# Making generalisations in geometry: students' views on the process: a case study

Paper

*2008 Annual Conference for the Psychology of Mathematics Education (PME 32): Mathematical Ideas: History, Education and Cognition.*Morelia, Mexico 17 - 21 Jul 2008 Morelia, Mexico.

Paper/Presentation Title | Making generalisations in geometry: students' views on the process: a case study |
---|---|

Presentation Type | Paper |

Authors | |

Author | Yevdokimov, Oleksiy |

Editors | Figueras, Olimpia, Cortina, Jose Luis, Alatorre, Silvia, Rojano, Teresa and Sepulveda, Armando |

Journal or Proceedings Title | Proceedings of the 2008 Annual Conference for the Psychology of Mathematics Education (PME 32) |

ERA Conference ID | 50226 |

Journal Citation | 4, pp. 441-448 |

Number of Pages | 8 |

Year | 2008 |

Place of Publication | Morelia, Mexico |

ISBN | 9789689020066 |

9786079501303 | |

Web Address (URL) of Paper | http://core.kmi.open.ac.uk/download/pdf/11038380.pdf |

Conference/Event | 2008 Annual Conference for the Psychology of Mathematics Education (PME 32): Mathematical Ideas: History, Education and Cognition |

Annual Conference of the International Group for the Psychology of Mathematics Education | |

Event Details | 2008 Annual Conference for the Psychology of Mathematics Education (PME 32): Mathematical Ideas: History, Education and Cognition Event Date 17 to end of 21 Jul 2008Event Location Morelia, Mexico |

Event Details | Annual Conference of the International Group for the Psychology of Mathematics Education PME |

Abstract | The paper presents results of the research focused on studying students' abilities to make generalisations in geometry. Students' activities in a classroom have been analysed through the evaluation of their inquiry work on different tasks that required deductive reasoning and non-routine approach to carry out possible generalisations. Cognitive processes regarding to different geometrical structures are described and analysed in detail. The special emphasis has been given to students' obstacles while making generalisations. |

Keywords | geometry; generalisations; inquiry activities |

ANZSRC Field of Research 2020 | 390109. Mathematics and numeracy curriculum and pedagogy |

490402. Algebraic and differential geometry | |

461199. Machine learning not elsewhere classified | |

Public Notes | This publication is copyright. It may be reproduced in whole or in part for the purposes of study, research, or review, but is subject to the inclusion of an acknowledgment of the source. |

Byline Affiliations | Department of Mathematics and Computing |

https://research.usq.edu.au/item/9z05z/making-generalisations-in-geometry-students-views-on-the-process-a-case-study

## Download files

###### Published Version

Yevdokimov_PME32_PV.pdf | ||

File access level: Anyone |

###### Accepted Version

Yevdokimov_PME32_AV.pdf | ||

File access level: Anyone |

##### 1967

total views##### 681

total downloads##### 1

views this month##### 0

downloads this month

## Export as

## Related outputs

##### Minimising mathematical anxiety in teaching mathematics and assessing studentâ€™s work

Yevdokimov, Oleksiy. 2021. "Minimising mathematical anxiety in teaching mathematics and assessing studentâ€™s work." Kollosche, David (ed.)*11th International Mathematics Education and Society Conference: Exploring new ways to connect (2021).*Virtual Germany.

##### Links between problems and their role in students' preparation for mathematical contests

Yevdokimov, Oleksiy. 2010. "Links between problems and their role in students' preparation for mathematical contests." Avotina, Maruta, Bonca, Dace, Falk de Losada, Maria, Ramana, Liga and Soifer, Alexander (ed.)*WFNMC6: 6th Congress of the World Federation of National Mathematics Competitions.*Riga, Latvia 25 - 31 Jul 2010 Australia.

##### Problem set 12

Yevdokimov, Oleksiy. 2013. "Problem set 12."*Australian Senior Mathematics Journal.*27 (2), pp. 63-63.

##### Problem set 11

Yevdokimov, Oleksiy. 2013. "Problem set 11."*Australian Senior Mathematics Journal.*27 (1), pp. 64-64.

##### On the analysis of indirect proofs: contradiction and contraposition

Jourdan, Nicolas and Yevdokimov, Oleksiy. 2016. "On the analysis of indirect proofs: contradiction and contraposition."*Australian Senior Mathematics Journal.*30 (1), pp. 55-64.

