think and reflect. The teachers affirmed that the games provided meaningful opportunities for the learners to practise the language. The findings of this research support the view that using the game-based resources supported children’s grasp of mathematical ideas and their confidence and ability to use the L2. Engaging with the content and language through the games led to deeper learning.

Keywords: CLIL, gaming, language, mathematics

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Authors: Michael Lousis

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Mathematical competence is the great aim of every mathematical teaching and learning endeavour. This can be defined as an idealised conceptualisation of the quality of cognition and the ability of implementation in practice of the mathematical subject matter, which is included in the curriculum, and is displayed only through performance of doing mathematics. The present study gives a clear definition of mathematical competence in the domains of Arithmetic and Algebra that stems from the explanation of the learners’ errors in these domains. The learners, whose errors are explained, were Greek and English participants of a large, international, longitudinal, comparative research program entitled the Kassel Project. The participants’ errors emerged as results of their work in dealing with mathematical questions and problems of the tests, which were presented to them. The construction of the tests was such as only the outcomes of the participants’ work was to be encompassed and not their course of thinking, which resulted in these outcomes. The intention was that the tests had to provide undeviating comparable results and simultaneously avoid any probable bias. Any bias could stem from obtaining results by involving so many markers from different countries and cultures, with so many different belief systems concerning the assessment of learners’ course of thinking. In this way the validity of the research was protected. This fact forced the implementation of specific research methods and theoretical prospects to take place in order the participants’ erroneous way of thinking to be disclosed. These were Methodological Pragmatism, Symbolic Interactionism, Philosophy of Mind and the ideas of Computationalism, which were used for deciding and establishing the grounds of the adequacy and legitimacy of the obtained kinds of knowledge through the explanations given by the error analysis. The employment of this methodology and of these theoretical prospects resulted in the definition of the learners’ mathematical competence, which is the thesis of the present study. Thus, learners’ mathematical competence is depending upon three key elements that should be developed in their minds: appropriate representations, appropriate meaning, and appropriate developed schemata. This definition then determined the development of appropriate teaching practices and interventions conducive to the achievement and finally the entailment of mathematical competence.

Keywords: representations, meaning, appropriate developed schemata, computationalism, error analysis, explanations for the probable causes of the errors, Kassel Project, mathematical competence

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Authors: Fatimah Alsaleh, Glenda Anthony

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The practicum experience is a critical component of any initial teacher education (ITE) course. As well as providing a near authentic setting for pre-service teachers (PSTs) to practice in, it also plays a key role in shaping their perceptions and sense of preparedness. Nevertheless, merely including a practicum period as a compulsory part of ITE may not in itself be enough to induce feelings of preparedness and efficacy; the quality of the classroom experience must also be considered. Drawing on findings of a larger study of secondary and intermediate level mathematics PSTs’ sense of preparedness to teach, this paper examines the influence of the practicum experience in particular. The study sample comprised female mathematics PSTs who had almost completed their teaching methods course in their fourth year of ITE across 16 teacher education programs in Saudi Arabia. The impact of the practicum experience on PSTs’ sense of preparedness was investigated via a mixed-methods approach combining a survey (N = 105) and in-depth interviews with survey volunteers (N = 16). Statistical analysis in SPSS was used to explore the quantitative data, and thematic analysis was applied to the qualitative interviews data. The results revealed that the PSTs perceived the practicum experience to have played a dominant role in shaping their feelings of preparedness and efficacy. However, despite the generally positive influence of practicum, the PSTs also reported numerous challenges that lessened their feelings of preparedness. These challenges were often related to the classroom environment and the school culture. For example, about half of the PSTs indicated that the practicum schools did not have the resources available or the support necessary to help them learn the work of teaching. In particular, the PSTs expressed concerns about translating the theoretical knowledge learned at the university into practice in authentic classrooms. These challenges engendered PSTs feeling less prepared and suggest that more support from both the university and the school is needed to help PSTs develop a stronger sense of preparedness. The area in which PSTs felt least prepared was that of classroom and behavior management, although the results also indicated that PSTs only felt a moderate level of general teaching efficacy and were less confident about how to support students as learners. Again, feelings of lower efficacy were related to the dissonance between the theory presented at university and real-world classroom practice. In order to close this gap between theory and practice, PSTs expressed the wish to have more time in the practicum, and more accountability for support from school-based mentors. In highlighting the challenges of the practicum in shaping PSTs’ sense of preparedness and efficacy, the study argues that better communication between the ITE providers and the practicum schools is necessary in order to maximize the benefit of the practicum experience.

