Academic literature on the topic '280118 Expanding knowledge in the mathematical sciences'

The ArgumentRecent studies in the philosophy of mathematics have increasingly stressed the social and historical dimensions of mathematical practice. Although this new emphasis has fathered interesting new perspectives, it has also blurred the distinction between mathematics and other scientific fields. This distinction can be clarified by examining the special interaction of the body and images of mathematics.Mathematics has an objective, ever-expanding hard core, the growth of which is conditioned by socially and historically determined images of mathematics. Mathematics also has reflexive capacities unlike those of any other exact science. In no other exact science can the standard methodological framework used within the discipline also be used to study the nature of the discipline itself.Although it has always been present in mathematical research, reflexive thinking has become increasingly central to mathematics over the past century. Many of the images of the discipline have been dictated by the increase in reflexive thinking which has also determined a great portion of the contemporary philosophy and historiography of mathematics.

The continuous development of education is important in order to ensure it keeps growing and improving. Professor Toshikazu Ikeda, College of Education, Yokohama National University, Japan, is a Professor of Mathematics who is a proponent of revolutionary knowledge growth through overturning, expanding, and integrating acquired knowledge and skills. This is about progression through bridging the gap between a knowledge goal and the existing knowledge base through developing techniques and pathways to that goal. Ikeda believes that by inserting revolutionary knowledge growth into the mathematics curriculum in Japan, children can be encouraged towards more independent and problem solving based thinking. He has performed an analysis of current teaching materials which involved examining local teaching materials in a specific area, using lessons to analyse and evaluate those materials and looking at long-term global teaching materials that give a deeper examination of specific topics, focusing on how and where it can be used and how students react to the content. In his work, Ikeda uses modelling as a problem solving tool and to develop techniques to deepen learning and lead to revolutionary knowledge growth. Ikeda is collaborating with Professor Max Stephens, Melbourne University, to produce lectures centred on revolutionary growth knowledge for students at teacher training colleges. A key part of Ikedaâ–™s work is teaching mathematical modelling in order to help students understand the importance of mathematics and develop their abilities.

The article developed an algorithm for calculating the coefficient of the impact of innovations on the growth rate of the final product. This mathematical apparatus is a tool for adequate adjustment of the economic system, taking into account the potential of its innovative development. Next, the problem of predicting the regional final product is solved using the Cobb-Douglas(innovation) model. In the calculations, the values of the parameters are determined by the Gradient method. The result obtained indicates the adequacy of the approach used. In addition, the assumptions and hypotheses put forward in the study create prerequisites for further expanding the amount of knowledge in the field of studying the innovative impact on the economy. The practical significance of the proposed models of innovative development of economic systems lies in the emergence of new opportunities for building the innovation policy of the state. Keywords: innovation activity, fuzzy model, Gradient method, innovation index

Mathematical models are increasingly used in life sciences. However, contrary to other disciplines, biological models are typically over-parametrized and loosely constrained by scarce experimental data and prior knowledge. Recent efforts on analysis of complex models have focused on isolated aspects without considering an integrated approach—ranging from model building to derivation of predictive experiments and refutation or validation of robust model behaviours. Here, we develop such an integrative workflow, a sequence of actions expanding upon current efforts with the purpose of setting the stage for a methodology facilitating an extraction of core behaviours and competing mechanistic hypothesis residing within underdetermined models. To this end, we make use of optimization search algorithms, statistical (machine-learning) classification techniques and cluster-based analysis of the state variables' dynamics and their corresponding parameter sets. We apply the workflow to a mathematical model of fat accumulation in the arterial wall (atherogenesis), a complex phenomena with limited quantitative understanding, thus leading to a model plagued with inherent uncertainty. We find that the mathematical atherogenesis model can still be understood in terms of a few key behaviours despite the large number of parameters. This result enabled us to derive distinct mechanistic predictions from the model despite the lack of confidence in the model parameters. We conclude that building integrative workflows enable investigators to embrace modelling of complex biological processes despite uncertainty in parameters.

