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Nuno Bastos holds a PhD degree in Mathematics, in the field of Fractional Calculus and Time Scales . In 2015, he received the Best Paper Award for the Signal Processing Journal by the European Association for Signal Processing (EURASIP) with the paper "Discrete-time fractional variational problems". He published academic works in different international scientific journals and was a member of the organising committees of national and international conferences. In the beginning, his interests were fractional calculus, calculus of variations, but nowadays he is mostly interested in mathematical education, educational technology, and the popularisation of mathematics. He is a professor at the Polytechnic Institute of Viseu and a member of CIDMA - Center for Research & Development in Mathematics and Applications.
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Identification

Personal identification

Full name
NUNO RAFAEL DE OLIVEIRA BASTOS

Citation names

  • BASTOS, NUNO
  • Nuno R. O. Bastos
  • N. R. O. Bastos

Author identifiers

Ciência ID
9511-2AB5-4F75
ORCID iD
0000-0003-1533-1075

Knowledge fields

  • Exact Sciences - Mathematics

Languages

Language Speaking Reading Writing Listening Peer-review
Portuguese (Mother tongue)
English Intermediate (B1) Intermediate (B1) Intermediate (B1) Intermediate (B1) Intermediate (B1)
Education
Degree Classification
2012/02/12
Concluded
 Matemática (Doutoramento)
Universidade de Aveiro, Portugal
"Cálculo fraccional em escalas temporais" (THESIS/DISSERTATION)
 Aprovado
Affiliation

Teaching in Higher Education

Category
Host institution 		Employer
2012/02/02 - Current Adjunct Teacher (Polytechnic Teacher) Instituto Politécnico de Viseu Escola Superior de Tecnologia e Gestão de Viseu, Portugal
2002/09/02 - 2012/02/11 Invited Assistant (Polytechnic Teacher) Instituto Politécnico de Viseu Escola Superior de Tecnologia e Gestão de Viseu, Portugal
Instituto Politécnico de Viseu Escola Superior de Tecnologia e Gestão de Viseu, Portugal
2002/05/15 - 2002/07/31 Invited Assistant (Polytechnic Teacher) Instituto Politécnico de Bragança Escola Superior de Tecnologia e Gestão, Portugal
2001/10/22 - 2002/02/28 Invited Assistant (Polytechnic Teacher) Instituto Politécnico de Bragança Escola Superior de Tecnologia e Gestão, Portugal
2001/02/20 - 2001/07/08 Tutor (University Teacher) Universidade do Porto Faculdade de Ciências, Portugal
2000/10/18 - 2001/01/18 Tutor (University Teacher) Universidade do Porto Faculdade de Ciências, Portugal
1999/11/25 - 2000/02/26 Tutor (University Teacher) Universidade do Porto Faculdade de Ciências, Portugal
Projects

Contract

Designation Funders
2024/09 - 2027/01 MAESTRO-AI - Math and Programming Education with Smart Teaching and Robust Outreach using AI at Universities
2024-1-PL01-KA220-HED-000244332
 Erasmus
2022/09/01 - 2023/10/31 IPV Inova e Inclui. IPV I2
POCH-02-53I2-FSE-000014
Researcher
Fundação para a Ciência e a Tecnologia
Concluded
2019/01/01 - 2019/12/31 Centro de Investigação e Desenvolvimento em Matemática e Aplicações
UID/MAT/04106/2019
UID/MAT/04106/2013
Universidade de Aveiro Centro de Investigação e Desenvolvimento em Matemática e Aplicações, Portugal

Universidade de Aveiro, Portugal
Fundação para a Ciência e a Tecnologia
Concluded
2011/01/01 - 2013/12/31 Projecto Estratégico - UI 4106 - 2011-2012
PEst-C/MAT/UI4106/2011
PEst-OE/MAT/UI4106/2014
Universidade de Aveiro Centro de Investigação e Desenvolvimento em Matemática e Aplicações, Portugal

