Dialogic Teaching is effective in fostering student learning; yet, it is hard to implement. Little research focused on secondary teachers’ learning of DT and on the link between teachers’ understanding and practices, although these two are usually strongly intertwined. Using a wide range of evidence, this case study systematically investigated and compared two secondary teachers’ understanding and practice of DT during their participation in a continuing professional development programme. The CPDP appeared effective to some extent. The (...) History teacher’s understanding of DT, i.e. being a co-learner, appeared highly effective in implementing DT, whereas the Mathematics teacher’s understanding of DT, i.e. creating a democratic learning environment, seemed only effective to some extent. Focusing on both teachers’ understanding and practice when developing DT seemed fruitful in explaining differences in practice. Future research could further explore to what extent understanding DT as being a co-learner facilitates professional development. (shrink)

The aim of this study is to investigate students’ conceptions about proof in mathematics and mathematics teaching. A five‐point Likert‐type questionnaire was administered in order to gather data. The sample of the study included 33 first‐year secondary school mathematics students . The data collected were analysed and interpreted using the methods of qualitative and quantitative analysis. The results have revealed that the students think that mathematical proof has an important place in mathematics (...) and mathematics education. The students’ studying methods for exams based on imitative reasoning which can be described as a type of reasoning built on copying proof, for example, by looking at a textbook or course notes proof or through remembering a proof algorithm. Moreover, they addressed to the differences between mathematics taught in high school and university as the main cause of their difficulties in proof and proving. (shrink)

This book offers an innovative introduction to the psychological basis of mathematics and the nature of mathematical thinking and learning, using an approach that empowers students by fostering their own construction of mathematical structures. Through accessible and engaging writing, award-winning mathematician and educator Anderson Norton reframes mathematics as something that exists first in the minds of students, rather than something that exists first in a textbook. By exploring the psychological basis for mathematics at every level - including (...) geometry, algebra, calculus, complex analysis and more - Norton unlocks students' personal power to construct mathematical objects based on their own mental activity, and illustrates the power of mathematics in organizing the world as we know it. Including reflections and activities designed to inspire awareness of the mental actions and processes coordinated in practicing mathematics, the book is geared towards current and future secondary and elementary mathematics teachers who will empower the next generation of mathematicians and STEM majors. Those interested in the history and philosophy that underpins mathematics will also benefit from this book, as well as those informed and curious minds attentive to the human experience more generally. Anderson Norton is Professor in the Department of Mathematics at Virginia Tech, USA, where he has been teaching mathematics courses for future teachers for 15 years. He is the editor of Constructing Number, and the co-author of Developing Fractions Knowledge and Numeracy for All Learners. (shrink)

Autonomous learning capacity is a key competency that supports teachers’ professional development. In this study, a stratified sampling method was used to recruit 396 junior and senior high school mathematics teachers in T city, one of the provincial city in China. A questionnaire with high reliability and validity developed prior to the study by the researchers was employed to measure their autonomous learning capacity and differences across groups. Twelve teachers were then selected for interviews. The results showed (...) satisfactory overall performance. By subdimension, teachers’ performance was the best in the development of study plans, followed by evaluation of learning outcomes, while they needed improvement in learning habit formation and proficiency in using learning methods. Furthermore, the analysis of differences across groups indicated that for autonomous learning capacity, female teachers were significantly better than their male peers; junior high school teachers were better compared to those in senior high school; teachers aged 41–50 underperformed those aged 51 and above; teachers who work in rural areas and townships did not perform worse than urban teachers; and those with doctoral degrees did not demonstrate considerable advantage over others. There were no significant differences in the overall autonomous learning capacity across years of teaching and job title groups. However, in the subdimensions, those with 21–30 years of teaching experience had lower proficiency in using learning methods and evaluation of learning outcomes, and teachers with senior titles did not demonstrate expected advantages in learning habit formation. (shrink)

The purpose of this paper is the influence of Science- Technology- Engineering- Art- Mathematics education on the Olympic education of primary and middle school students. The research object is the Beijing Olympic model school. The frame structure and educational concept of STEAM education are studied, and a questionnaire survey on the current situation of Olympic education is conducted. Finally, improvement measures based on the survey results are provided combined with STEAM education, and the teaching effect is analyzed. The (...) results show that after the improvement of the educational model, the student’s mastery of the Olympic knowledge has been greatly improved. The proportion of students who can master all knowledge increases from 5.78 to 8.45%, by 2.67%. The proportion of students with knowledge of most Olympic sports increases from 48.6 to 55.67%, by 7.07%. The proportion of students with little or no knowledge drops to 1.54%. Meanwhile, students are increasingly interested in Olympic events, especially after being inspired by the STEAM education model. The proportion of students who are very concerned about Olympic events has increased by 6.45%. The proportion of students who are more concerned about Olympic events has increased by 5.11%. Thus, the Olympic education work has achieved some results. Students gradually become interested in the Olympic events. They begin to actively pay attention to the Olympic events and learn the Olympic spirit. Then, their physical literacy is improved. (shrink)

This book's activities highlight the important cycle of exploration, conjecture, and justification in all five mathematical strands. Students recognize patterns and make conjectures, learn the value of a counterexample, explore the strengths and weaknesses of visual proofs, discover the power of algebraic representations, and learn that theoretical approaches can substantiate empirical results. The supplemental CD-ROM features interactive electronic activities, master copies of activity pages for students, and additional readings for teachers. --publisher description.

ABSTRACT: The Smith Report has generated central questions about the mathematics education of UK adolescents. This paper highlights the close match between the goals of school mathematics, adolescence and exploratory pedagogy. This is contrasted with the prescriptive nature of current regimes. In particular, without careful attention to pedagogy it is possible that the introduction of different pathways may lead to a failure to achieve the outcomes desired by employers and universities, and to inequity in provision for students.

This article discusses the role of mathematics during physics lessons in upper-secondary school. Mathematics is an inherent part of theoretical models in physics and makes powerful predictions of natural phenomena possible. Ability to use both theoretical models and mathematics is central in physics. This paper takes as a starting point that the relations made during physics lessons between the three entities Reality, Theoretical models and Mathematics are of the outmost importance. A framework has been developed (...) to sustain analyses of the communication during physics lessons. The study described in this article has explored the role of mathematics for physics teaching and learning in upper-secondary school during different kinds of physics lessons. Observations are from three physics classes led by one teacher. The developed analytical framework is described together with results from the analysis of the 7 lessons. The results show that there are some relations made by students and teacher between theoretical models and reality, but the bulk of the discussion in the classroom is concerning the relation between theoretical models and mathematics. The results reported on here indicate that this also holds true for all the investigated organizational forms lectures, problem solving in groups and labwork. (shrink)

