Learners’ use of domain-specific computer-based feedback to overcome logical circularity in deductive proving in geometry

• Published in: ZDM Vol. 50; no. 4; pp. 699 - 713
• Main Authors: Fujita, Taro, Jones, Keith, Miyazaki, Mikio
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-08-2018; Springer; Springer Nature B.V
• Subjects: Circularity; Computer Mediated Communication; Construction; Education; Error Correction; Feedback; Feedback (Response); Foreign Countries; Geometric Concepts; Geometry; Instructional Effectiveness; Intervention; Interviews; Learning; Learning Processes; Mathematical Logic; Mathematics; Mathematics Education; Observation; Original Article; Pythagoras (570?-490 BC); Secondary School Students; Students; Support systems; Teachers; Teaching Methods; Web Based Instruction; United Kingdom; Geometry; Logical circularity; Computer-based feedback; Proving
• ISSN: 1863-9690; 1863-9704
• DOI: 10.1007/s11858-018-0950-4

Much remains under-researched in how learners make use of domain-specific feedback. In this paper, we report on how learners’ can be supported to overcome logical circularity during their proof construction processes, and how feedback supports the processes. We present an analysis of three selected episodes from five learners who were using a web-based proof learning support system. Through this analysis we illustrate the various errors they made, including using circular reasoning, which were related to their understanding of hypothetical syllogism as an element of the structure of mathematical proof. We found that, by using the computer-based feedback and, for some, teacher intervention, the learners started considering possible combinations of assumptions and conclusion, and began realising when their proof fell into logical circularity. Our findings raise important issues about the nature and role of computer-based feedback such as how feedback is used by learners, and the importance of teacher intervention in computer-based learning environments.