Proof levels of graph theory students under the lens of the Van Hiele model

Abstract

This work is devoted to exploring proof abilities in Graph Theory of undergraduate students of the Degree in Computer Engineering and Technology of the University of Seville. To do this, we have designed a questionnaire consisting of five open-ended items that serve as instrument to collect data concerning their proof skills when dealing with graphs. We have thus analysed them adapting the methodology for computing the degrees of acquisition of the Van Hiele levels. Our analysis leads to different proof profiles of Graph Theory students whose characteristics provide empirical support to consider proof levels in Graph Theory from the perspective of the Van Hiele model.

KEYWORDS:

• Levels of reasoning
• proof
• graph theory
• Van Hiele model

SUBJECT CLASSIFICATIONS CODE:

• 97K30

Acknowledgements

The first author would like to thank to Universidad de Zaragoza for its support during his stay in Zaragoza (January-February 2022) and the second author would like to thank to Universidad de Sevilla for its support during his stay in Sevilla (November-December 2021).

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 Congress of the European Society for Research in Mathematics Education.

2 International Congress on Mathematical Education.

3 International Network for Didactic Research in University Mathematics.

4 Research in Undergraduate Mathematics Education.

5 Problems, Resources, and Issues in Mathematics Undergraduate Studies.

 

Additional information

Funding

The first author is partially supported by Universidad de Sevilla (Spain) [‘VI Plan Propio de Investigación y Transferencia’], the second author is partially supported by Spanish Agencia Estatal de Investigación (Spain) [grant number PID2020-115652GB-I00], the third author is partially supported by Spanish MICINN (Spanish Ministry of Science and Innovation) [grant number PID2019-104964GB-I00]. The first author belongs to the research group FQM-226 (Junta de Andalucía, Spain), the second and third authors belong to the research group S60_20R (Gobierno de Aragón, Spain), and the fourth author belongs to the research group TIC-146 (Junta de Andalucía, Spain).