This study examines the associations of constructivist beliefs and classroom climate on teachers' self-efficacy in instruction, classroom management, and student engagement among Australian secondary mathematics teachers. To do this, it uses the integrated model of teachers' self-efficacy with the concept of analysis of teaching tasks. The study uses structural equation modeling to analyze data from 495 mathematics teachers in the Teaching and Learning International Survey 2013. The results reveal the integrated model is a (...) valid theoretical framework to explain Australian secondary mathematics teachers' self-efficacy. Teachers' constructivist beliefs and classroom climate are positively and statistically significantly related to teachers' self-efficacy in instruction, classroom management and student engagement. In contrast, constructivist beliefs have no significant correlation with classroom climate. (shrink)

Microgames are rapidly gaining increased attention and are highly being considered because of the technology-based media that enhances students’ learning interests and educational activities. Therefore, this study aims to develop a new construct through confirmatory factor analysis, to comprehensively understand the factors influencing the use of microgames in mathematics class. Participants of the study were the secondary school teachers in West Java, Indonesia, which had a 1-year training in microgames development. We applied a quantitative approach to (...) collect the data via online questionnaires through google form. Structural Equation Modelling with AMOS software was used to analyze the proposed model. Empirical results confirmed the perceived easy to use and subjective norm influence relationship with teachers’ microgame usage behaviors and intentions. In this condition, SN was found to have the initial significant influence on behavioral intention, as attitude, BI, and facilitating conditions also correlated with the actual use of microgames. Furthermore, the largest influential factor was BI, with the results subsequently showing that TPACK had no significant influence on the actual use of microgames. This report is expected to help bridge the gap across several previous studies, as well as contribute to the explanation and prediction of the factors influencing the teachers’ mathematical utilization of the study’s program. Besides this, it also helps to increase the use of microgames in teaching and learning activities. (shrink)

The study aims to help primary and secondary school students develop a good habit of physical exercise by exploring the current situation of physical exercise of primary and secondary school students and analyzing the factors affecting their physical exercise. Then, intervention strategies are figured out for different groups of students and help them develop a good habit of physical exercise. From the perspective of educational psychology and parents’ entrepreneurship education, the research on the physical exercise of primary (...) and secondary school students is conducted by a questionnaire survey, mathematical statistics and literature review. A total of 280 students from five schools in Tianjin are selected as the research subjects, and the current situation of students’ physical exercise in these five schools is investigated. The results show that 40.5% of boys and 39.4% of girls can take physical exercise more than three times a week; 48.9% of the students do physical exercise for more than 30 mins each time; the students who usually take regular exercise at school account for 82.1%. The physical exercise that students always do is running, badminton and table tennis, which rank the top three among the sports they do. The students usually play basketball, volleyball, and football, and they rarely do the sports like swimming, Wushu, and aerobics. This result is closely related to the characteristics and places of primary and middle school students. The survey shows that the physical exercise awareness of most primary and secondary school students is correct; most students can participate in physical exercise, but few students can do it regularly; parents’ support, parents’ habits of doing exercise, and family’s spending on physical exercise have a significant impact on developing students’ habits of doing physical exercise. Based on the above, it is concluded that the primary and secondary stage is very important for students. Physical education teachers should follow the principle of teaching different students with different methods, enrich teaching materials, and improve teaching quality. The study provides a reference for the reform of PE to guide primary and middle school students to participate in sports activities, improving students’ physical quality. (shrink)

This book is a series of essays by distinguished scholars concerned with the improvement of primary, secondary, and tertiary studies, most especially in arts but also in mathematics and science. It is concerned with past ideas about education in Australia, most particularly with the traditions that have yielded an education that has proven most beneficial to Australia in terms of comparison with other countries; and it advocates and emphasises how this tradition can be maintained and improved in specific (...) ways. Essays focus on primary and secondary education in music, and art, mathematics, history and the classics, on the improvement of memory and vocabulary, but more particularly on university education, discussing the purpose of education, learning in general, the use of the seminar, the necessity of freedom of debate, the inadequacies and contradictions of French and Anglo-post modernism, the teaching of history, of philosophy, and its branch aesthetics, mathematics, equality in education, teaching at university and funding of the whole enterprise. The authors are all well known in their disciplines and some are experts, internationally recognised in their fields. This book features essays by: David Daintree, Karl Schmude, Simon Haines, Kevin Donnelly, Matthew Lesh, Chris Berg & Bella d'Abrera, David Furse-Roberts, Greg Melleuish, Steven Schwartz, Blaise Joseph, James Franklin, Christopher Allen, Richard Gill, Jeremy Bell, Barry Spurr, David Brooks, Natalie Kennedy, Sarah Williams, Sarah Lawrence, Ivan Francis Head. (shrink)

