MathIS - Reinvigorating Mathematics for the Information Society

FCOMP-01-0124-FEDER-007254

Our Vision

The Information Society requires highly qualified professionals who can design complex systems with increasing levels of safety and reliability. But it also requires a high degree of "mathematical proficiency" from its individuals, meaning the ability to use mathematical language and methods to model situations/scenarios and reason productively through these models in order to solve problems. This literacy and capability has become a key element of democratic citizenship.

This project gathers computer scientists, math teachers, mathematicians and others who recognize the need for new approaches to the teaching and learning of mathematical skills. We aim to exploit and combine the dynamics of algorithmic problem solving and calculational reasoning on both maths education and the practice of software engineering, boosting the abilities students need to overcome the challenges they will encounter through life.

The overall approach stems from two decades of research on correct-by-construction program design which brought to scene a whole discipline of problem-solving and shed light on the underlying mathematical structures, modeling and reasoning principles. A most relevant consequence has been the systematization of a calculational style of reasoning which can greatly improve on the traditional verbose proofs in natural language, proceeding in a formal, essentially syntactic way Read more.

Team

• JoseNunoOliveira [UM Staff]
• LuisSoaresBarbosa [UM Staff]
• JoseBarros [UM Staff]
• JorgeSousaPinto [UM Staff]
• PedroRangelHenriques [UM Staff]
• Joao Ferreira [PhD Student]
• Alexandra Mendes [PhD Student]
• and several grant holders

Goals

The project aims to produce relevant contributions in the following areas:

• Design calculi foundations and principles.
• Calculational methods and the principles of algorithimic problem solving, as a basis for reinvigorating the teaching and practice of Mathematics in the context of modern IT-driven societies.
• Innovative computer-based tools to support the envisaged methodological shifts.

Results

• Publications

Project info

[1] M. A. Barbosa and L. S. Barbosa. A perspective on service orchestration. Sci. Comput. Program., Elsevier, 74(9):671–687, 2009.

[2] L. S. Barbosa and Sun Meng. Bringing class diagrams to life. Innovations in Systems and Software Engineering, Springer, 6(1-2):91–98, 2010.

[3] N. Oliveira, N. F. Rodrigues, and Pedro R. Henriques. Domain-specific language for coordination patterns. Comput. Sci. Inf. Syst., 8(2):343–359, 2011.

[4] Roland Backhouse and João F. Ferreira. On Euclid’s algorithm and elementary number theory. Sci. Comput. Program., Elsevier, 76(3):160–180, 2011.

Book Chapters

[1] Sun Meng and L. S. Barbosa. A coalgebraic semantic framework for reasoning about interaction designs. In Kevin Lano, editor, UML2 Semantics and Applications, pages 249–279. John Wiley and Sons, Inc., 2009.

[2] J.N. Oliveira. Extended static checking by calculation using the pointfree transform. In Ana Bove, Luís Soares Barbosa, Alberto Pardo, and Jorge Sousa Pinto, editors, Language Engineering and Rigorous Software Devel- opment, International LerNet ALFA Summer School 2008, Piriapolis, Uruguay, Revised Tutorial Lectures, volume 5520 of Lecture Notes in Computer Science, pages 195–251. Springer, 2009.

Conference Papers

[1] João F. Ferreira and Alexandra Mendes. Student’s feedback on teaching mathematics through the calculational method. In 39th ASEE/IEEE Frontiers in Education Conference. IEEE, 2009.

[2] P.F. Silva, J. Visser, and J.N. Oliveira. Galois: A language for proofs using Galois connections and fork algebras. In PLMMS’09 - ACM SIGSAM 2009 International Workshop on Programming Languages for Mechanized Mathematics Systems. Munich, Germany. ACM, 2009.

[3] J. F. Ferreira, A. Mendes, R. Backhouse, and L. S. Barbosa. Which mathematics for the information society? In J. Gibbons and J. N. Oliveira, editors, Inter. Conf. on Teaching Formal Methods (TFM’09), pages 39–56. Springer Lect. Notes Comp. Sci. (5846), 2009.

[4] H. Macedo and J.N. Oliveira. Matrices as arrows. In John Power Magne Haveraaen, Marina Lenisa and Monika Seisenberger, editors, Proc. of CALCO-JR 2009, Udine, Italy, September 7-10, 2009. Tech. Rep. 5-2010of the University of Udine, 2009.

[5] M. A. Martins, A. Madeira, and L. S. Barbosa. Refinement by interpretation. In Dang Van Hung and Padmanabhan Krishnan, editors, 7th IEEE International Conference on Software Engineering and Formal Methods (SEFM’09), pages 250–259. IEEE Computer Society Press, 2009.

[6] M. D. Campos and L. S. Barbosa. Implementation of an orchestration language as a Haskell domain specific language. In F. Arbab and M. Sijarni, editors, Proc. FOCLASA’09, Electr. Notes Theor. Comput. Sci. (255), pages 45–64. Elsevier, 2009.