Neuron types (e.g., pyramidal cells) within one area of the brain are often considered homogeneous, despite variability in their biophysical properties. Here we review literature demonstrating variability in the electrical activity of CA1 hippocampal pyramidal cells (PCs), including responses to somatic current injection, synaptic stimulation, and spontaneous network-related activity. In addition, we describe how responses of CA1 PCs vary with development, experience, and aging, and some of the underlying ionic currents responsible. Finally, we suggest directions that may be the most impactful in expanding this knowledge, including the use of text and data mining to systematically study cellular heterogeneity in more depth; dynamical systems theory to understand and potentially classify neuron firing patterns; and mathematical modeling to study the interaction between cellular properties and network output. Our goals are to provide a synthesis of the literature for experimentalists studying CA1 PCs, to give theorists an idea of the rich diversity of behaviors models may need to reproduce to accurately represent these cells, and to provide suggestions for future research.

Introduction. In recent years, teachers of most technical and natural sciences faculties find the level of freshmen starting a course of higher mathematics insuf-ficient to comprehend the basics of logical constructions. It is difficult for students to clearly realize that, for example, they should learn to prove a statement as a theorem or give a counter-example; in mathematics there are such terms as necessary and sufficient conditions, cause and effect; the system of equations and their totality are dif-ferent things; the properties of mathematical objects are subject of study; solving inequalities or equations requires understanding but not mechanical memorization. All these semantic subtleties make up the concept of mathematical culture based on clear logic reasoning and conclusion. Logical thinking is required in most activities, from business to programming. The relevance of the research is caused by the neces-sity to create a new educational environment free from such negative facts that some students have a low level of mathematical knowledge, skills and abilities; they are enable to independently acquire new mathematical knowledge and skills; their experience in mathematical, communicative and cognitive activity, necessary for a successful future career, is insufficient. International and Ukrainian scientists in the field of pedagogy and psychology diversely studied the problems of intellectual development and mathematical culture of students. (Jean Piaget , Jerome Seymour BrunerLev Vygotsky, Yuriy Hilbukh, Leonid Zankov, Vasilii Davydov, Daniil Elkonin, G.S. Kostiuk, Z.I. Kalmykova, N.O. Menchynska, S. L.Rubinstein, V.F. Palamarchuk, N.F.Talysina etc).The purpose of the articleis to generalize the pedagog-ical essence of mathematical culture, determine the place and role of mathematical education in the formation of students' mathematical culture, study pedagogical pre-requisites and specific technologies of its formation while teaching mathematics and determine conditions for crea-tion of the culture of mathematical language. The methods of analysis, comparison, explication, ab-straction are used in the study. Results. The development of mathematical culture of students involves a number of stages: formation of the student as a subject of educational mathematical activity; awareness of the mathematical education value; creating a holistic view of mathematical activity of the student; understanding mathematical learning materials; reflection of the general structure of mathematical activity in the educational activity; mathematical language acquisition, ability to correctly express and explain operations, ability to use mathematical signs and symbols; gaining under-standing of mathematical modeling as a mathematical method of reality cognition; mastering the system of mathematical concepts, general methods of operations; intellectual and spiritual development of students, includ-ing the development of mathematical thinking, meeting the requirements of modern information society, the develop-ment of children's motivation, creativity, research skills. The culture of mathematical language can only devel-op if the student has a sufficiently strong scientific base that allows him not to concentrate on thinking about the scientific accuracy of a story but to focus on how to speak. Originality. The Internet provides lots of opportunities to develop mathematical culture and present information of different nature: 1) mathematical information for com-pulsory learning i.e. comprehensible knowledge, filled with personal meaning should become a student's acqui-sition; 2) mathematical information for expanding ideas about the subject i.e. elements of logic, combinatorics, probability theory; 3) background information plays an important role in acquiring information, realizing its value, and creating the interest and need to study mathematics.Conclusions. The level of mathematical culture of stu-dents significantly increases under condition of taking nto account the leading ideas of modern international and Ukrainian psychological and pedagogical science about intellectual development of the personality; theoreti-cal substantiation of the content of students' mathemati-cal culture; working out a science-based approach to the technology of development of mathematical qualities of the personality when studying mathematics. In order to improve the culture of mathematical lan-guage, it is necessary to increase the classroom time for the development of oral language skills; allocate 10-15 minutes for oral questioning at every lesson; organize home test papers with an oral performance report in the form of an interview; conduct credit tests orally. Such forms of work contribute to the development of students' mathematical language