This study aims to determine the opinions of teachers of Religious Culture and Ethics Course (DKAB) about subject-based classroom application in-depth. The research has been carried from qualitative research methods with a case study design. In order to determine the working group of the study, criteria sampling was used in the first stage, and the maximum diversity sampling method was used in the next step. The sample of this research consists of 8 DKAB teachers working in Ankara (...) province. A semi-structured interview form has been used as a data collection tool in the study. The data of the qualitative of this research has been analyzed with both descriptive and content analysis by NVivo 10 program. In order to ensure validity and reliability in the study, credibility, transferability, consistency, and verifiability strategies have been used. When the research data were analyzed, four themes were formed: positive opinions about the application, negative opinions and problems related to the application, contribution of the practice to religious education and training, and recommendations about the application. DKAB teachers find the application more positive than the classroom system. It has been found that the practice of subject-based classrooms is a motivational tool for Primary School students, while it causes some problems for lower secondary school and upper secondary school students.Summary: Learning environments are among the key elements in the acquisition of 21st-century skills. Classrooms are also a part of the learning environment. Classes are the learning environment in which teachers and students spend most of their education and training process. In this context, subject-based classroom application is one of the preferred methods in the arrangement of classrooms.Subject-based classroom application means that the teachers have a special classroom related to their branches in the school building, and students attend the teacher's classroom according to the syllabus. In this practice, the teacher can decorate walls, floor, ceiling, column, and beam of the classroom with students’ study materials such as banner, poster, painting, cartoon to make the course more effective and efficient and to create a psychological atmosphere called classroom atmosphere-air.This application aims to activate the student by enriching the classroom and make learning effective and efficient. The classroom equipped with appropriate equipment and materials provides a favorable environment for the implementation of effective teaching strategies. The application can create “class/classroom culture” by using ordinary meanings and symbols related to the course. It provides students the opportunity to exhibit their products and contributes to students' self-regulation skills development. Besides, real-life practices or practices close to reality can be brought into the classroom. As a result, permanent learning can be realized with the possibility of creating a shared living space and the number of sensory organs participating in learning.This current study aims to address in-depth information about the opinions of Religious Culture and Moral Ethics (DKAB) teachers in primary, secondary, and high schools regarding the subject-based classroom application. When the studies in the literature are examined, it is seen that the studies related to the subject-based classroom application have increased since 2010. However, it is clear that this research is directed towards social studies, geography, science, and mathematics courses and is based on the opinions of students, teachers, and administrators at the secondary school level. In the context of DKAB course, there has been no research including the views of teachers, students, or school administrators regarding the application of subject-based classrooms. This study is carried out revealing perspectives of DKAB teachers by examining their opinions on the subject-based classroom application and contribute to the field. The research was conducted with a case study design from the qualitative research methods. The participants consist of 8 DKAB teachers working in Ankara province. A mixed purposive sampling method was used to determine the study group. In the first stage, the teachers implementing the DKAB classrooms application were taken as criteria. In the next step, the study group was determined within the framework of the maximum diversity sampling method by considering the variables such as school level, gender, age, education level, duration of teachers' work. The data were collected through a semi-structured interview form with expert opinion. In the form, there are nine main questions and probe questions, which include questions related to subject-based classrooms application, the contribution of the application to religious education and training, the contribution of teachers to professional and personal development, the effect of teachers' belonging to the school, the effectiveness, and improvement of the application. Permission has been obtained from the Ankara Provincial Directorate of National Education and participants via consent form for the interview. The interviews were recorded in audio, 169.58-minute audio recording transcripts, and 52-page interview data obtained. The qualitative data of this research has been analyzed with both descriptive and content analysis by NVivo 10 program. In order to ensure validity and reliability in the study, credibility, transferability, consistency, and verifiability strategies have been used.When the data of the research were analyzed, the opinions of DKAB teachers about the subject-based classrooms application categorized under four themes; positive and negative opinions/problems about the practice, the contribution of the practice to religious education and teaching and practical suggestions. Under the theme of positive opinions on the application, positive aspects for the teacher, student, parents, and comparison with the classroom system were formed. According to the participants, the practice of DKAB classroom is a “facilitation” element for the teacher because of the factors such as the teacher not moving around the classroom, not carrying material, having freedom to organize the classroom, and material regularity. In this application, since the teacher has a class of his own, the teacher adopts and owns the classroom and the sense of belonging to school increases. This sense of belonging is felt so strongly that there is even a participant who plans to retire if the application is abandoned. The positive aspects of the application for the students are that; a classroom is a motivating tool, the boards and walls can be used, and the student has the opportunity to exhibit their activities. When compared with the classroom system, it was stated that as a result of the branch classroom practice, the school equipment could be better protected, class order and cleaning easier, and the success of the students would be increased.The negative views of the participants on the application were grouped under the categories of students, teachers, and parents. Not having a fixed class of their own, continually relocating and losing time in recess, staying in the classroom door when the classroom is locked, not adopting the classroom and lack of lockers constitute the negative aspects of the application for the students. The overuse of classrooms, less use of teachers' rooms, lack of communication between colleagues are the negative aspects of the application for the teachers. It was stated by (75%) most of the participants that branch classroom application contributed to the continual learning of students in religious education and teaching. To make the application more functional, DKAB teachers have proposed arrangements such as improving physical infrastructure, enriching teaching materials, and arranging school syllabus and keeping classrooms open. As a result, teachers find the application more positive than the classroom system. While it is a motivation tool for primary school students, it causes some problems for secondary and high school students, such as carrying bags, staying at the door, and wasting time. In this sense, the application is recommended to be applied in primary schools that have a sufficient number of classrooms. Also, the system should be applied in secondary and high schools where the number of students is low, or the number of classrooms is sufficiently provided that the problems experienced by the students are eliminated. School administrations and teachers need to take necessary measures to make the application effective and efficient. (shrink)

In this paper, we discuss a proposal for reform in the teaching of Euclidean geometry that reveals the symbiotic relationship between axiomatics and pedagogy. We examine the role of intuition in this kind of reform, as expressed by Mario Pieri, a prominent member of the Schools of Peano and Segre at the University of Turin. We are well aware of the centuries of attention paid to the notion of intuition by mathematicians, mathematics educators, philosophers, psychologists, historians, and others. (...) To set a context for Pieri’s proposal, we only seek to open a small window on views of the pedagogical role of intuition, from primary education to university study that may have informed early 20th century efforts to improve the teaching of geometry at the secondary school level. Pieri addressed the topic of intuition in many of his axiomatizations, including those in projective geometry which was his main area of concentration in foundations. We focus here primarily on his axiom systems for elementary geometry, which embraced the transformational approach of Felix Klein’s vision for the subject. Our goal is to convey Pieri’s thoughts on how to integrate two types of intuition, denoted as sensible and rational, in his endeavors to improve the teaching of the geometry of Euclid. We show how Pieri’s views on geometric intuition and pedagogical reform were either ignored or misrepresented in several notable publications at the turn of the 20th century. In particular, we give Pieri a voice in response to specific comments made in the early 1900s by Federigo Enriques, Ugo Amaldi, and Florian Cajori in widely circulated publications inspired by Klein. (shrink)

A large portion of mathematics education centers heavily around imitative reasoning and rote learning, raising concerns about students’ lack of deeper and conceptual understanding of mathematics. To address these concerns, there has been a growing focus on students learning and teachers teaching methods that aim to enhance conceptual understanding and problem-solving skills. One suggestion is allowing students to construct their own solution methods using creative mathematical reasoning, a method that in previous studies has been contrasted against algorithmic (...) reasoning with positive effects on test tasks. Although previous studies have evaluated the effects of CMR, they have ignored if and to what extent intrinsic cognitive motivation play a role. This study investigated the effects of intrinsic cognitive motivation to engage in cognitive strenuous mathematical tasks, operationalized through Need for Cognition, and working memory capacity. Two independent groups, consisting of upper secondary students, practiced non-routine mathematical problem solving with CMR and AR tasks and were tested 1 week later. An initial t-test confirmed that the CMR group outperformed the AR group. Structural equation modeling revealed that NFC was a significant predictor of math performance for the CMR group but not for the AR group. The results also showed that WMC was a strong predictor of math performance independent of group. These results are discussed in terms of allowing for time and opportunities for struggle with constructing own solution methods using CMR, thereby enhancing students conceptual understanding. (shrink)