##### Problem set 8

Yevdokimov, Oleksiy. 2011. "Problem set 8."*Australian Senior Mathematics Journal.*25 (2), pp. 63-63.

##### Problem set 7

Yevdokimov, Oleksiy. 2011. "Problem set 7."*Australian Senior Mathematics Journal.*25 (1), pp. 64-64.

##### Problem set 6

Yevdokimov, Oleksiy. 2010. "Problem set 6."*Australian Senior Mathematics Journal.*24 (2), pp. 64-64.

##### Problem set 5

Yevdokimov, Oleksiy. 2010. "Problem set 5."*Australian Senior Mathematics Journal.*24 (1), pp. 64-64.

##### Problem set 9

Yevdokimov, Oleksiy. 2012. "Problem set 9 ."*Australian Senior Mathematics Journal.*26 (1), pp. 64-64.

##### Problem set 10

Yevdokimov, Oleksiy. 2012. "Problem set 10."*Australian Senior Mathematics Journal.*26 (2), pp. 63-63.

##### Notes about teaching mathematics as relationships between structures: a short journey from early childhood to higher mathematics

Yevdokimov, Oleksiy. 2012. "Notes about teaching mathematics as relationships between structures: a short journey from early childhood to higher mathematics."*The De Morgan Journal.*2 (1), pp. 69-83.

##### Cognitive development of proof

Tall, David, Yevdokimov, Oleksiy, Koichu, Boris, Whiteley, Walter, Kondratieva, Margo and Cheng, Ying-Hao. 2012. "Cognitive development of proof." Hanna, Gila and de Villiers, Michael (ed.)*Proof and proving in mathematics education*. Dordrecht, Germany. Springer. pp. 13-49

##### On creating a 'free of anxiety' assessment environment for students with special needs

Yevdokimov, Oleksiy. 2011. "On creating a 'free of anxiety' assessment environment for students with special needs ."*NORSMA6: New Trends in Special Needs Education in Mathematics: Problems and Possibilities.*Kristiansand, Norway 02 - 04 Nov 2011 Kristiansand, Norway.

##### Problem set 4

Yevdokimov, Oleksiy. 2009. "Problem set 4."*Australian Senior Mathematics Journal.*23 (2), pp. 63-63.

##### Problem set 3

Yevdokimov, Oleksiy. 2009. "Problem set 3."*Australian Senior Mathematics Journal.*23 (1), pp. 63-63.

##### On the nature of mathematical education of engineers: identifying hidden obstacles and potential for improvement

Yevdokimov, Oleksiy. 2008. "On the nature of mathematical education of engineers: identifying hidden obstacles and potential for improvement." Alpers, Burkhard, Hibberd, Stephen, Lawson, Duncan, Mustoe, Leslie and Robinson, Carol (ed.)*2008 Mathematical Education of Engineers Conference .*Loughborough, United Kingdom 06 - 09 Apr 2008 Loughborough, UK.

##### Higher order reasoning produced in proof construction: how well do secondary school students explain and write mathematical proofs?

Yevdokimov, Oleksiy. 2009. "Higher order reasoning produced in proof construction: how well do secondary school students explain and write mathematical proofs?" Lin, Fou-Lai, Hsieh, Feng-Jui, Hanna, Gila and de Villiers, Michael (ed.)*ICMI Study 19 Working Conference: Proof and Proving in Mathematics Education.*Taipei, Taiwan 10 - 15 May 2009 Taipei.

##### Theoretical perspectives of the process of making conjectures [in Spanish]

Canadas, Maria, Deulofeu, Jordi, Figueiras, Lourdes, Reid, David A. and Yevdokimov, Oleksiy. 2008. "Theoretical perspectives of the process of making conjectures [in Spanish]."*Ensenanza de las Ciencias.*26 (3), pp. 431-444.

##### Notes on 'perpetual question' of problem solving: how can learners best be taught problem-solving skills?

Yevdokimov, Oleksiy and Taylor, Peter. 2008. "Notes on 'perpetual question' of problem solving: how can learners best be taught problem-solving skills?"*Journal of the Korean Society of Mathematical Education Series D: Research in Mathematical Education.*12 (3), pp. 179-191.

##### Problem set 2

Yevdokimov, Oleksiy. 2008. "Problem set 2."*Australian Senior Mathematics Journal.*22 (2), pp. 63-64.

##### Problem set 1

Yevdokimov, Oleksiy. 2008. "Problem set 1."*Australian Senior Mathematics Journal.*22 (1), pp. 63-64.