Keywords: impact, mathematics, practicum experience, pre-service teachers, sense of preparedness

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Authors: Sibawu Witness Siyepu

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This study explores the effects of instructional design using blended learning in the learning of radian measures among Engineering students. Blended learning is an education programme that combines online digital media with traditional classroom methods. It requires the physical presence of both lecturer and student in a mathematics computer laboratory. Blended learning provides element of class control over time, place, path or pace. The focus was on the use of Khan Academy to supplement traditional classroom interactions. Khan Academy is a non-profit educational organisation created by educator Salman Khan with a goal of creating an accessible place for students to learn through watching videos in a computer assisted computer. The researcher who is an also lecturer in mathematics support programme collected data through instructing students to watch Khan Academy videos on radian measures, and by supplying students with traditional classroom activities. Classroom activities entails radian measure activities extracted from the Internet. Students were given an opportunity to engage in class discussions, social interactions and collaborations. These activities necessitated students to write formative assessments tests. The purpose of formative assessments tests was to find out about the students’ understanding of radian measures, including errors and misconceptions they displayed in their calculations. Identification of errors and misconceptions serve as pointers of students’ weaknesses and strengths in their learning of radian measures. At the end of data collection, semi-structure interviews were administered to a purposefully sampled group to explore their perceptions and feedback regarding the use of blended learning approach in teaching and learning of radian measures. The study employed Algebraic Insight Framework to analyse data collected. Algebraic Insight Framework is a subset of symbol sense which allows a student to correctly enter expressions into a computer assisted systems efficiently. This study offers students opportunities to enter topics and subtopics on radian measures into a computer through the lens of Khan Academy. Khan academy demonstrates procedures followed to reach solutions of mathematical problems. The researcher performed the task of explaining mathematical concepts and facilitated the process of reinvention of rules and formulae in the learning of radian measures. Lastly, activities that reinforce students’ understanding of radian were distributed. Results showed that this study enthused the students in their learning of radian measures. Learning through videos prompted the students to ask questions which brought about clarity and sense making to the classroom discussions. Data revealed that sense making through reinvention of rules and formulae assisted the students in enhancing their learning of radian measures. This study recommends the use of Khan Academy in blended learning to be introduced as a socialisation programme to all first year students. This will prepare students that are computer illiterate to become conversant with the use of Khan Academy as a powerful tool in the learning of mathematics. Khan Academy is a key technological tool that is pivotal for the development of students’ autonomy in the learning of mathematics and that promotes collaboration with lecturers and peers.

Keywords: algebraic insight framework, blended learning, Khan Academy, radian measures

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Authors: Sereen Itani

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As the world aspires for technological innovation, Innovative Robotics Technology-Supported Pedagogic Models in STEAM Education (Science, Technology, Engineering, Arts, and Mathematics) are critical in our global education system to build and enhance the next generation 21st century skills. Thus, diverse international schools endeavor in attempts to construct an integrated robotics and technology enhanced curriculum based on interdisciplinary subjects. Accordingly, it is vital that the globe remains resilient in STEAM fields by equipping the future learners and educators with Innovative Technology Experiences through robotics to support such fields. A variety of advanced teaching methods is employed to learn about Robotics Technology-integrated pedagogic models. Therefore, it is only when STEAM and innovations in Robotic Technology becomes integrated with real-world applications that transformational learning can occur. Robotics STEAM education implementation faces major challenges globally. Moreover, STEAM skills and concepts are communicated in separation from the real world. Instilling the passion for robotics and STEAM subjects and educators’ preparation could lead to the students’ majoring in such fields by acquiring enough knowledge to make vital contributions to the global STEAM industries. Thus, this necessitates the establishment of Pedagogic models such as Innovative Robotics Technologies to enhance STEAM education and develop students’ 21st-century skills. Moreover, an ICT innovative supported robotics classroom will help educators empower and assess students academically. Globally, the Robotics Design System and platforms are developing in schools and university labs creating a suitable environment for the robotics cross-discipline STEAM learning. Accordingly, the research aims at raising awareness about the importance of robotics design systems and methodologies of effective employment of robotics innovative technology-supported pedagogic models to enhance and develop (STEAM) education globally and enhance the next generation 21st century skills.