Any study of the 'Scientific Revolution' and particularly Descartes' role in the debates surrounding the conception of nature (atoms and the void v. plenum theory, the role of mathematics and experiment in natural knowledge, the status and derivation of the laws of nature, the eternality and necessity of eternal truths, etc.) should be placed in the philosophical, scientific, theological, and sociological context of its time. Seventeenth-century debates concerning the nature of the eternal truths such as '2 + 2 (...) = 4' or the law of inertia turn on the question of whether these truths were created along with nature, or were uncreated and subsisting in God's mind. One's answer to that question has direct consequences for conceptions of the necessity/contingency of mathematical and natural knowledge, how knowledge of such truths is accomplished by humans, and what grounds these truths. In this paper, I review the positions of four successors to Descartes' philosophy on the question of the eternal truths to illustrate how in specific ways that question with its theological, metaphysical, modal, and epistemological dimensions concerned the objectivity and certainty of the discoveries of the new science. Author Recommends: Clarke, Desmond. Descartes' Philosophy of Science . University Park, Penn State Press, 1982. This work provides an account of Descartes as a practicing scientist whose rationalism is mitigated by reliance on experiment and experience. Author re-examines Descartes' philosophical and scientific works in this new light. Dear, Peter. Revolutionizing the Sciences: European Knowledge and its Ambitions, 1500–1700 . Princeton, Princeton University Press, 2001. This work provides a useful overview of the issues and thinkers of the Scientific Revolution. Of particular relevance is chapter 8 on Cartesian and Newtonian science. Funkenstein, Amos. Theology and the Scientific Imagination from the Middle Ages to the Seventeenth Century . Princeton, Princeton University Press, 1986. This work is an advanced study of the theological and metaphysical foundations of early modern science. Discussions include questions of God's nature, God's knowledge in relation to human knowledge, providence, the laws of nature, and the truths of mathematics. In particular, chapter 3 discusses Descartes' account of the eternal truths and divine omnipotence. Garber, Daniel. Descartes' Metaphysical Physics . Chicago, University of Chicago Press, 1992. This work examines how Descartes' metaphysical doctrines of God, soul, and body set the groundwork for his physics. It includes a study of God and the grounds for the laws of physics (chapter 9). Henry, John. The Scientific Revolution and the Origins of Modern Science . 3rd ed. New York, Palgrave, Macmillan Press, 2008. This work provides a brief, general, and informative overview of the Scientific Revolution, including the themes of method, magic, religion, and culture. Osler, Margaret J. Divine Will and the Mechanical Philosophy: Gassendi and Descartes on Contingency and Necessity in the Created World . Cambridge, Cambridge University Press, 1994. This work is an examination and comparison of the mechanical philosophies of Gassendi and Descartes. It offers in-depth discussion of the issue of voluntarism and intellectualism in the period and how that related to conceptions of laws of nature and the eternal truths. Shapin, Steven. The Scientific Revolution . Chicago, University of Chicago Press, 1996. This work provides a critical synthesis of as well as a guide to recent scholarship in the history of science for a general readership. Online Materials Dr. Robert A. Hatch's Scientific Revolution Website: http://web.clas.ufl.edu/users/rhatch/pages/03-Sci-Rev/SCI-REV-Home/ A compendium of resources for the study of Scientific Revolution. Early English Books Online: http://eebo.chadwyck.com/home Early English Books Online (EEBO) contains digital facsimile page images of virtually every work printed in England, Ireland, Scotland, Wales and British North America and works in English printed elsewhere from 1473 to 1700. Early Modern Resources: http://www.earlymodernweb.org.uk/emr/ Early Modern Resources is a gateway for all those interested in finding electronic resources relating to the early modern period in history. Gallica, the Digital Library of the Bibliothèque Nationale de France: http://gallica.bnf.fr/ An ever-growing digital library which includes numerous primary and secondary texts of relevance to Descartes and his role in Scientific Revolution. Hatfield, Gary, 'René Descartes', The Stanford Encyclopedia of Philosophy. Spring 2009 ed. Ed. Edward N. Zalta; URL: http://plato.stanford.edu/archives/spr2009/entries/descartes/ Slowik, Edward, 'Descartes' Physics', The Stanford Encyclopedia of Philosophy. Winter 2008 ed. Ed. Edward N. Zalta; URL: http://plato.stanford.edu/archives/win2008/entries/descartes-physics/ Syllabus Sample Syllabus: Cartesian Science The following is five weeks covering Cartesian Science in a course on Descartes or the Scientific Revolution, or 17th-century theories of matter, or related themes on early modern truth and method, especially on the continent. This material is best suited to a graduate level audience, but it could be modified to suit an upper-division undergraduate course, as the readings are basically primary texts whose context and background can be explained in lectures. Week 1: Cartesian Revolution in France • Scientific method • Role of mathematics and experiment • Certainty of scientific knowledge Readings: Hatfield, Gary, 'René Descartes', The Stanford Encyclopedia of Philosophy. Spring 2009 ed. Ed. Edward N. Zalta; URL: http://plato.stanford.edu/archives/spr2009/entries/descartes/ Descartes, Discourse on Method , Parts 1–3 Descartes, Meditations on First Philosophy , First Meditation. Week 2: Descartes' Scientific Treatises • Mechanization and mathematization of nature • Primary–secondary quality distinction Readings: Discourse on Method, Parts 4–6 Selections from Descartes' Scientific Essays: The World or Treatise on Light (ATXI 3–48); Treatise on Man (ATXI 119–202); Optics (ATVI 82–147). Slowik, Edward, 'Descartes' Physics', The Stanford Encyclopedia of Philosophy. Winter 2008 ed. Ed. Edward N. Zalta; URL: http://plato.stanford.edu/archives/win2008/entries/descartes-physics/ Henry, John, 'The Mechanical Philosophy,' chapter 5. The Scientific Revolution and the Origins of Modern Science . 3rd ed. Macmillan, 2008. Week 3: Descartes' Theory of Nature • Descartes' derivation of the law of conservation and the three laws of motion • God's role in the metaphysics and physics of nature Readings: Selections from Principles of Philosophy, Preface (all); Letter to Elizabeth; Part I: 1–8; Part II: 1–45, 55, 64; Part III: 1–4, 15–19, 45–47; Part IV: 187–207. John Henry, 'Religion and Science,' chapter 6. The Scientific Revolution and the Origins of Modern Science . 3rd ed. Macmillan, 2008. Week 4: Post-1650 Cartesian Science: Necessity and Contingency in Nature • Debates on God, Creation, and Causes Readings: Easton, Patricia, 'What is at Stake in the Cartesian Debates on the Eternal Truths?' Philosophy Compass 4.2 (2009): 348–62. Malebranche, Nicolas, 'Elucidation 10', from The Search after Truth (1674). Note: All selections available in Nicolas Malebranche (1992). Philosophical Selections , edited by S. Nadler, Hackett. Gottfried Leibniz (1714) Monadology . Week 5: Causes in Nature and Morals • Theodicy as an explanation of defect and evil in a lawful universe: Malebranche v. Leibniz Readings: Nicolas Malebranche, Elucidation XVI (on occasionalism), and Treatise on Nature and Grace, Discourse One, Part 1. Gottfried Leibniz (1706), Theodicy. Focus Questions Weekly questions can be used to focus the readings. This can be done in a web or e-mail discussion thread, as a weekly assignment, or for in class discussion. I require students to post a short paragraph in response to the question or some posting by a classmate on the question. Students are required to post by 10 a.m. the day before we meet for class on a course website. Week 1: According to Descartes, what role does skepticism play in scientific reasoning? Week 2: Comment on the following: 'But I am supposing this machine to be made by the hands of God, and so I think you may reasonably think it capable of a greater variety of movements than I could possibly imagine in it, and of exhibiting more artistry than I could possibly ascribe to it' [ Treatise on Man ; ATXI 120]. Week 3: What is Descartes' conception of the relation between the metaphysics and physics of nature? Week 4: Critically discuss the positions of Descartes, Malebranche, and Leibniz on what provides the foundation for the certitude of natural knowledge? Week 5: Explain why both Malebranche and Leibniz consider moral sin to be analogous to natural defect? Seminar/Project Idea Hold a debate on the question of the status of the eternal truths. The proposition will be Descartes' position: 'Eternal truths must be both created and necessary if certainty in science is to be possible'. Format: 1. At the beginning of the 5-week module, students will be assigned to one of three roles: Team A, Team B, and judge's panel. Students will be given the debate proposition, but will not be told which team will take the affirmative and which team the negative until the time of the debate. 2. Recommend a variation on the Classic Debate Format to encourage the development of argument: sequence begins with affirmative construction (8 minutes), negative construction (8 minutes), second affirmative construction (8 minutes), second negative construction (8 minutes), first negative rebuttal (4 minutes), first affirmative rebuttal (4 minutes), final negative rebuttal (4 minutes) and final affirmative rebuttal (4 minutes). 3. Judges Panel: will consist of 3–4 judges who will assess the performance of Teams A and B. Judgment should be based on the persuasiveness of the team position. 4. Debate will be held at the end of the fifth week, or semester, whichever makes most sense given the course length and structure. Acknowledgements The author gratefully acknowledges the immensely helpful comments and suggestions by the participants in her graduate seminar on the Scientific Revolution: Benjamin Chicka, Sarah Jacques-Ross, Richard Ross, Marcella Stockstill, and Zohra Wolters. (shrink)