The article identifies some aspects of the methodology of research of administrative services in the field of construction. The author points out the importance of applying in the practice of scientific knowledge the correct and complete arsenal of research methods and tools, which directly affects its comprehensiveness and quality, correctness of results. The author points out the position that having its own tasks, content and internal organization, the theory of administrative services in the field of construction is aimed at expanding, deepening, refining, systematizing, and improving the reliability of scientific data. The author defines the method of research of administrative services in the field of construction as rules or prescriptions of purposeful theoretical or practical activity within administrative services in the field of construction, as well as knowledge of rational methods, techniques, operations, procedures for their implementation. The author defends the position, the methodology must be determined through the doctrine of the method and study of the system of such methods, and we believe that the most important interpretation of the methodology of research of administrative services in construction is that it is a system of methods, approaches, methods of administrative science. rights during the implementation of research on administrative services in the field of construction. Within the study, the author points out the existence of methods-operations (analysis, synthesis, deduction, induction, etc.), which are mainly technology of working with scientific material, which should be distinguished from complex methods such as dialectics, synergetic, which are inherent in all sciences and effective within each with it. At the same time, private methods are used in jurisprudence: historical, concrete-sociological, psychological, mathematical, statistical methods and other methods. The author also proves the important role of the comparative law method.

The article substantiates the conditions and tasks for the implementation of the competence-based approach in the vocational training in the European educational space. Methods of scientific research applied: analysis of scientific literature and documentary sources − to determine the scientific and theoretical basis of the competency approach as a trend; theoretical generalization, systematization of research − to justify the conditions for the implementation of the competence approach in educational activities; grouping − to structure the reasons for the need to modernize education; prognostic − to identify pedagogical conditions for the development of key competencies. The main provisions of European level documents on the skills and key competencies of a competitive specialist for the modern labor market are identified. The key competencies characterized include: creativity, communication, critical thinking, curiosity, metacognition; digital literacy, IT skills, technology skills; basic reading, media, information, financial, scientific, mathematical literacy; intercultural communication skills, leadership skills, global awareness; initiative, independence, perseverance, responsibility, adaptability; subject knowledge, engineering and innovative thinking and understanding of natural sciences. It is revealed that the reform of European education is aimed at the systematic transformation of pedagogical practices and assessment of learning outcomes, the structuring of disciplinary knowledge and ensuring the sustainability of the core curriculum, providing opportunities for flexible operational adjustments against a changing world. The general directions of realization of tasks of the competence approach are defined: development of programs of preparation of applicants for work, education, life after graduation based on the formation of professional and "general" skills, abilities to apply knowledge; purposeful development of educational initiatives: expanding opportunities for internships, practical training in projects and gaining experience in local associations and communities; acquisition of skills of independent work with digital resources; providing entrepreneurial opportunities in formal and non-formal education; ensuring digital literacy; extensive use of blended learning technology, consideration of automated learning opportunities; directing the attention of the public and managers to the development and maintenance of communication and cooperation skills; in-depth analysis of data on the success of students in the social and cultural context to develop a policy of equal educational opportunities; aligning the teacher training and professional development program with the skills required by the 21st century society.