[7] M. A. Martins, A. Madeira, and L. S. Barbosa. Refinement by interpretation in a general setting. In J. Derrick E. Boiten and S. Reeves, editors, Proc. Refinement Workshop 2009, Electr. Notes Theor. Comput. Sci. (256), pages 105–121. Elsevier, 2009.

[8] M. A Barbosa, L. S. Barbosa, and J.C. Campos. A coordination model for interactive components. In F. Arbab and M. Sirjani, editors, Proc. of FSEN 2009, Kish, Iran, pages 416–430. Springer Lect. Notes Comp. Sci. (5961), 2010.

[9] Nuno Oliveira, N. F. Rodrigues, Pedro R. Henriques, and L. S. Barbosa. A pattern language for architectural analysis. In SBLP 2010 14th Brazilian Symposium in Programming Languages, volume 2, pages 167–180, Slavador, Brasil, September 2010. SBC — Brazilian Computer Society (ISSN: 2175-5922).

[10] João F. Ferreira. Designing an algorithmic proof of the two-squares theorem. In Claude Bolduc, Jules Desharnais, and Béchir Ktari, editors, Mathematics of Program Construction, Proc. 10th International Conference, MPC 2010, Québec City, Canada, June 21-23, 2010., volume 6120 of Lecture Notes in Computer Science, pages 140– 156. Springer, 2010.

[11] L. S. Barbosa and M. H. Martinho. Should mathematics remain invisible? In EIMI 2010 - International Conference Educational Interfaces between Mathematics and Industry, pages 85–95. CIM - Centro Internacional de Matemática, Portugal, October 2010.

[12] João F. Ferreira, Alexandra Mendes, Alcino Cunha, Carlos Baquero, Paulo F. Silva, L.S. Barbosa, and J. N. Oliveira. Logic training through algorithmic problem solving. In Patrick Blackburn, Hans P. van Ditmarsch, María Manzano, and Fernando Soler-Toscano, editors, Tools for Teaching Logic - Proc. Third International Congress, TICTTL 2011, Salamanca, Spain, June 1-4, 2011., volume 6680 of Lecture Notes in Computer Science, pages 62–69. Springer, 2011.

[13] Sara Fernandes, A. Cerone, and L.S. Barbosa. Exploiting the floss paradigm in collaborative e-learning — application to e-government. In David Ferriero and Haiyan Qian, editors, Open Innovation for Global Change — Proc. International Conference on Theory and Practice of Electronic Governance, ICGOV’12. ACM Press, 2012.

[14] Sara Fernandes, A. Cerone, and L.S. Barbosa. A preliminary analysis of learning awareness in FLOSS projects. In Antonio Cerone and Donatella Persico, editors, InSuEdu 2012 - Proc. 1st International Symposium on Innovation and Sustainability in Education, Lecture Notes in Computer Science (in print). Springer, October 2012.

[15] L. S. Barbosa and M. H. Martinho. Mathematical literacy as a condition for sustainable development. In Antonio Cerone and Donatella Persico, editors, InSuEdu 2012 - Proc. 1st International Symposium on Innovation and Sustainability in Education, Lecture Notes in Computer Science (in print). Springer, October 2012.

PhD Theses

[1] João F. Ferreira. Principles and Applications of Algorithmic Problem Solving. PhD thesis, University of Nottingham, 2010.

[2] Alexandra M. Silva. Kleene Coalgebra. PhD thesis, University of Nijmegen, 2010.

[3] Alexandra Mendes. Structured Editing of Handwritten Mathematics. PhD thesis, University of Nottingham, 2012.

Project Summary

Modern IT-driven societies demand highly skilled professionals who can successfully design complex systems at ever-increasing levels of reliability and security. But is also requires from the general user a higher degree of "mathematical fluency", i.e., the ability to resort to mathematical language and method to build models of problems and situations and reasoning effectively within them. Such an ability is at the heart of what it means "to understand" and it may be considered a fundamental ingredient of democratic citizenship. That effective use of Mathematics has enormous economic potential in the IT society has already been acknowledged by the eminent computer scientist E.W. Dijkstra, who once put it that "high technology so celebrated today is essentially a mathematical technology".

There is little hope, however, that such expectations and demands be met by current standards in school maths education. Not only there is a disturbing gap between style and contents of middle school and high school maths, but also never have indicators and statistics been so appalling in what concerns the country's overall ranking in maths education. Worst of all, mathphobia - which seems to be spreading everywhere - has become a hot spot for the media.

This situation calls for emergency policies capable of reinvigorating maths education and its effective application at all problem-solving levels. This should include not only the uniform adoption of well-established calculation techniques which have proven to scale up from the school desk to the engineer's desk tackling complex, real-life problems, but also the design of innovative tools able to support such a technological challenge in a uniform and effective way.

In this context, MathIS aims to exploit the dynamics of algorithmic problem solving and calculational reasoning in both maths education and the practice of software engineering, in an integrated way, thus meeting the challenges of nowadays and future information society.