In the lesson study approach, researchers and teachers work together to solve teaching and learning problems identified by practitioners. This paper presents three examples of lesson study conducted with different audiences (primary and secondary) in mathematics and physics. The authors analyze the different postures built and adopted by researchers in each of these situations and try to identify some conditions and constraints more or less favorable to building a partnership between researchers and practitioners. The lesson (...) study’s approaches seem to be part of collaborative research, under certain conditions, especially in connection to researchers postures that accompany these research groups. These conditions meet the idea of the double likelihood that characterizes collaborative research. (shrink)

This study aimed to investigate the longitudinal trends in mathematical competencies of Grade 8 students in a public high school located in Zamboanga del Sur, Philippines. The study collected data over a period of six academic years, allowing for a comprehensive analysis of students' performance in 16 distinct mathematical competences of basic education curriculum. These topics include, but are not limited to, special products and factors, factoring, and basic concepts of probability. Using a quantitative research design, the (...) class='Hi'>study analyzed both numerical and secondary data to identify patterns or trends in students' mathematical competencies. Trends were analyzed through regression analysis using slopes. The significance of these trends was then evaluated using t-tests for the standard error of slopes. The statistical analysis revealed significant upward trends in certain mathematical topics, indicating an improvement in the students' competencies over the six academic years. However, certain topics displayed downward or stable trends, indicating areas for improvement in the teaching methods used for these topics. The study highlights the importance of flexible and adaptable approaches to mathematics education. It emphasizes the need for constant evaluation and improvement of teaching methods to enhance student learning outcomes. The findings of this study provide valuable insights for educators and policymakers to guide evidence-based decision-making and improve the quality of mathematics education in the new normal setup. Implications and future research directions are incorporated in the study. (shrink)

This textbook, which is completely self-contained and can be read by anyone with a secondary school education, is the result of the author's material prepared over the past 15 years of teaching introductory natural language semantics to graduate and undergraduate students at McGill University. The intended audience comprises undergraduate and graduate students in linguistics as well as those in philosophy, computer science and psychology with an interest in natural language semantics. The aim of the textbook is to teach (...) the fundamentals of natural language semantics, with English as the principal, though not the exclusive, target language. The principal aim of the textbook is to provide the student with all the basics necessary to be able him or her read research in natural language semantics, regardless of the theory assumed by the author of the research. In contrast to other textbooks in the field, which aim to introduce students to a particular theory of natural language semantics, this textbook seeks to give to its reader a clear overview of the kind of natural language phenomena which, at least prima facie, fall within the ambit of an investigation of natural language semantics; to assist the reader in developing a mastery of the mathematical tools used to formulate hypotheses about the natural language phenomena studied; and to impart to the reader an appreciation of the interplay between hypothesis and data. As a result, the textbook is rich in its presentation of the patterns of English, drawing extensively on the best and most contemporary descriptive grammars of English. The textbook also has more than 500 exercises, with answers to half of them. (shrink)

The stability of low student math scores has been a concern of education systems around the world for many years. While teaching practices are pointed out as a determining factor in student engagement and the quality of student learning, they are only the tip of the iceberg. Much work has shown that these practices are strongly colored by epistemological beliefs as well as by beliefs related to the teaching and learning of the school discipline under investigation. On this (...) subject, if some research reports a peremptory influence of beliefs on teaching practices, others present more moderate results by underlining, for example, the permeability of beliefs in pre-service training. Based on the results of a quantitative study that identified three belief profiles (pro-traditional, anti-traditionnal, flexible) among 190 future secondary school mathematics teachers in their final year of training, this contribution aims to shed qualitative light on the articulation between beliefs and teaching practices of eleven of them. The analysis of the semi-directive interviews highlights the reconcilable nature of transmissive and constructivist conceptions of teaching-learning. Moreover, the presence of similar pedagogical practices, supported in training, within profiles with contrasting beliefs argues in favor of a belief-practice non-linearity. (shrink)

Considerable research has demonstrated that teachers’ self-efficacy plays a major role in implementing instructional practices in classroom lessons. Only few studies, however, have examined the interplay between how teachers’ self-efficacy and the challenges that lie outside their influence are related to their implementation of cognitive-activation strategies (CAS), especially in science classrooms. Using the Trends in Mathematics and Science Study (TIMSS) 2015 data from Grades 4, 5, 8, and 9, we explored the extent to which teachers’ self-efficacy in (...) class='Hi'>teaching science and the perceived time constraints explained variation in the enactment of general and inquiry-based CAS. Overall, the findings revealed that highly self-efficacious teachers reported more frequent implementation of both general and inquiry-based CAS, whereas those who perceived strong time constraints reported a less frequent use of inquiry-based CAS. We further found that these relations differed significantly between primary- and secondary-school teachers and discuss these findings in light of teachers’ professional competences and the resources for science activities in primary and secondary education. We point to the theoretical implications of this study for enhancing the conceptual understanding of generic and specific aspects of CAS and the practical implications for teacher education, professional development, and educational policy. (shrink)