Universidade de Aveiro, Portugal
Fundação para a Ciência e a Tecnologia
Concluded
Outputs

Publications

Book chapter
  1. BASTOS, NUNO. "Estratégias para envolver ativamente os estudantes no processo de aprendizagem". In Pedagogia no ensino superior: concretizações e inquietações no Instituto Politécnico de Viseu, edited by Maria Pacheco Figueiredo; Amanda Rodrigues Franco. Viseu, Portugal: Escola Superior de Educação de Viseu, 2022.
    Published
  2. Santos, Vanda; Bastos, Nuno R. O.. "Critical Thinking on Mathematics in Higher Education: Two Experiences". In Technology and Innovation in Learning, Teaching and Education, 156-167. Springer International Publishing, 2021.
    10.1007/978-3-030-73988-1_11
Conference abstract
  1. Santos, V.; Nuno R. O. Bastos. "Metodologias Ativas com Recurso a Tecnologias no Ensino Superior". Paper presented in 8.º Congresso Olhares Sobre a Educação, Viseu, 2020.
    Published
Conference paper
  1. Nuno Rafael Oliveira Bastos; Maria Paula de Sousa Oliveira; Isabel Ferreira. "ACTIVE LEARNING IN A VOCATIONAL EDUCATION AND TRAINING PROGRAMME". 2023.
    10.21125/edulearn.2023.1525
  2. Nuno Rafael Oliveira Bastos. "THE USE OF SELF-ASSESSMENT AND FLIPPED CLASSROOM IN AN UNDERGRADUATE MATHEMATICS COURSE FOR MANAGEMENT STUDENTS". 2023.
    10.21125/edulearn.2023.1273
  3. Vanda Santos; Nuno Rafael Oliveira Bastos. "OPEN MIDDLE PROBLEMS: MATH CHALLENGES THAT PROMOTE DEBATE AND CRITICAL THINKING". 2023.
    10.21125/edulearn.2023.0998
  4. Maria Paula de Sousa Oliveira; Andreia Hall; Nuno Rafael Oliveira Bastos; Dina Seabra; Elsa Assunção; Maria João Barroso. "THE GEOGEBRA BOOK: A TOOL TO ENGAGE STUDENTS". 2023.
    10.21125/edulearn.2023.0645
  5. Nuno Bastos; Nuno Rafael O. Bastos. "BREAKOUT ROOMS: A COLLABORATIVE SPACE THAT WORKS". 2022.
    10.21125/edulearn.2022.1808
  6. Nuno Bastos; Vanda Santos. "ACTIVITIES WITH DESMOS AND GEOGEBRA FOR FORMATIVE AND AUTOMATIC FEEDBACK". 2022.
    10.21125/edulearn.2022.1768
  7. Nuno Bastos; Lucília Dias; Maria Paula Oliveira. "AN EXPERIENCE WITH DESMOS IN THE STUDY OF THE QUADRATIC FUNCTION". 2022.
    10.21125/edulearn.2022.1069
  8. Nuno Bastos; Nuno Rafael O. Bastos. "USE OF DESMOS TO ENGAGE STUDENTS IN CALCULUS". 2022.
    10.21125/edulearn.2022.1812
  9. Vanda Santos; Andreia Hall; Nuno Rafael O. Bastos; Cristina M.R. Caridade. "ACTIVE LEARNING DURING THE COVID-19 PANDEMIC - A TRIPLE EXPERIMENT". 2022.
    10.21125/edulearn.2022.0340
  10. Nuno Rafael O. Bastos. "IN-SERVICE MATH TEACHER TRAINING WORKSHOPS WITH TECHNOLOGY INTEGRATION: SOME EXAMPLES". Paper presented in EDULEARN21, 2021.
    10.21125/edulearn.2021.2515
  11. Nuno Rafael O. Bastos; Vanda Santos. "USING DIGITAL TOOLS TO ENHANCE ACTIVE METHODOLOGIES IN HIGHER EDUCATION". 2021.
    10.21125/edulearn.2021.2520
  12. Figueiredo, Maria; Matias, Rogério; Alves, Valter; Bastos, Nuno; Duarte, Rui Pedro; Ferreira, Bruno; Cunha, Carlos. "PROFESSIONAL DEVELOPMENT FOR HIGHER EDUCATION TEACHING STAFF: AN EXPERIENCE OF PEER LEARNING IN A PORTUGUESE POLYTECHNIC". 2020.
    10.21125/inted.2021.1270
  13. Almeida, Ricardo; Bastos, R. O. Nuno; Monteiro, M. Teresa T.. "An optimization method for the best fractional order to estimate real data analysis". 2015.
Journal article
  1. Andreia O. Hall; Nuno R. O. Bastos. "String art with repeating decimals". Journal of Mathematics and the Arts (2024): https://doi.org/10.1080/17513472.2024.2386645.
    10.1080/17513472.2024.2386645