The project's overall approach stems from two decades of research on correct-by-construction program design which brought to scene a whole discipline of problem-solving and shed light on the underlying mathematical structures, modelling and reasoning principles. A most relevant consequence has been the systematization of a calculational style of reasoning which can greatly improve on the traditional verbose proofs in natural language, proceeding in a formal, essentially syntatic way.

At the educational level, MathIS will reframe a collection of themes in pre-university mathematics along these lines and assess its merits not only on the development of general calculational and algorithmic skills, but also as a tool for discovery. (Recall, for example, that it was the formal manipulation of Maxwell's equations that led to conjecturing the existence of electromagnetic waves, confirmed experimentally shortly afterwards.)

At the software engineering level, MathIS will push forward in the development of new algorithmic design calculi in the emerging area of global computating.

On the technology side, MathIS will capitalize on recent developments and increased flexibility in Human-computer interaction technology, which we believe is mature enough to provide an infra-structure for the envisaged methodological shift. In this context, a second axis in MathIS concerns the development of innovative computer-based tools exploiting Tablet PC technologies, as well as e-learning principles and platforms (in particular, associated to the semantic-driven automatic correction of algorithms). Such tools will provide learning environments oriented to calculational reasoning and algorithmic problem solving, which, although consistent with traditional blackboard-style teaching, will exploit enhanced facilities provided by computers.

Lab Training Workshops

• III Lab Training Workshop Computação sem fronteiras ... Matemática em Movimento (16-20 Julho 2012)

• II Lab Training Workshop Computação sem fronteiras ... Matemática em Movimento (18-22 Julho 2011)

• I Lab Training Workshop Computação sem fronteiras ... Matemática em Movimento (19-23 Julho 2010)
  • Folheto (PDF)

Primeiro Encontro do Projecto Matisse (29 Março 2008)

Proposta, anúncios e imprensa

• Proposta: Que Matemática para a Sociedade da Informação? (PDF)
• Anúncio com objectivos e programa (PDF)
• Matemática e Cidadania, Luís S. Barbosa -- Artigo de opinião e anúncio, Jornal ComUM (PDF)

Objectivos

• Numa sociedade onde é crescente a iliteracia matemática, mas que, paradoxalmente, da Matemática depende cada vez mais, propomo-nos a reflectir sobre o significado que tem "pensar matematicamente" no contexto aberto da Sociedade da Informação;

• Pretendemos fazê-lo a partir de um corpo de princípios e métodos que nos parece possível destilar de vários anos de investigação e ensino em Ciências de Computação e que serão porventura relevantes para partilhar com as comunidades mais vastas da Educação e da Matemática;

• Pretendemos, por fim, lançar um desafio a colegas professores de Matemática em diversos níveis do Ensino para um diálogo que sentimos urgente.

Programa

Clique no título da apresentação para ver os slides correspondentes.

-- 26 Mai 2010

Projecto MathIS

( English description - FCOMP-01-0124-FEDER-007254)

A Sociedade da Informação requer profissionais altamente qualificados que possam conceber sistemas complexos com níveis cada vez maiores de fiabilidade e segurança. Mas requer também do conjunto da sociedade um grau elevado de "fluência matemática", entendendo-se por esta a capacidade de recorrer à linguagem e ao método matemático para modelar problemas e situações e raciocinar produtivamente no interior desses modelos. Tal capacidade e literacia tornou-se um elemento fundamental da cidadania democrática.

O projecto MathIS é formado por informáticos, professores de matemática, matemáticos e outras pessoas que reconhecem a necessidade de novas aproximações ao ensino/aprendizagem da Matemática.

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Alguns Marcos

Junho 2012 — Defesa PhD Alexandra Mendes (Structured Editing of Handwritten Mathematics).

18-22 Julho, 2011 — Segunda workshop Computação sem fronteiras ... Matemática em movimento para alunos do Ensino Secundário.

18 Outubro 2011 — Alexandra Silva recebe o Prémio Científico IBM 2010.

Junho 2011 — Artigo com survey das Lab Training Workshops publicado na TICTTL 2011: Logic training through algorithmic problem solving. Detalhes aqui

Dezembro 2010 — Defesa PhD Alexandra Silva (Kleene Coalgebra).

Dezembro 2010 — Defesa PhD João F. Ferreira (Principles and Applications of Algorithmic Problem Solving).

19-23 Julho, 2010 — Primeira workshop Computação sem fronteiras ... Matemática em movimento para alunos do Ensino Secundário.

Novembro 2009 — Primeiro survey da experiência MathIS publicado na TFM 2009: Which mathematics for the information society?. Detalhes aqui

24 Abril, 2009 — Primeiro artigo do projecto aceite: Students' Feedback on Teaching Mathematics Through The Calculational Method aceite na Frontiers in Education 2009. Detalhes aqui

1 Janeiro, 2009 — Comunicação da homolgação e início oficial do MathIS

14 Abril, 2008 — Primeira versão da página do projecto disponível.

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