continent. 1.4 (2011): 242—252. Introduction The following two works were produced by visual artist Jonas Staal and writer Vincent W.J. van Gerven Oei during a visit as artists in residence at The Bag Factory, Johannesburg, South Africa during the summer of 2010. Both works were produced in situ and comprised in both cases a public intervention conceived by Staal and a textual work conceived by Van Gerven Oei. It was their aim, in both cases, to produce complementary works that could (...) be read “through each other,” in which the movement of artistic construction would be imitated by textual deconstruction and vice versa. Both works deal with the way in which capital, apartheid, and monumentality are interwoven in South-African society. The Missing Link addresses a monument for democracy, erected on the premises of a private corporation running both an amusement park and the Apartheid Museum franchise. The textual intervention accompanying this public intervention investigates the limits of the inclusiveness of the anti-discrimination section in the South-African constitution, itself a monumental work of democracy. The Monument for the Distribution of Wealth deals with the history and eventual dissolution of a monumental square, commemorating the Soweto Uprising, in one of the poorest townships of Johannesburg. The history accompanying this public dismemberment of memory is equally fragmented, which is expressed by the many voices recounting uncertain and perhaps even irrelevant “facts” about the genius loci, the way in which the memorial space has actually entered into the memory of the inhabitants surrounding it. Next to their individual practices, Staal and Van Gerven Oei have worked together on a number of projects ever since 2007, including several art residencies. Their work involves an investigation of the different interfaces between art, politics, and public space in media ranging from theater and public interventions, to video installations and (co-authored) textual works. The Missing Link Missing Link (1) Missing Link (2) Missing Link (3) Intervention on the monument entitled The Seven Pillars of the Constitution , part of the Apartheid Museum in Johannesburg, South Africa. The Seven Pillars represent the constitutional values propagated in South Africa since the abolition of the apartheid regime. The monument and museum were built by the Gold Reef Resorts corporation, which is also responsible for the theme park and casino next to it. By placing the word “capitalism” on the wall surrounding the museum, the capitalist system and the constant social divisions that it implies are interpreted as sophistic continuations of apartheid politics. Through the capitalist system, apartheid is still operational within South African society. Whereas during the apartheid regime, the separation clearly ran along race divisions, in the current, “democratic” system, the same actual separation is sustained without it being an explicit element of the foundations of the country, i.e. the constitution. This intervention foregrounds the constant role of capitalism is both periods. At the same time the intervention acknowledges that contemporary Western artisthood is a mirror of the privileges that are offered by the capitalist system, and the type of artist that it produces. The intervention initiates a critical discourse concerning the capitalist system situated within the disaster of capitalism itself, in other words: through the desire to break with the presumption that art would be able to operate outside the capitalist system and to confirm that art—and the artist himself—is in fact modeled on this system. The public intervention by Staal was supplemented by a textual intervention by Van Gerven Oei: a proposition to alter the seventeenth amendment of the South African constitution. Even though the anti-discrimination legislation in South-Africa is one of the most stringent and inclusive in the world, one factor—wealth—remains outside its scope, thus continuing the schisms along racial lines produced during the apartheid regime: §9.3. The state may not unfairly discriminate directly or indirectly against anyone on one or more grounds, including race, gender, sex, pregnancy, marital status, ethnic or social origin, colour, sexual orientation, age, disability, religion, conscience, belief, culture, language, birth, and wealth. Monument for the Distribution of Wealth Intervention concerning the June 16 Memorial Acre in Central Western Jabavu, one of the poorest townships of Johannesburg. The monument comprises a park on which different are placed recalling an important protest the black population against the former apartheid regime. In 1976, from a school adjacent to the park, they started a massive protest against the introduction of Afrikaans in the school curriculum. The police reacted violently, and shot several hundreds of students. The construction of the June 16 Memorial Acre was started in 2005, and from the start was the paragon of corruption. Coordinated by local politicians, some family members of the protest leader from 1976 gained control of the realization of the monument, outside the regulation through external institutions. The available budget of 41 million rand (at that time well over 5 million euro) was largely embezzled. In the meantime, the monument has become fully dilapidated and defaced. The park has become overgrown with weeds and covered in a layer of dirt, and the local population is slowly plundering the square to use the material for the construction and decoration of their own houses. The Monument for the Distribution of Wealth develops the dynamics already existent around the June 16 Memorial Acre. Without obtaining official permission in advance, several local inhabitants were hired to break down the monument, sort the materials, and offer it to the neighborhood. Thus, the redistribution of wealth after the fall of the apartheid regime is finally taking place, albeit from the mere remains of the capital that was once invested in the community. The words “monument” and “for free” are spray-painted on the stacks of material, both in English and Zulu, as these are locally the most common languages. Van Gerven Oei supplemented Staal’s public intervention with an account of the history of the monument based on a series of interviews. The account clarifies how the different interests within the protest 1976 are reflected in the exceeding decay of the park, and how in the end those interests were represented by the June 16 Memorial Acre. Monument for the Distribution of Wealth 1: Removing stones Monument for the Distribution of Wealth 3: Pulling down statues Monument for the Distribution of Wealth 4: Offering the material Monument for the Distribution of Wealth 5: Offering the material Monument for the Distribution of Wealth 6 The next day A Fragmentary History of the Monument for the Distribution of Wealth, Formerly Known as the June 16 Memorial Acre in Central Western Jabavu, Soweto Vincent W.J. van Gerven Oei The following text, based on interviews and online research aims to provide parts of a history of the park in front of Morris Isaacson High School in Central Western Jabavu, Soweto. The idea for the transformation of the park into a memorial site has its source in the events of June 16, 1976: the start of the the student uprising in Soweto. The development of the park was started in the early 1980s, and the actual transformation into a memorial site, the June 16 Memorial Acre, was initiated in 2005. Over the last few years, several monumental additions have been made to the park: A marble monument with three pillars was revealed on June 16, 2006. A sculpture of a book and several billboards on June 16, 2008. A sculpture of student leader Tsietsi Mashinini on June 16, 2010. The park was transformed into the Monument for the Distribution of Wealth on August 3, 2010. According to the entry “Youth Struggle” on the website South African History Online, the Bantu Education Act was introduced in 1953 . In 1954 , Dr Verwoerd, Minister of Native Affairs, stated: “What is the use of teaching the Bantu child mathematics when it cannot use it in practice? That is quite absurd.” According to the entry “Soweto uprising” on Wikipedia, the Afrikaans Medium Decree was issued in 1974 , forcing all black schools to use Afrikaans and English in a 50-50 mix as languages of instruction. The Regional Director of Bantu Education (Northern Transvaal Region), J.G. Erasmus, told Circuit Inspectors and Principals of Schools that from January 1, 1975 , Afrikaans had to be used for mathematics, arithmetic, and social studies from standard five (7th grade). English would be the medium for general science and practical subjects. Indigenous languages would be used for religion instruction, music, and physical culture. According the entry “Soweto uprising” on Wikipedia, on April 30, 1976 , students from the Orlando West Junior School in Soweto went on strike, refusing to go to school. Their example was followed by other schools in Soweto. A student from Morris Isaacson High School, Toboho “Tsietsi” Mashinini, proposed a meeting on June 13, 1976 to discuss further action. According to Weizmann Hamilton’s article “The Soweto Uprising 1976,” which appeared in the September 1986 edition of Inqaba Ya Basebenzi (Fortress of the Revolution), on June 13, 1976 , the South African Students’ Movement called a meeting at the Donaldson Community Center in Orlando. 300-400 Students representing 55 schools decided to hold a mass demonstration on June 16. According to Brian Mokhele, member of the Joint Community Safety Forum, Dr Edelstein was the first victim of the Soweto uprising and killed the day before the march on June 15, 1976 . Edelstein was an administrator at the pass office in Jabavu and gave golf courses to the local community. Edelstein was put in a garbage bin and pierced by pickaxes. The garbage bin was left at the very spot of the murder for many years. A few years ago, a child was beheaded at the same spot, and the basketball court next to it has been abandoned since. According to Marcus Neustetter, founder of the Trinity Session, this story is untrue. According the entry “Soweto uprising” on Wikipedia, on June 16 , Tsietsi Mashinini led students from Morris Isaacson High School to join up with others who walked from Naledi High School. A crowd of between 3,000 and 10,000 eventually ended up near Orlando High School. According to Raymond Marlowe, a local photographer, Tsietsi Mashinini was heading the march. According to the entry “Hector Pieterson” on Wikipedia, Dr Edelstein died on June 16, 1976 , stoned to death by mob and left with a sign around his neck proclaiming “Beware Afrikaaners.” The first child to die that day was called Hastings Ndlovu. According to Pat Motsiri, Orlando West is claiming struggle heritage through the Hector Pieterson Museum, while Hector Pieterson was from Jabavu. According to Pat Motsiri, his generation effectively struggled between 1980 and 1991, forcing the release of Nelson Mandela and negotiations with the apartheid regime while the 1976-generation was safely in exile. Nevertheless, this has not been recognized in any monument. After the abolition of apartheid, the generation from 1976 returned from exile, occupied important government and ANC positions, creating an abundance of 1976 memorials and refusing to acknowledge that this was only possible because of the younger generation’s struggle. He calls this a generational conflict. According to Archibald Dlamini, the park officer responsible for the Memorial Acre, he started working for the municipality in 1978. In 1981/82 , Isaac Makhele from Pimville, who used to work in the cemetery business, was the first developer of the park. It used to be just a normal park until City Parks decided to develop the Memorial Acre in 2006. In 2007 the work was stopped by the community. According to Brian Mokhele, he left the country in 1989 after he participated in the riots of 1986. But when he returned in 1999 he found that nothing had changed. He says that they were promised to be protected by the Constitution, but that reality is different. The police uses fear to suppress them so that they don’t come out to talk openly. He has been arrested twice, both times harassed and tortured by the police, but in the end always released without indictment. He says that this is their way to threaten communities to back off from politics. According to Moses, who is sitting outside rolling a joint, Brian knows everything. He tells Brian to tell me everything he knows. According to Brian Mokhele, Tsietsi Mashinini was possibly murdered in 1990 during his exile in New York. Two weeks before he was supposed to return to South Africa, his papers in order, he was found dead under mysterious circumstances. His coffin was sealed when he was buried. According to Pat Motsiri, he came up with the idea for the Memorial Acre in 2003 . He submitted the documents for the proposal to the council, which sidelined him as soon as the budget came out in 2005 . According to Brian Mokhele, there was on estimation R 41,000,000 spent to redesign the park and turn it into the Memorial Acre. The millions were divided by Amos Masondo, the mayor of Soweto, the local councilor Bongani D. Zondi, and the director of the city of Johannesburg, Pat Lephunya. They were dividing the money between several contractors: Tsietsi Mashinini’s brothers were involved in the development of the park, they got the tender to do the green areas, the landscaping. Construction was done by other companies, some did the paving, the toilets, etc. EMBA, a private company appointed by the municipality was in control of the money flow, but the money was quickly gone. According to Raymond Marlowe, the contractor bought a BMW with the money. According to Archibald Dlamini, the Mashinini brothers got the tender, so the space would look more like the other places around in Soweto. It was agreed that after they were done, they would return the property to the municipality. They did whatever they could do. According to Mafaisa, a member of the Jabavu business community, he was one of the contractors for the landscaping and the pavement under Mpho Mashinini, one of the brothers. He says that I should contact Mavi for information on Mpho. According to Poi Stuurman, a local youth worker, Mafaisa is one of the guys who ran away with the money. According to Mavi, Mpho Mashinini was never a contractor. The contracts were organized by Sbu Butelezi, the former head of the Gauteng Department for Public Works. The June 16 Foundation and the Mashinini brothers will be the beneficiaries of the park when it is finished. According to Brian Mokhele, City Parks did not accept the Memorial Acre because it was not finished. The rest of the year, the unfinished park is not maintained, as should have happened. This was done deliberately so that in the end they can just clean the whole thing up and have a reason to redo the whole park. According to Brian Mokhele, the Mashinini brothers now work for the government. People that manipulate for money purposes always come from the government’s side. Because the park was left unfinished, the people from the neighborhood are taking away the stones to decorate their own homes with. According to Archibald Dlamini, because City Parks doesn’t accept responsibility of the park, he officially has nothing the guard, except for his cottage, which is municipal property. The thieves come at night and destroy the park, but he cannot do anything because he is sleeping. According to the website of the Thanda Foundation on June 16, 2006 a bronze statue of Hector Pieterson, the first child to die in the 1976 protests, made by Kobus Hattingh and Jacob Maponyane was unveiled in the Maponya Mall in Soweto. The statue is sculpted after the famous image shot by Sam Nzima of Mbuyisa Makhubo carrying the dead body of the boy. The sculpture was sponsored by the Thanda Foundation, founded by the Swedish entrepreneur Dan Olofsson and South-African entrepreneur Matthews Phosa. According to the official website of the City of Johannesburg, the Memorial Acre and Artwork were unveiled in 2006. According to a blog post on sowetouprisings.com, the Memorial Acre was still under development on July 24, 2006. According to Archibald Dlamini, City Parks only cleans up the park once a year just before the June 16 celebrations. Everybody is waiting for the Mashinini brothers to finish their job. The last time he talked with them was in 2007 . According to a sign on the school grounds of the Morris Isaacson High School, the June 16 Trail will be finished in 2008 . According to a blog post on sowetouprisings.com, the Memorial Acre contains another monument erected in Tsietsi’s honor. The monument was created as part of the Sunday Times Heritage Public Art program. Its physical form resembles a giant book which symbolizes the crisis in education experienced in 1976. On the face of the book is the map of the route taken by the students from Morris Isaacson High School in Central Western Jabavu to Phefeni Junior Secondary in Orlando West (currently the site of the Hector Pieterson Museum), while the back cover of the ‘book’ is inscribed with a tribute to Tsietsi Mashinini. The monument was revealed on June 16, 2008 . According to Marcus Neustetter, the billboards on the Memorial Acre were part of a school project realized in 2008. Following several workshops, the students from different high schools along the June 16 Trail were invited to work with artists on the billboards, while the neighborhood community was invited to watch the process during the festivities on June 15 and 16, 2008 . The billboards were supposed to be removed because of construction works on the Memorial Acre, which never ended up happening. According to Brian Mokhele, the former toilet facilities were converted into a house for the park officer. This park officer has been working for city parks for more than 12-15 years, but does nothing here, because the park, including the new toilet buildings, is not finished. The government is now moving around looking for people to take this job because they stopped it. They confronted everybody who was going in and chased them away. According to John, in 2009 , some girls, around 16 or 17 years old, were raped by four men who had been drinking in a local shebeen. When the bar quit they said that they would go home by car, but instead raped the girls on the Memorial Acre nearby. This happened in the unfinished toilets, because the doors couldn’t be closed. According to Brian Mokhele, there used to be some fences around the park because of the construction work that was eventually stopped, but these were also stolen. According to Archibald Dlamini, people from the neighborhood started about two and a half years ago, and the last piece was stolen near the end of 2009 . Sometimes he would catch someone with a roll of fence, and then use it for his own cottage. According to the official website of the City of Johannesburg, a statue of Tsietsi Mashinini by Johannes Pokhela was revealed on June 16, 2010 , “Youth Day.” According to Shirley Makutoane, deputy principal of Isaac Morrison High School, the statue of Tsietsi Mashinini, funded by the June 16 Foundation, has temporarily been placed within the school perimeter. The statue will be moved to the Memorial Acre when it will be finished, in 2011 . According to Brian Mokhele, beside the June 16 Foundation, there is also a June 16 Memorial Acre Foundation. Both foundations are quarreling about the money involved in the Memorial Acre project. Nobody knows who’s involved in them. According to Marcus Neustetter, the June 16 Foundation consists of people that were part of 1976 protest movement, local government officials, representatives of the Hector Pieterson Museum, and the council. According to students from the Isaac Morrison High School, the statue of Tsietsi Mashinini is on the school ground because on the Memorial Acre it would be vandalized by youths from White City, an adjacent neighborhood. Accorcing to Brian Mokhele, the statue of Tsietsi should eventually be mounted on the Memorial Acre. It is wrong that the statue is in the school at the moment, because it is not a public school. He wants the statues to depict the massiveness of the force that was coming into Soweto after the protests. According to Brian Mokhele, City Parks, City of Jo’burg, City Lights, and SAPS are making some sort of plan to take the plan back. They want to remove the trees from the Memorial Acre, and redesign the Memorial Acre into a relaxing park, without political content. They want to depoliticize the square. In doing so,they will have their own employment and not use local workforces. According to Brian Mokhele, the community wants to remove the monuments, amphitheater, and sculptures from the Memorial Acre because they do not resemble anything. The sculptures should be depicting the truth of what happened, because the Memorial Acre is a political heritage site. He wants to involve the people that actually participated in the struggle to make the monument so that everyone can enjoy it and get a better understanding of the struggle heritage. Therefore, he proposes collective ideology in which everyone has a say. This would prevent future vandalization of the monument. According to Pat Motsiri, the sculptures must depict the event around June 16, 1976. Like the story of Dr Edelstein, who was pierced by pickaxes, forced into a garbage bin and burned alive. According to Jonas Staal, the Memorial Acre should be destroyed, its elements stacked on pallets, thus forming the Monument for the Distribution of Wealth . According to Mafaisa, his men can do the work quickly. He has about twenty men working under him. (shrink)