  2. Nuno R. O. Bastos; Touria Karite. "Mathematical Methods in Applied Sciences". Axioms (2024): https://doi.org/10.3390/axioms13050327.
    10.3390/axioms13050327
  3. Daniel Machado; Nuno Bastos; Andreia Hall; Sónia Pais. "Volume of geometric solids on the Desmos platform – A didactic experience in Cape Verde". European Journal of Science and Mathematics Education (2023): https://doi.org/10.30935/scimath/12788.
    10.30935/scimath/12788
  4. Bastos, Nuno R. O.. "Calculus of variations involving Caputo-Fabrizio fractional differentiation". Statistics, Optimization & Information Computing 6 1 (2018): http://dx.doi.org/10.19139/soic.v6i1.466.
    10.19139/soic.v6i1.466
  5. Almeida, Ricardo; Bastos, Nuno R. O.; Monteiro, M. Teresa T.. "A fractional Malthusian growth model with variable order using an optimization approach". Statistics, Optimization & Information Computing 6 1 (2018): http://dx.doi.org/10.19139/soic.v6i1.465.
    10.19139/soic.v6i1.465
  6. BASTOS, NUNO; Almeida, Ricardo. "A Discretization of the Hadamard fractional derivative". MATHEMATICAL SCIENCES AND APPLICATIONS E-NOTES 4 1 (2016): 31-39.
    Published
  7. Almeida, Ricardo; Bastos, Nuno R. O.; Monteiro, M. Teresa T.. "Modeling some real phenomena by fractional differential equations". Mathematical Methods in the Applied Sciences 39 16 (2015): 4846-4855. http://dx.doi.org/10.1002/mma.3818.
    10.1002/mma.3818
  8. Almeida, Ricardo; Bastos, Nuno R. O.. "A Numerical Method to Solve Higher-Order Fractional Differential Equations". Mediterranean Journal of Mathematics 13 3 (2015): 1339-1352. http://dx.doi.org/10.1007/s00009-015-0550-2.
    10.1007/s00009-015-0550-2
  9. BASTOS, NUNO; Almeida, Ricardo; Torres, Delfim F. M.. "A Discretization Method to Solve Fractional Variational Problems with Dependence on Hadamard Derivatives". International Journal of Difference Equations 9 1 (2014): 3-10.
    Published
  10. Bastos, N.R.O.; Ferreira, R.A.C.; Torres, D.F.M.. "Discrete-time fractional variational problems". Signal Processing 91 3 (2011): 513-524. http://www.scopus.com/inward/record.url?eid=2-s2.0-78049333168&partnerID=MN8TOARS.
    10.1016/j.sigpro.2010.05.001
  11. Bastos, N.R.O.; Ferreira, R.A.C.; Torres, D.F.M.. "Necessary optimality conditions for fractional difference problems of the calculus of variations". Discrete and Continuous Dynamical Systems 29 2 (2011): 417-437. http://www.scopus.com/inward/record.url?eid=2-s2.0-78651241495&partnerID=MN8TOARS.
    10.3934/dcds.2011.29.417
  12. BASTOS, NUNO; Torres, Delfim F. M.. "Fractional derivatives and integrals on time scales via the inverse generalized Laplace transform". International Journal of Mathematics & Computation 11 11 (2011):
    Published
  13. BASTOS, NUNO; Torres, Delfim F. M.. "Combined Delta-Nabla Sum Operator in Discrete Fractional Calculus". Commun. Frac. Calc 1 (2010): 41-47.
    Published
Newspaper article
  1. Almeida, Ricardo; Bastos, Nuno R.O.. "An approximation formula for the Katugampola integral", The objective of this paper is to present an approximation formula for the Katugampola fractional integral, that allows us to solve fractional problems with dependence on this type of fractional operator. The formula only depends on first-order derivatives, and thus converts the fractional problem into a standard one. With some examples, we show the accuracy of the method, and then we present the , 2016, http://hdl.handle.net/10773/15021.
Activities