Keywords: education, robotics, STEAM (Science, Technology, Engineering, Arts and Mathematics Education), challenges

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Authors: Olteanu Constanta, Olteanu Lucian

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Researchers note that algebraic reasoning and sense making is essential for building conceptual knowledge in school mathematics. Consequently, pre-service teachers’ own reasoning and sense making are useful in fostering and developing students’ algebraic reasoning and sense making. This article explores the forms of reasoning and sense making that pre-service mathematics teachers exhibit and use in the process of analysing problem-posing tasks with a focus on first-degree equations. Our research question concerns the characteristics of the problem-posing tasks used for reasoning and sense making of first-degree equations as well as the characteristics of pre-service teachers’ reasoning and sense making in problem-posing tasks. The analyses are grounded in a post-structuralist philosophical perspective and variation theory. Sixty-six pre-service primary teachers participated in the study. The results show that the characteristics of reasoning in problem-posing tasks and of pre-service teachers are selecting, exploring, reconfiguring, encoding, abstracting and connecting. The characteristics of sense making in problem-posing tasks and of pre-service teachers are recognition, relationships, profiling, comparing, laddering and verifying. Beside this, the connection between reasoning and sense making is rich in line of flight in problem-posing tasks, while the connection is rich in line of rupture for pre-service teachers.

Keywords: first-degree equations, problem posing, reasoning, rhizomatic assemblage, sense-making, variation theory

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Authors: Sevket Ceyhun Cetin, Mehmet Oren

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According to existing educational research studies, students learn better with high teacher quality. Therefore, professional development has become a crucial way of increasing the quality of novices and veteran in-service teachers by providing support regarding content and pedagogy. To answer what makes PD effective, researchers have studied different PD models and revealed some critical elements that need to be considered, such as duration of a PD and the manner of delivery (e.g., lecture vs. engaging). Also, it has been pointed out that if PDs are prepared as one-size-fits-all, they most likely be ineffective in addressing teachers’ needs toward improving instructional quality. Instead, teachers’ voices need to be heard, and the foci of PDs should be determined based on their specific needs. Thus, this study was conducted to identify professional development needs of middle school mathematics teachers based on their self-evaluation of their performances in light of teaching standards. This study also aimed to explore whether the PD needs with respect to years of teaching experience (novice vs. veteran). These teachers had participated in a federally-funded research grant, which aimed to improve the competencies of 6-9 grade-level mathematics teachers in pedagogy and content areas. In the research project, the participants had consistently videoed their lessons throughout a school year and reflected on their performances, using Teacher Advanced Program (TAPTM) rubric, which was based on the best practices of teaching. Particularly, they scored their performances in the following areas and provided evidence as the justifications of their scores: Standards and Objectives, Presenting Instructional Content, Lesson Structure and Pacing, Activities and Materials, Academic Feedback, Grouping Students, and Questioning. The rating scale of the rubric is 1 through 5 (i.e., 1=Unsatisfactory [performance], 3=Proficient, and 5=Exemplary). For each area mentioned above, the numerical scores of 77 written reports (for 77 videoed lessons) of 24 teachers (nnovices=12 and nveteran=12) were averaged. Overall, the average score of each area was below 3 (ranging between 2.43 and 2.86); in other words, teachers judged their performances incompetent across the seven areas. In the second step of the data analysis, the lowest three areas in which novice and veteran teachers performed poorly were selected for further qualitative analysis. According to the preliminary results, the lowest three areas for the novice teachers were: Questioning, Grouping Students, and Academic Feedback. Grouping Students was also one of the lowest areas of the veteran teachers, but the other two areas for this group were: Lesson Structure & Pacing, and Standards & Objectives. Identifying in-service teachers’ needs based on their reflective practitioner experiences provides educators very crucial information that can be used to create more effective PD that improves teacher quality.

