Knowledge Resource
Research Summary: What makes a “good” counterexample? Criteria for the comparison of counterexamples and for fostering subject matter-oriented reflections among preservice teachers
- Original authors
- Attribution requires verification
- Original source
- Frontiers in Education
- Summary & Analysis prepared by
- Aziz Shuaib Ausi
- Resource type
- Research Summary / Knowledge Resource
- Resource published on AZIZ OS
- 26 September 2026
- Last updated
- 27 September 2026
- Reading time
- 1 min
- Publication type
- Knowledge Resource
- Availability
- Open access
About this Summary & Analysis
AZIZ OS provides independently prepared summaries and analytical interpretations of externally published research and knowledge sources. The underlying works remain attributable to their original authors and rights holders. This resource is intended to improve accessibility and understanding and does not replace the original publication.
Research from Frontiers in Education (International) explores the characteristics of effective counterexamples in mathematics education. The study identifies criteria for comparing counterexamples, drawing from existing literature and original contributions, and investigates how preservice teachers apply these criteria. Counterexamples are recognized for their role in refining conjectures, refuting false statements, and stimulating conceptual change in students.
Why it matters
Understanding what constitutes an effective pedagogical tool, such as a 'good' counterexample, is crucial for improving educational outcomes and developing robust curricula. This knowledge informs the design of teaching methodologies that more effectively address student misconceptions and foster deeper conceptual understanding in complex subjects.
Key insights
- Counterexamples are fundamental in mathematics for refining conjectures and disproving false statements.
- They serve an educational purpose by promoting conceptual change among students.
- The effectiveness of a counterexample in convincing students of a statement's incorrectness depends on multiple factors.
- A set of criteria for comparing counterexamples in educational settings has been compiled from literature and original research.
- The study empirically examined which criteria preservice teachers utilize when evaluating counterexamples.
Source
Frontiers in Education — https://www.frontiersin.org/articles/10.3389/feduc.2026.1904577
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Citation
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Verification
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- Verification ID
- ASA-EXE-2026-00954
- Version
- v1.0 · r0
- Issued
- 26 September 2026
- Resource prepared by
- Aziz Shuaib Ausi
- Resource status
- Research Summary / Knowledge Resource
- Underlying work
- What makes a “good” counterexample? Criteria for the comparison of counterexamples and for fostering subject matter-oriented reflections among preservice teachers
- Original authors
- Attribution requires verification
- Original source
- Frontiers in Education
- Provenance status
- Attribution requires verification
- Rights
- Underlying publication rights remain with the respective copyright holder(s). Refer to the original source for authoritative publication and licensing information.
This verification confirms the AZIZ OS resource record and its documented provenance. It does not establish authorship of the underlying external work.