Oral presentation

Presentation title Event name
Host (Event location)
2023/10/04 CALCULUS: EXPLORING THE WORLD OF OPEN MIDDLE PROBLEMS AND GEOGEBRA International Conference on Math Education and Technology 2023 (ICMET 2023)
(Aveiro, Portugal)
2023/07 THE USE OF SELF-ASSESSMENT AND FLIPPED CLASSROOM IN AN UNDERGRADUATE MATHEMATICS COURSE FOR MANAGEMENT STUDENTS EDULEARN23- 15th International Conference on Education and New Learning Technologies
(Palma de Maiorca, Spain)
2023/07 ACTIVE LEARNING IN A VOCATIONAL EDUCATION AND TRAINING PROGRAMME EDULEARN23- 15th International Conference on Education and New Learning Technologies
(Palma de Maiorca, Spain)
2022/08 Exploring symmetry through portuguese tiles in historical monuments Bridges Aalto 2022
(Helsínquia, Finland)
2022/07 Interlacing Islamic Art with the Teaching of Symmetry in Portuguese Schools Symmetry Art and Science: 12th Symmetry Congres
(Porto, Portugal)
2022/07 Use of Desmos to engage students in Calculus EDULEARN22- 14th International Conference on Education and New Learning Technologies
(Palma de Maiorca, Spain)
2022/07 Breakout rooms: a collaborative space that works EDULEARN22- 14th International Conference on Education and New Learning Technologies
(Palma de Maiorca, Spain)
2022/04 Estratégias para envolver ativamente os estudantes no processo de aprendizagem Encontro de Práticas de Promoção da Aprendizagem Ativa (e mais!) no Ensino Superior
(Viseu, Portugal)
2021/07 In-service Math Teacher Training Workshops With Technology Integration: Some Examples EDULEARN21- 13th International Conference on Education and New Learning Technologies
(Palma de Maiorca, Spain)
2021/07 Using Digital Tools To Enhance Active Methodologies In Higher Education EDULEARN21- 13th International Conference on Education and New Learning Technologies
(Palma de Maiorca, Spain)
2021/05 Rosáceas e Simetrias Ciclo de Atividades Online Museu da Matemática UFMG
(Brazil)
2020/12 Critical Thinking on Mathematics in Higher Education: Two Experiences TECH-EDU 2020 - 2nd International Conference on Technology and Innovation in Learning, Teaching and Education
2019/12 Numerical Study for Fractional Populations Growth Model of a Variable-Order Fractional Derivative 8th Podlasie Conference on Mathematics (8PCM)
(Bialystok, Poland)
2019/06 Optimality conditions for variational problems containing a derivative with a non-singular kernel VI Workshop on Computational Data Analysis and Numerical Methods (VI WC- DANM)
(Covilhã, Portugal)
2019/04 Will mathematics surprise the most skeptical student? IV Encontro de Investigação e Práticas em Educação (EIPE 2019)
(Coimbra, Portugal)