##### Problem solving activities in a constructivist framework: exploring how students approach difficult problems

Yevdokimov, Oleksiy and Passmore, Tim. 2008. "Problem solving activities in a constructivist framework: exploring how students approach difficult problems." Goos, Merrilyn, Brown, Ray and Makar, Katie (ed.)*31st Annual Conference of the Mathematics Education Research Group of Australasia (MERGA 31).*Brisbane, Australia 28 Jun - 01 Jul 2008 Adelaide, Australia.

##### The conjecturing process: perspectives in theory and implications in practice

Yevdokimov, Oleksiy, Canadas, Maria, Deulofeu, Jordi, Figueiras, Lourdes and Reid, David. 2007. "The conjecturing process: perspectives in theory and implications in practice."*Journal of Teaching and Learning.*5 (1), pp. 55-72.

##### Asymptotically accurate flow completion time distributions under fair queueing

Addie, R. G. and Yevdokimov, Oleksiy. 2008. "Asymptotically accurate flow completion time distributions under fair queueing." Green, Richard (ed.)*Australasian Telecommunication Networks and Applications Conference (ATNAC 2007): Next Generation Networks: Enabling Closer International Cooperation.*Christchurch, New Zealand 02 - 05 Dec 2007 Piscataway, NJ. United States. https://doi.org/10.1109/ATNAC.2007.4665290

##### Using the history of mathematics for mentoring gifted students: Notes for teachers

Yevdokimov, Oleksiy. 2007. "Using the history of mathematics for mentoring gifted students: Notes for teachers." Milton, Ken, Reeves, Howard and Spencer, Toby (ed.)*The 21st Biennial Conference of the Australian Association of Mathematics Teachers Inc..*Hobart, Australia 06 - 09 Jul 2007 Adelaide, Australia.

##### Inquiry activities in a classroom: extra-logical processes of illumination vs logical process of deductive and inductive reasoning. A case study

Yevdokimov, Oleksiy. 2006. "Inquiry activities in a classroom: extra-logical processes of illumination vs logical process of deductive and inductive reasoning. A case study ." Novotna, Jarmila, Stehlikova, Nada, Kratka, Magdalena and Moraova, Hana (ed.)*30th Conference of the International Group for the Psychology of Mathematics Education.*Prague, Czech Republic 16 - 21 Jul 2006 Prague, Czech Republic.

##### Using materials from the history of mathematics in discovery-based learning

Yevdokimov, Oleksiy. 2006. "Using materials from the history of mathematics in discovery-based learning ." Furinghetti, Fulvia, Kaijser, Sten and Tzanakis, Constantinos (ed.)*ICME 10 Satellite Meeting of the International Study Group on the Relations between the History and Pedagogy of Mathematics.*Uppsala, Sweden 12 - 17 Jul 2004 Heraclion, Greece.

##### About a constructivist approach for stimulating students' thinking to produce conjectures and their proving in active learning of geometry

Yevdokimov, Oleksiy. 2006. "About a constructivist approach for stimulating students' thinking to produce conjectures and their proving in active learning of geometry." Bosch, Marianna, Perpinan, Marta and Portabella, M. Angels (ed.)*4th Congress of the European Society for Research in Mathematics Education.*Sant Feliu de Guixols, Spain 17 - 21 Feb 2005 Barcelona, Spain.

##### On development of students' abilities in problem posing: a case of plan geometry

Yevdokimov, Oleksiy. 2005. "On development of students' abilities in problem posing: a case of plan geometry ." Gagatsis, Athanasios, Spagnolo, Filippo, Makrides, Gregory and Farmaki, Vassiliki (ed.)*4th Mediterranean Conference on Mathematics Education.*Palermo, Italy 28 - 30 Jan 2005 Palermo, Italy.

##### Protecting small flows from large ones for quality of service

Addie, R. G., Yevdokimov, Oleksiy, Braithwaite, Stephen and Millsom, David. 2007. "Protecting small flows from large ones for quality of service." Bernstein, David, Dini, Petre, Hladka, Eva, Reza, Hassan, Romascanu, Dan and Sankar, Krishna (ed.)*2nd International Conference on Digital Telecommunications (ICDT 2007).*San Jose, United States 01 - 06 Jul 2007 Piscataway, NJ. United States. https://doi.org/10.1109/ICDT.2007.68