Over the past few years we have seen an increasing number of legal proceedings related to inappropriately implemented technology. At the same time career paths have diverged from the foundation of statistics out to Data Scientist, Machine Learning and AI. All of these new branches being fundamentally branches of statistics and mathematics. This has meant that formal training has struggled to keep up with what is required in the plethora of new roles. Mathematics as a taught subject is (...) still based in decades old teaching specifications and has not been updated centrally as a curriculum to include new technologies, coding or ethics. This subject area is firmly split between ICT and Mathematics in secondary school, continuing on to be split between Computer Science and Mathematics at University. As we move forwards with technology we see these once seperate fields becoming increasingly intertwined. We propose that existing provision for concepts such as ethics and societal responsibility in analysis currently exist but have not been incorporated into the mainstream curriculum of School or University. This is partially due to the split between fields in an educational setting but also the speed with which education is able to keep up with Industry and its requirements. Principles and frameworks of socially responsible modelling beginning at school level means that ethics and real-life modelling are introduced much earlier than normal. Integrating these concepts with philosophical principles of society and politics ensures a suitable background for future modellers and users of technology to draw on. Modelling is currently undertaken in technical sciences at University but the Subject Benchmark Statements are not current (Subject Benchmark Statements describe the nature of study and the academic standards expected of graduates in specific subject areas. They show what graduates might reasonably be expected to know, do and understand at the end of their studies). Even in 2019 the UK did not yet have Benchmark Statements that discuss the learning to be done in Higher Education around AI and advanced Machine Learning. Where there is provision for AI and Data Science within degree courses ethics is not generally highlighted as a key concept. As such there can be a lack of focus on the teaching of modelling or ethics as specific skills. The skills required to use a basic statistical model, for example would not be sufficient to start from scratch and build an ethical model reflecting real-world scenarios with which to inform policy or organisational decision making. This is a skill in itself and includes such aspects as awareness of data quality, ethics, user implementation problems, context and an understanding of the environment that the model is being created in. As the field of analytics has progressed so quickly in the last decade modules such as those covering AI have simply been bolted on to Maths or Computing degrees rather than being fully detailed as key areas of study or driving new, more integrated courses of study. This paper posits that gaps at primary, secondary and tertiary educational levels need to be addressed. Implementing and integrating key concepts from school level is essential so that areas such as assumptions, caveats, quality assurance and answering the right questions with constructive challenge become a cultural fixture. This not only helps developers of technology but users of rapidly developing technology also. In addition, leadership and soft skills as part of this education will ensure that a cultural shift can take place and promote continuous improvement in analysis within organisations. The addition of key concepts throughout the educational system and the updating of potentially outdated curriculums is key to ensuring a functional society. A society where every citizen is a user of tech and those that develop it can be ethical and socially responsible in its development. (shrink)