Supervision

Thesis Title
Role 		Degree Subject (Type)
Institution / Organization
2022/09 - 2023/07 Instagram no Ensino (Secundário) da Matemática A
Co-supervisor
 Mestrado em Matemática para Professores (Master)
2021/10 - 2022/12/16 Aprendizagens ativas em matemática com recurso ao GeoGebra: a função exponencial
Supervisor
 Mestrado em Matemática para Professores (Master)
Universidade de Aveiro, Portugal
2021/10 - 2022/12/16 Aprendizagens ativas nos domínios da estatística e das probabilidades com recurso a ferramentas digitais
Co-supervisor
 Mestrado em Matemática para Professores (Master)
Universidade de Aveiro, Portugal
2020/11 - 2021/12 Era das Ferramentas Digitais na Sala de Aula de Matemática - Números Racionais
Supervisor of Paulo Eurico Adrega Lourenço
 Matemática para Professores (Master)
Universidade de Aveiro, Portugal
2020/10 - 2021/07/12 Aprendizagens Ativas no domínio das funções reais com recurso a ferramentas digitais
Co-supervisor of Maria Lucília Barros Dias
 Matemática para Professores (Master)
Universidade de Aveiro, Portugal
2020/10 - 2021/07/07 Volumes de Sólidos Geométricos - Aprendizagens Ativas com Recurso a Ferramentas Digitais
Supervisor of Daniel Joaquim Carvalho Machado
 Matemática para Professores (Master)
Universidade de Aveiro, Portugal
2019/09 - 2021/01/22 Arte islâmica e o ensino da geometria: um casamento perfeito
Co-supervisor
 Mestrado em Matemática para Professores (Master)
Universidade de Aveiro, Portugal

Event organisation

Event name
Type of event (Role) 		Institution / Organization
2023/10/02 - Current International Conference on Math Education and Technology 2023 (ICMET 2023) (2023/10/02 - 2023/10/04)
Conference (Member of the Organising Committee)
2023/05/02 - Current 36º Encontro do Seminário Nacional de História da Matemática (2023/10/20 - 2023/10/21)
Meeting (Member of the Organising Committee)
 Universidade de Aveiro, Portugal

Jury of academic degree

Topic
Role 		Candidate name (Type of degree)
Institution / Organization
2023/07/13 Raciocínio dedutivo no ensino da matemática no ensino secundário
(Thesis) Main arguer
 Maria do Rosário Fernandes Gomes de Almeida (Master)
Universidade de Aveiro, Portugal
2022/12 Aprendizagens ativas em matemática com recurso ao GeoGebra: a função exponencial
Supervisor
 Elsa Maria Godinho de Assunção (Master)
Universidade de Aveiro, Portugal
2022/12 Aprendizagens ativas nos domínios da estatística e das probabilidades com recurso a ferramentas digitais
Supervisor
 Isabel Cristina Barbosa Ferreira (Master)
Universidade de Aveiro, Portugal
2022/11/18 Aprendizagem ativa e gamificação no ensino da Matemática
(Thesis) Main arguer
 Mercedes Maria Coutinho Soares Pinto (Master)
Universidade de Aveiro, Portugal
2022/07 Estratégicas dinâmicas de aprendizagem em Matemática no domínio da trigonometria
(Thesis) Main arguer
 Maria João Barroso (Master)
Universidade de Aveiro, Portugal
2021/12 Era das Ferramentas Digitais na Sala de Aula de Matemática - Números Racionais
Supervisor
 Paulo Eurico Adrega Lourenço (Master)
Universidade de Aveiro, Portugal
2021/07/07 Volumes de Sólidos Geométricos - Aprendizagens Ativas com Recurso a Ferramentas Digitais
Supervisor
 Daniel Joaquim Carvalho Machado (Master)
Universidade de Aveiro, Portugal
2021/02/11 Estudo da Geometria do Círculo em Cursos de Educação e Formação para Adultos
(Thesis) Main arguer
 Alberto Alexandre dos Reis Cunha Taveira (Master)
Universidade de Aveiro, Portugal
2020/07/21 Avaliação diagnóstica em Matemática. Um instrumento online sobre as conceções de alunos de 5.o ano sobre o sinal de igual.
(Thesis) Main arguer
 António Manuel Mota Pereira Menino (Master)
Universidade de Aveiro, Portugal
2019/10/30 Uma abordagem ao Cálculo das Variações e Teoria de Controlo Ótimo
(Thesis) Main arguer
 Domingos Miguel Ilombo (Master)
Universidade de Aveiro, Portugal
2019/06/26 Condições necessárias e suficientes de otimalidade para funcionais dependendo de derivadas fracionárias de ordem variável
(Thesis) Main arguer
 Manuel Augusto Tomás Gomes (Master)
Universidade de Aveiro, Portugal
2019/05 Magia ou Matemática ? Truques e aprendizagens no 3º ciclo do ensino básico
(Thesis) Main arguer
 Ana Sofia Silva Mesquita Matos (Master)
Universidade de Aveiro, Portugal
2016/12/22 Circo Matemático
(Thesis) Main arguer
 Luísa Maria Milheiro Lima Costa Marques (Master)
Universidade de Aveiro, Portugal
2015/12/18 MAGIA MATEMÁTICA COM NÚMEROS
(Thesis) Main arguer
 ILDA MARIA DA SILVA BASTOS (Master)
Universidade de Aveiro, Portugal
2015/07/06 MAGIA MATEMÁTICA COM CARTAS
(Thesis) Main arguer
 MARIA MANUELA CORREIA RODRIGUES (Master)
Universidade de Aveiro, Portugal