Computational Thinking (CT) is a set of logical-operational cognitive skills or processes of reasoning, based on Computer Science. Abstraction, pattern recognition, algorithmic reasoning, and decomposition are examples of some of these skills that form the four pillar of CT. Some researchers have considered these skills as useful, and even mandatory to to cognitive development of the schoolchildren. In this paper, we present practical aspects and the possible contributions of CT in the development of competence of reading and interpreting English texts. Didactic interventions were carried out in high school classes of a public school, supported by the Bring Your Own Device (BYOD) approach, in which the students used their own smartphones. During these interventions, the students developed concept maps and podcasts, performed online exercises and the traditional exam, all of that composed the set of evaluation instruments. It was possible to understand that the CT skills are intrinsically present and contributed to the development of the reading and writing skills in English. According to testimonials, we highlight that the BYOD approach provided new conceptions and perspectives on the use of electronic equipment in function of the students’ learning.ResumoO Raciocínio Computacional (RC) é um conjunto de habilidades ou processos cognitivos lógico-operacionais de raciocínio, fundamentadas na Ciência da Computação. Abstração, reconhecimento de padrões, raciocínio algorítmico e decomposição são exemplos de algumas dessas habilidades que formam os quatro pilares do RC. Alguns pesquisadores consideram essas habilidades úteis, e até mesmo fundamentais, para o desenvolvimento cognitivo dos estudantes. Nesse sentido, este relato de experiência tem por objetivo apresentar aspectos práticos e possíveis contribuições do RC no desenvolvimento da competência de leitura e interpretação de textos de diferentes naturezas na disciplina de língua inglesa. Para isso, realizaram-se intervenções didáticas em uma turma do ensino médio de uma escola pública, apoiadas na abordagem Bring Your Own Device ou, simplesmente, BYOD, em que os estudantes usaram seus próprios aparelhos celulares. Durante o desenvolvimento das intervenções, os estudantes construíram mapas conceituais e podcasts, realizarem exercício online e a tradicional prova, os quais compuseram o conjunto de instrumentos avaliativos do bimestre. Por meio dessas intervenções, foi possível identificar como as habilidades do RC estiveram intrinsecamente presentes e contribuíram para o desenvolvimento da competência de leitura e escrita em língua inglesa, elencada pelos Parâmetros Curriculares Nacionais. Conforme relatos, além da articulação didática com o RC, a abordagem BYOD proporcionou à professora e aos estudantes novas concepções e perspectivas sobre o uso de equipamentos eletrônicos em função da aprendizagem deles mesmos.Palavras-chave: Raciocínio computacional, Ensino de inglês, Mobile learning, Educação em computação.Keywords: Computational thinking, English teaching, Mobile learning, Computer science education.ReferencesALBERTA Education. School Technology Branch. Bring your own device: a guide for schools. 2012. Disponível em:http://education.alberta.ca/admin/technology/research.aspx. Acesso em: 01 fev. 2017.ALLAN, Walter; COULTER, Bob; DENNER, Jill; ERICKSON, Jeri; LEE, Irene; MALYN-SMITH, Joyce; MARTIN, Fred. Computational thinking for youth. White Paper for the ITEST Learning Resource Centre na EDC. Small Working Group on Computational Thinking (CT), 2010. Disponível em: http://stelar.edc.org/publications/computational-thinking-youth. Acesso em: dez 2017.ARAÚJO, Ana Liz; ANDRADE, Wilkerson; GERRERO, Dalton Serey. Pensamento Computacional sob a visão dos profissionais da computação: uma discussão sobre conceitos e habilidades. In: Anais dos Workshops do VI Congresso Brasileiro de Informática na Educação. v. 4, n 1, 2015. p. 1454-1563.ARMONI, Michal. Computing in schools: On teaching topics in computer science theory. ACM Inroads, v. 1, n. 1, p. 21-22. 