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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
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Hans Humenberger – International Journal of Mathematical Education in Science and Technology, 2025
Hands-on experiments with overturning some prisms (partially filled with water) lead students to a conjecture which can be confirmed by using a 3D geometry programme and reinterpreting the process of "overturning of a prism" in an appropriate way. But such confirmations are not a proof and particularly cannot answer the question…
Descriptors: Geometry, Mathematics Instruction, Computer Software, Mathematical Logic
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Eileen Fernández; Elise Lahiere; Eliza Leszczynski – Journal of Mathematics Education at Teachers College, 2025
One of our favorite face-to-face teaching frameworks is "Launch, Explore, Summarize" (LES). However, transitioning LES activities to online settings challenged us to reimagine how learning and its interactions could be supported in this new environment. We explore our experience transitioning an LES lesson on the quadrilateral hierarchy…
Descriptors: Online Courses, Mathematics Instruction, Geometry, Constructivism (Learning)
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David Fraivert; Moshe Stupel – International Journal for Technology in Mathematics Education, 2024
Problem solving and proofs have always played a major role in mathematics. They are, in fact, the heart and soul of the discipline. The using of a number of different proof techniques for one specific problem can display the beauty, and elegance of mathematics. In this paper, we present one specific, interesting geometry problem, and present four…
Descriptors: Geometry, Problem Solving, Mathematics Instruction, Validity
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Abboud, Elias – International Journal of Mathematical Education in Science and Technology, 2023
In this article, we consider certain minimization problems. If d[subscript 1], d[subscript 2] and d[subscript 3] are the distances of a boundary or inner point to the sides of a given triangle, find the point which minimizes d[subscript 1][superscript n] + d[subscript 2][superscript n] + d[subscript 3][superscript n] for positive integer n. These…
Descriptors: Computer Software, Mathematics Instruction, Geometry, Calculus
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Bradley Graeme Welch; Juan Carlos Ponce Campuzano – International Journal of Mathematical Education in Science and Technology, 2025
In this paper, we explore how the typical second year undergraduate topic of matrix diagonalisation can be applied to solve a geometric problem which arises frequently in Vector Calculus: to find the curve of intersection of a plane and a surface. We use GeoGebra, which offers a cost-free and dynamic interface, to explore a specific variant of…
Descriptors: Geometry, Computer Software, Computer Assisted Instruction, Undergraduate Students
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Sandra Vorensky – Mathematics Teacher: Learning and Teaching PK-12, 2024
The Great Mini-Golf Project requires students to use a ruler to identify measurements to the quarter-inch, with careful precision and accuracy, which supported the Standards for Mathematical Practice 5 and 6: using appropriate tools to solve mathematical problems with precision (NGA Center & CCSSO, 2010). This project also supported Standard…
Descriptors: Mathematics Instruction, Geometry, Measurement, Athletics
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McCartney, Mark – International Journal of Mathematical Education in Science and Technology, 2021
An elementary method to calculate the area, centroid and volume of rotation of the Koch curve is presented. Classroom extensions are provided to allow students to investigate the method used.
Descriptors: Mathematics Instruction, Teaching Methods, Geometry, Computation
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Miškovic, Vladimir – Australian Mathematics Education Journal, 2021
In the third of a series, the author describes how symmetrical quintic functions can be expressed in three equivalent formats--like other symmetrical functions. Quadratic functions have a line of symmetry through their vertex and cubic functions have 1800 rotational symmetry around their point of inflection. However, polynomial functions of degree…
Descriptors: Mathematics Instruction, Teaching Methods, Algebra, Geometry
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Moshe Stupel; David Fravert; Jay M. Jahangiri – International Journal for Technology in Mathematics Education, 2024
The 1989 good old days' quote from the "Field of Dreams" by Kevin Costner that "If you build it, he or they will come" is no longer going to be attractive, especially in the field of mathematics education. One such challenging subject in the field of mathematics education is the teaching and learning of geometry. It is the aim…
Descriptors: Mathematical Logic, Mathematical Concepts, Educational Technology, Graphs
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Enrique Ortiz – Mathematics Teacher: Learning and Teaching PK-12, 2023
This article presents an original puzzle that supports students' development of visual thinking and geometry ideas based on the Van Hiele levels of geometric thought. The "Triangle Puzzle" is one of many tools teachers can use to guide students' learning of geometry. The Van Hiele's theory provides a way to assess and support this…
Descriptors: Puzzles, Geometry, Mathematics Instruction, Geometric Concepts
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Lozada-Cruz, German – International Journal of Mathematical Education in Science and Technology, 2021
This note deals with some variants of the integral mean value theorem. Mainly a variant of Sahoo's theorem and a variant of Wayment's theorem were proved. Our approach is rather elementary and does not use advanced techniques from analysis. The simple auxiliary functions were used to prove the results.
Descriptors: Mathematics Instruction, Teaching Methods, Geometry, Problem Solving
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Prasad, Priya V.; Boyce, Steven – PRIMUS, 2022
Exploring non-Euclidean geometries is a common way for College Geometry instructors to highlight subtleties in Euclidean geometry. The concept of congruence, going undefined or informally defined in multiple axiomatic systems, is particularly susceptible to conflation with the idea of "same measure." Taxicab geometry provides a context…
Descriptors: College Mathematics, Geometry, Geometric Concepts, Preservice Teachers
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Wares, Arsalan – International Journal of Mathematical Education in Science and Technology, 2020
In this article, the author describes an occurrence of the golden ratio in the context of regular hexagons. The method described can be used to construct the golden ratio. This is one of many ways one can construct the golden ratio.
Descriptors: Geometry, Mathematics Instruction, Teaching Methods
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Joana Conceição; Margarida Rodrigues – Mathematics Teacher: Learning and Teaching PK-12, 2024
Can You Build It? is an engaging Improve It! task that asks children to construct 3D shapes based on 2D depictions. Students' initial 3D creations often need revision, and as they build and re-build, they develop spatial relationships. This task was implemented in a first-grade class, connected to composing 3D geometric shapes to address the…
Descriptors: Mathematics Instruction, Geometric Concepts, Task Analysis, Grade 1
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