Ad Hoc journal article review

Journal title (ISSN) Publisher
2023/03 - Current Bulletin of the Iranian Mathematical Society
2023/03 - Current Contemporary Mathematics
2022/11 - Current Chaos, Solitons & Fractals
2022/07 - Current Journal of Sensor and Actuator Networks
2022/05 - Current Sensors
2022/03 - Current Boletim da Sociedade Paranaense de Matemática
2021/12 - Current Fractal and Fractional
2021/11 - Current Symmetry
2021/10 - Current Mathematics
2021/05 - Current Mathematical Biosciences and Engineering
2021/01 - Current Journal of Mathematical Modeling
2020/09 - Current Results in Physics
2019/04 - Current Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics
2018/07 - Current Axioms
2017/12 - Current The European Physical Journal B
2017/10 - Current Applied Mathematics and Computation
2017/08 - Current Journal of Applied Mathematics and Computing
2017/07 - Current Journal of Computational and Applied Mathematics
2017/04 - Current International Journal of Computer Mathematics
2017/04 - Current Journal of Computer Mathematics
2016/10 - Current International Journal of Dynamical Systems and Differential Equations
2016/10 - Current Journal of Taibah University for Science
2016/08 - Current International Journal of Difference Equations
2016/06 - Current Arabian Journal of Mathematics
2016/03 - Current Fractional Differential Calculus
2016/02 - Current Mathematical Methods in the Applied Sciences
2015/12 - Current Journal of Dynamical and Control Systems
2015/11 - Current Journal of Mathematical Analysis
2014/12 - Current Discrete Dynamics in Nature and Society
2014/08 - Current Advances in Difference Equations
2014/02 - Current Journal of Mathematics and Mathematical Sciences
2014/01 - Current Signal Processing
2011/11 - Current Optimization

Committee member

Activity description
Role 		Institution / Organization
2023/10/02 - Current Scientific Commitee of International Conference on Math Education and Technology 2023 (ICMET 2023)
Member

Conference scientific committee

Conference name Conference host
2023/10/02 - 2023/10/04 International Conference on Math Education and Technology 2023 (ICMET 2023) Aveiro

Journal scientific committee

Journal title (ISSN) Publisher
2022/09 - Current Axioms (Guest Editor for a Special Issue: Mathematical Methods in the Applied Sciences) (2075-1680) MDPI
Distinctions

Other distinction

2015 Best Paper Award for the Signal Processing Journal