2010. DOI=http://dx.doi.org/10.1145/1721933.1721941BARBOSA, Márcio Lobo; ALVES, Álvaro Santos; JESUS, José Carlos Oliveira; BURNHAM, Teresinha Fróes. Mapas conceituais na avaliação da aprendizagem significativa. In: Anais do XVI Simpósio Nacional de Ensino de Física, v. 14, 2005, p. 1-4.BELL, Tim; WITTEN, Ian; FELLOWS, Mike. Ensinando Ciência da Computação sem o uso do computador. Computer Science Unplugged, 2011.BOCCONI, Stefania; CHIOCCARIELLO, Augusto; DETTORI, Giuliana; FERRARI, Anusca; ENGELHARDT, Katja. Developing computational thinking in compulsory education Implications for policy and practice. European Commission, JRC Science for Policy Report. 2016.BRASIL, Ministério da Educação. Secretaria da Educação Básica. PCN+ ensino médio: Orientações educacionais complementares aos parâmetros curriculares nacionais, Brasília: MEC. 2002. Disponível em: http://portal.mec.gov.br/seb/arquivos/pdf/linguagens02.pdf. Acesso em: set 2017.BRASIL. Ministério da Educação (MEC). Base Nacional Comum Curricular. 2017. Disponível em: http://basenacionalcomum.mec.gov.br/. Acesso em: set 2017.BRITANNICA, Encyclopaedia. Phenol: Encyclopaedia Britannica Online Academic Edition. Encyclopædia Britannica Inc. 2012. Disponível em: https://www.britannica.com/. Acesso em: 01 fev. 2017.BROOKSHEAR, J-Glenn. Ciência da Computação: uma visão abrangente. Porto Alegre, Bookman Editora, 2005.CHARLTON, Patricia; LUCKIN, Rosemary. Computational thinking and computer science in schools. What The Research Says’ Briefing, v. 2. 2012. [s.p.]CHIOFI, Luiz Carlos; OLIVEIRA, Marta Regina Furlan de. O uso das tecnologias educacionais como ferramenta didática no processo de ensino e aprendizagem. In: Anais da III Jornada de Didática - Jornada de Didática: Desafios para a Docência e II Seminário de Pesquisa do CEMAD. Londrina, 2014. [s.p.]COMPUTER AT SCHOOL. Computational Thinking: a guide for teachers. Hodder Education - the educational division of Hachette UK Digital Schoolhouse, 2015. Disponível em: https://community.computingatschool.org.uk/resources/2324/single. Acesso em: 01 set 2017.CORREIA, Paulo Rogério Miranda; SILVA, Amanda Cristina; ROMANO JÚNIOR, Jerson Geraldo. Mapas conceituais como ferramenta de avaliação na sala de aula. Revista Brasileira de Ensino de Física, v. 32, n. 4, p. 4402-4408. 2010.COSTA, Giselda dos Santos. Mobile learning: explorando potencialidades com o uso do celular no ensino-aprendizagem de língua inglesa como língua estrangeira com alunos da escola pública. 2013. 201f. Tese (Doutorado em Letras). Faculdade de Letras. Universidade Federal de Pernambuco. Recife. 2013.CSIZMADIA, Andrew; SENTANCE, Sue. Teachers’ perspectives on successful strategies for teaching Computing in school. In: IFIP TCS. 2015. Disponível em: <http://community.computingatschool.org.uk/files/6769/original.pdf>. Acesso em março 2018.CSIZMADIA, Andrew; CURZON, Paul; DORLING, Mark; HUMPHREYS, Simon; NG, Thomas; SELBY, Cynthia; WOOLLARD, John. Computational thinking: A guide for teachers. Computing at Schools, 2015. Disponível em: https://community.computingatschool.org.uk/files/8550/original.pdf>. Acesso em: 26 out. 2017.DIAS, Reneildes; JUCÁ, Leina; FARIA, Raquel. High Up: ensino médio. Cotia, SP: Macmillan, 2013.GOOGLE FOR EDUCATION. What is Computational Thinking? Computational Thinking for Educators. 