Keywords: mathematics teacher, professional development, self-reflection, video data

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Authors: Wedad Albalawi

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The mathematical inequalities have been the core of mathematical study and used in almost all branches of mathematics as well in various areas of science and engineering. The inequalities by Hardy, Littlewood and Polya were the first significant composition of several science. This work presents fundamental ideas, results and techniques and it has had much influence on research in various branches of analysis. Since 1934, various inequalities have been produced and studied in the literature. Furthermore, some inequalities have been formulated by some operators; in 1989, weighted Hardy inequalities have been obtained for integration operators. Then, they obtained weighted estimates for Steklov operators that were used in the solution of the Cauchy problem for the wave equation. They were improved upon in 2011 to include the boundedness of integral operators from the weighted Sobolev space to the weighted Lebesgue space. Some inequalities have been demonstrated and improved using the Hardy–Steklov operator. Recently, a lot of integral inequalities have been improved by differential operators. Hardy inequality has been one of the tools that is used to consider integrity solutions of differential equations. Then dynamic inequalities of Hardy and Coposon have been extended and improved by various integral operators. These inequalities would be interesting to apply in different fields of mathematics (functional spaces, partial differential equations, mathematical modeling). Some inequalities have been appeared involving Copson and Hardy inequalities on time scales to obtain new special version of them. A time scale is defined as a closed subset contains real numbers. Then the inequalities of time scales version have received a lot of attention and has had a major field in both pure and applied mathematics. There are many applications of dynamic equations on time scales to quantum mechanics, electrical engineering, neural networks, heat transfer, combinatorics, and population dynamics. This study focuses on double integrals to obtain new time-scale inequalities of Copson driven by Steklov operator. They will be applied in the solution of the Cauchy problem for the wave equation. The proof can be done by introducing restriction on the operator in several cases. In addition, the obtained inequalities done by using some concepts in time scale version such as time scales calculus, theorem of Fubini and the inequality of H¨older.

Keywords: time scales, inequality of Hardy, inequality of Coposon, Steklov operator

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Authors: Anandit Sachdev

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Auroville, a settlement in Tamil Nadu, India, is based on the principles of ‘human unity’as defined by Indian philosopher Sri Aurobindo. The settlement was conceptualized on these principles by Sri Aurobindo’s spiritual partner Mirra Alfassa, known as ‘The Mother’ to the Aurovillians. In common perception, the settlement is an experiment in achieving ‘human unity’ through sustainable living. Since its inception in late 1960s, the settlement has attracted people from a variety of nationalities, each understanding, seeking, and rendering ‘human unity’ in their own unique way. This multiplicity of inhabitation has created and continues to create complex and layered human and more-than-human geographies, which are collectively understood as Auroville. This essay builds on these multiple narratives of local metaphysical and every inhabitation of spiritual and philosophical ideas of Sri Aurobindo as rendered in materiality by the Mother. The research aims to assess how theseforms of everyday spirituality conflict, interact, and engage with the principles of Auroville. The research further aims to understands how, if at all, the diverse landscapes of social, cultural, and infrastructural conflictssynthesizewhen perceived through the lens of spirituality. The research does so by detailing the different forms of the built environment which evoke the transcendental and its underlying processes. While doing so, it aims to understand how different manifestations of interiority within the Aurovillian landscape tie back to the self and its entanglements. By analysing the settlement through a spiritual lens, the research ultimately ties together questions relating to the built environment and ontology and asks how each facilitates a continuous synthesis with the other. Lastly, the paper enquires if these ongoing processes of synthesis of built space and ontological entanglements are what can be conceptualized as ‘human unity’ as perceived by Sri Aurobindo himself.

Keywords: sacrality, sacred, spirituality, philosophy, Indian philosophy, auroville, India

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Authors: Zahra Alikhani Koopaei

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In the fifth lesson of the third-grade mathematics book, students are introduced to the concept of multiplication. However, some students showed a lack of interest in learning this topic. To address this, a simple electronic multiplication table was designed with the aim of making the concept of multiplication entertaining and engaging for students. It provides them with moments of excitement during the learning process. To achieve this goal, a device was created that produced a bell sound when two wire ends were connected. Each wire end was connected to a specific number in the multiplication table, and the other end was linked to the corresponding answer. Consequently, if the answer is correct, the bell will ring. This study employs interactive and engaging methods to teach mathematics, particularly to students who have previously shown little interest in the subject. By integrating game-based learning and critical thinking, we observed an increase in understanding and interest in learning multiplication compared to before using this method. This further motivated the students. As a result, the intelligent multiplication table was successfully designed. Students, under the instructor's supervision, could easily construct the device during the lesson. Through the implementation of these operations, the concept of multiplication was firmly established in the students' minds. Engaging multiple intelligences in each student enhances a more stable and improved understanding of the concept of multiplication.

Keywords: intelligent multiplication table, design, construction, education, increased interest, students

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