The incorporation of technology by teachers as a teaching tool is a challenge. Our aim is to analyse whether ICT resources influence the use of pedagogical models and active methodologies by secondary school teachers in Melilla to teach Mathematics. In this cross-sectional quantitative study, a sample n= 61 (83.56% of the population) was evaluated using a validated 20-item questionnaire with three indicators: B.1 Methodologies and Pedagogical Models, B.2 Teaching Practice and C.3 ICT Resources in the (...) teaching environment. Statistical power allows extrapolation of the findings. (shrink)

By the end of the 19th century, mathematics teaching underwent a crisis of similar proportion in several European countries. Constrained by the values of classical Antiquity, which dominated in secondary education, mathematics was taught as a formal discipline enhancing elementary geometry and intended as some gymnastics of the mind. Moreover, a specific feature in Germany was that the country was split up into numerous independent states each having a separated educational system of its own. Many of (...) these conferred an only marginal status to mathematics instruction. This complex situation is analyzed for the traditional school system for boys, as well as for the emerging system for girls, and for primary schooling.The study describes the key initiatives by Felix Klein, who forged a dynamic movement of teachers for modernising secondary school teaching. Their culmination in the famous “Meran” reform program is depicted, a program which became the starting point for the first international reform movement in mathematics teaching. (shrink)