2015. Disponível em: <https://computationalthinkingcourse.withgoogle.com/unit?lesson=8&unit=1. Acesso em: set 2017.LEE, Irene; MARTIN, Fred; DENNER, Jill; COULTER, Bob; ALLAN, Walter; ERICKSON, Jeri; MALYN-SMITH, Joyce; WERNER, Linda. Computational thinking for youth in practice. ACM Inroads, v. 2, n. 1, 2011. p. 32-37.LIUKAS, Linda. Hello Ruby: adventures in coding. New York: Feiwel & Friends, 2015.LU, Zhao.; YING, Lu. Application of Podcast in Teaching and Learning Oral English for Non-English Majors. In: International Conference on Computational and Information Sciences, Shiyang, 2013. p. 1935-1938. doi: 10.1109/ICCIS.2013.506MANNILA, Linda; VALENTINA, Dagiene; DEMO, Barbara; GRGURINA, Natasa; MIROLO, Claudio; ROLANDSSON, Lennart; SETTLE, Amber. Computational thinking in K-9 education. In: Proceedings of the working group reports of the 2014 on innovation & technology in computer science education conference. ACM, 2014. p. 1-29.MOREIRA, Antonio Marco. Mapas conceituais e aprendizagem significativa (concept maps and meaningful learning). Cadernos do Aplicação, v. 11, n. 2, 1998. p. 143-156.NCSEC. Team 11 in 2000. Concept map. 2000. National Computation Science Education Consortium Disponível em: <http://www.ncsec.org/team11/ Rubric Concep tMap.doc>. Acesso em: set. 2017.NOVAK, Joseph. D. Meaningful learning: The essential factor for conceptual change in limited or inappropriate propositional hierarchies leading to empowerment of learners. Science education, Wiley Online Library, v. 86, n. 4, 2002. p. 548-571.NOVAK, Joseph. Learning creating and using knowledge: Concept maps as facilitative tools in schools and corporations. [S.l.]: Routledge, 2010.PAIVA, Luiz Fernando; FERREIRA, Ana Carolina; ROCHA, Caio; BARRETO, Jandiaci; MELHOR, André; LOPES, Randerson; MATOS, Ecivaldo. Uma experiência piloto de integração curricular do raciocínio computacional na educação básica. In: Anais dos Workshops do Congresso Brasileiro de Informática na Educação, v. 4, 2015. p. 1300-1309.RACHID, Laura. Cenário da educação básica no Brasil é alarmante, aponta Ideb. Revista Educação. São Paulo, 04 set. 2018. Disponível em: http://www.revistaeducacao.com.br/cenario-da-educacao-basica-no-brasil-e-alarmante/. Acesso em: 26 de setembro de 2018.RODRIGUEZ, Carla; ZEM-LOPES, Aparecida Maria; MARQUES, Leonardo; ISOTANI, Seiji. Pensamento Computacional: transformando ideias em jogos digitais usando o Scratch. In: Anais do Workshop de Informática na Escola. p. 62-71. 2015.SILVA, Edson Coutinho. Mapas conceituais: propostas de aprendizagem e avaliação. Administração: Ensino e Pesquisa, [S.l.], v. 16, n. 4, p. 785-815, dez. 2015. ISSN 2358-0917. Disponível em: <https://raep.emnuvens.com.br/raep/article/view/385/196>. Acesso em: 06 nov. 2017. doi: https://doi.org/10.13058/raep.2015.v16n4.385.SILVA, Edson Coutinho. Mapas Conceituais: Modelos de Avaliação. Concept Mapping to Learn and Innovate. In: Proc. of Sixth Int. Conference on Concept Mapping. Santos, Brazil. 2014.WING, Jannette. Computational thinking. Communications of the ACM, v. 49, n. 3, p. 33-35, 2006.WING, Jannette. Computational thinking and thinking about computing. Philosophical transactions of the royal society of London A: mathematical, physical and engineering sciences, v. 366, n. 1881, 2008. p. 3717-3725.XU, Zhichang. Problems and strategies of teaching English in large classes in the People's Republic of China. In: Expanding Horizons in Teaching and Learning. Proceedings of the 10th Annual Teaching Learning Forum. 2001. p. 7-9.ZORZO, Avelino Francisco; RAABE, André Luís Alice; BRACKMANN, Christian Puhlmann. Computação: o vetor de transformação da sociedade. In: FOGUEL, D.; SCHEUENSTUHL, M. C. B. Desafios da Educação Técnico-Científica no Ensino Médio. Rio de Janeiro: Academia Brasileira de Ciências, 2018. p. 154-163.e3116073