| Counter-examples for refinement of conjectures and proofs in primary school mathematics K Komatsu The Journal of Mathematical Behavior 29 (1), 1-10, 2010 | 64 | 2010 |
| Task design principles for heuristic refutation in dynamic geometry environments K Komatsu, K Jones International Journal of Science and Mathematics Education 17 (4), 801-824, 2019 | 54 | 2019 |
| A framework for proofs and refutations in school mathematics: Increasing content by deductive guessing K Komatsu Educational Studies in Mathematics 92, 147-162, 2016 | 49 | 2016 |
| Proof validation and modification in secondary school geometry K Komatsu, K Jones, T Ikeda, A Narazaki The Journal of Mathematical Behavior 47, 1-15, 2017 | 42 | 2017 |
| Fostering empirical examination after proof construction in secondary school geometry K Komatsu Educational Studies in Mathematics 96 (2), 129-144, 2017 | 38 | 2017 |
| Interplay between paper-and-pencil activity and dynamic-geometry-environment use during generalisation and proving K Komatsu, K Jones Digital Experiences in Mathematics Education 6 (2), 123-143, 2020 | 27 | 2020 |
| Generating mathematical knowledge in the classroom through proof, refutation, and abductive reasoning K Komatsu, K Jones Educational Studies in Mathematics 109 (3), 567-591, 2022 | 23 | 2022 |
| Proof problems with diagrams: An opportunity for experiencing proofs and refutations K Komatsu, Y Tsujiyama, A Sakamaki, N Koike For the Learning of Mathematics 34 (1), 36-42, 2014 | 18 | 2014 |
| Rethinking the discovery function of proof within the context of proofs and refutations K Komatsu, Y Tsujiyama, A Sakamaki International Journal of Mathematical Education in Science and Technology 45 …, 2014 | 16 | 2014 |
| Potentials for Spatial Geometry Curriculum Development with Three-Dimensional Dynamic Geometry Software in Lower Secondary Mathematics. M Miyazaki, R Katoh, H Arai, F Ogihara, Y Oguchi, T Morozumi, M Kon, ... International journal for technology in mathematics education 19 (2), 2012 | 16 | 2012 |
| Principles of task design to foster proofs and refutations in mathematical learning: Proof problem with diagram K Komatsu, Y Tsujiyama Task design in mathematics education: Proceedings of ICMI Study 22, 471-479, 2013 | 15 | 2013 |
| The role of “opportunity to learn” in the geometry curriculum: A multilevel comparison of six countries C Bokhove, M Miyazaki, K Komatsu, K Chino, A Leung, IAC Mok Frontiers in Education 4, 63, 2019 | 12 | 2019 |
| 算数・数学教育における証明指導の改善 小松孝太郎 (No Title), 2014 | 12 | 2014 |
| Lakatos’ Heuristic Rules as a Framework for Proofs and Refutations in Mathematical Learning: Local-Counterexample and Modification of Proof| Request PDF K Komatsu Pre-proceedings of the 12th International Congress on Mathematical Education …, 2012 | 10 | 2012 |
| How do students generalize a conjecture through proving?: The importance of boundary cases between example and counterexample K Komatsu Proceedings of PME 35 3, 89-96, 2011 | 9 | 2011 |
| Teaching and learning authentic mathematics: The case of proving AJ Stylianides, K Komatsu, K Weber, GJ Stylianides Handbook of cognitive mathematics, 727-761, 2022 | 8 | 2022 |
| Proofs and refutations in school mathematics: A task design in dynamic geometry environments K Komatsu, K Jones DCU Institute of Education and ERME, 2017 | 8 | 2017 |
| Explanatory unification by proofs in school mathematics K Komatsu, T Fujita, K Jones, N Sue For the Learning of Mathematics 38 (1), 31-37, 2018 | 7 | 2018 |
| 数学的探究における action proof の活用の促進-事例研究を通して 小松孝太郎 日本数学教育学会誌 91 (R93), 3-29, 2010 | 7 | 2010 |
| Curriculum development for explorative proving in lower secondary school geometry: Focusing on the levels of planning and constructing a proof M Miyazaki, J Nagata, K Chino, H Sasa, T Fujita, K Komatsu, S Shimizu Frontiers in Education 4, 31, 2019 | 6 | 2019 |
Keith JonesAssociate Professor of Mathematics Education, University of SouthamptonVerified email at soton.ac.uk
