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Saeed Salehi – International Journal of Mathematical Education in Science and Technology, 2025
A fascinating and catchy method for proving that a number of special lines concur is using the concept of locus. This is now the classical method for proving the concurrency of the internal angle bisectors and perpendicular side bisectors of a triangle. In this paper, we prove the concurrency of the altitudes and the medians by showing that they…
Descriptors: Mathematical Logic, Validity, Geometry, Geometric Concepts
Moshe Stupel; Jay M. Jahangiri – International Journal of Mathematical Education in Science and Technology, 2025
In this article, we state an interesting geometric conservation property between the three angle bisectors of three similar right triangles and provide a proof without words for its justification. A GeoGebra applet is also presented to help with the understanding of the progression of the proof from inductive to deductive stage.
Descriptors: Geometry, Mathematics Instruction, Computer Software, Teaching Methods
Andreas Bergwall – International Journal of Mathematical Education in Science and Technology, 2025
Students' difficulties with proofs are well documented. To remedy this, it is often recommended that reasoning and proving be focused on in all grades and content areas of school mathematics. However, proofs continue to have a marginal place in many classrooms, or are only given explicit attention in courses in Euclidean geometry. Geometry is also…
Descriptors: Mathematics Instruction, Mathematical Logic, Validity, Geometry
Carolina Henríquez-Rivas; Andrea Vergara-Gómez – European Journal of Science and Mathematics Education, 2025
Although research highlights the importance of analyzing the geometric work of teachers, there are few validated instruments in this line. This study presents the processes of design and validation of a forced-choice questionnaire that allows the characterization, from a theoretical basis, of how geometry teachers organize their teaching practice.…
Descriptors: Geometry, Geometric Concepts, Teaching Methods, Mathematics Instruction
Fangli Xia; Mitchell J. Nathan; Kelsey E. Schenck; Michael I. Swart – Cognitive Science, 2025
Task-relevant actions can facilitate mathematical thinking, even for complex topics, such as mathematical proof. We investigated whether such cognitive benefits also occur for action predictions. The action-cognition transduction (ACT) model posits a reciprocal relationship between movements and reasoning. Movements--imagined as well as real ones…
Descriptors: Undergraduate Students, Geometry, Mathematical Concepts, Mathematics Instruction
Kimberly Dwyer; Angela M. Kelly – Journal for Research in Mathematics Education, 2025
This quantitative correlational study examines school-level longitudinal outcomes of eighth-grade algebra universal acceleration in 15 U.S. school districts when compared with selective acceleration in 289 school districts. Universally accelerated school districts had higher enrollments, with large effect sizes, in geometry, algebra 2, and…
Descriptors: Algebra, Grade 8, Mathematics Instruction, Acceleration (Education)
Rudy Baez; Henry Sanchez; Neril Sandeep; Duli Pllana – International Journal of Research in Education and Science, 2025
Educational institutions around the world have been integrating AI into their educational practices. Many studies and reports highlight both the advantages and disadvantages of this integration. This paper focuses on the positive aspects of AI in education, specifically through the lens of a high school geometry project at a technology-focused…
Descriptors: Creativity, Critical Thinking, High School Students, Urban Schools