The conceptual and architectural design of a system supporting exploratory learning of mathematics generalisation

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5794 LNCS, Issue , 2009, Pages 22-36

  Pearce, Darren ^a   Poulovassilis, Alexandra ^a  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

Exploratory Learning; Intelligent Support; Mathematics Generalisation; Teacher Assistance Tools

Indexed keywords

EXPLORATORY LEARNING; GENERALISATION; INTELLIGENT SUPPORT; MATHEMATICS GENERALISATION; PROOF OF CONCEPT; TESTING METHODOLOGY;

ARCHITECTURAL DESIGN; E-LEARNING; ELECTRIC CONDUCTIVITY MEASUREMENT; KNOWLEDGE ACQUISITION; MATHEMATICAL TECHNIQUES; MULTI AGENT SYSTEMS;

TEACHING;

EID: 70450219491     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-04636-0_5     Document Type: Conference Paper

References (17)

1. Küchemann, D., Hoyles, C.: Investigating factors that influence students' mathematical reasoning. In: PME XXV, vol. 3, pp. 257-264 (2001)
2. Healy, L., Hoyles, C.: A study of proof conceptions in algebra. Journal for Research in Mathematics Education 31(4), 396-428 (2000)
3. Mason, J., Graham, A., Johnston-Wilder, S.: Developing Thinking in Algebra. Paul Chapman Publishing, Boca Raton (2005)
4. Geraniou, E., Mavrikis, M., Noss, R., Hoyles, C.: A learning environment to support mathematical generalisation in the classroom. In: Proceedings of CERME 6, Lyon, France (2009)
5. Lesh, R., Kelly, A.E.: A constructivist model for redesigning AI tutors in mathematics. In: Laborde, J. (ed.) Intelligent learning environments: The case of geometry. Springer, New York (1996)
6. Kynigos, C.: Insights into pupils' and teachers' activities in pupil-controlled problem-solving situations. In: Information Technology and Mathematics Problem Solving: Research in Contexts of Practice, pp. 219-238. Springer, Heidelberg (1992)
7. Hoyles, C., Sutherland, R.: Logo Mathematics in the Classroom. Routledge, New York (1989)
8. Kirscher, P., Sweller, J., Clark, R.E.: Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiental and inquiry-based learning. Educational Psychologist 41(2), 75-86 (2006)
9. Mavrikis, M., Geraniou, E., Noss, R., Hoyles, C.: Revisiting pedagogic strategies for supporting students' learning in mathematical microworlds. In: Proceedings of the International Workshop on Intelligent Support for Exploratory Environments at EC-TEL 2008 (2008)
10. Cocea, M., Magoulas, G.: Combining intelligent methods for learner modelling in exploratory learning environments. In: Proceedings of the International Workshop on Combinations of Intelligent Methods and Applications at ECAI 2008, pp. 13-18 (2008)
11. Cocea, M., Gutierrez-Santos, S., Magoulas, G.: Challenges for intelligent support in exploratory learning: the case of shapebuilder. In: Proceedings of the International Workshop on Intelligent Support for Exploratory Environments at EC-TEL 2008 (2008)
12. Thompson, P.W.: Mathematical microworlds and intelligent computer-assisted instruction. In: Artificial intelligence and instruction: Applications and methods, Boston, MA, pp. 83-109. Addison-Wesley Longman Publishing Co., Inc. (1987)
13. Hoyles, C.: Microworlds/schoolworlds: The transformation of an innovation. In: Keitel, C., Ruthven, K. (eds.) Learning from computers: mathematics education and technology, pp. 1-17. Springer, Berlin (1993)
14. Gutierrez, S., Mavrikis, M., Pearce, D.: A learning environment for promoting structured algebraic thinking in children. In: Proceedings of ICALT, Santander, Spain (2008)
15. Noss, R., Hoyles, C., Mavrikis, M., Geraniou, E., Gutierrez-Santos, S., Pearce, D.: Broadening the sense of 'dynamic': a microworld to support students' mathematical generalisation. The International Journal on Mathematics Education (ZDM) 41(5) (to appear, 2009)
16. Pearce, D., Poulovassilis, A.: Architecture specification of MiGen v1 (April 2009) Version 0.2., http://www.migen.org/publications/reports/arch-spec/ 0-2
17. Fielding, R.T.: Representational State Transfer (REST). In: Architectural styles and the design of network-based software architectures, ch. 5. University of California, Irvine (2000); PhD Thesis