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Ayan, Rukiye; Isiksal-Bostan, Mine – International Journal of Mathematical Education in Science and Technology, 2019

The purpose of this study was to examine middle school students' proportional reasoning, solution strategies and difficulties in real life contexts in the domain of geometry and measurement. The underlying reasons of the difficulties were investigated as well. Mixed research design was adopted for the aims of the study by collecting data through…

Descriptors: Middle School Students, Mathematics Instruction, Mathematical Concepts, Geometry

Patkin, Dorit; Plaksin, Olga – International Journal of Mathematical Education in Science and Technology, 2019

In this study, we aim to explore the extent of mathematics pre-service teachers' ability to apply their procedural understanding combined with spatial perception for drawing conceptual conclusions related to angles in a pyramid. The participants are 16 pre-service high school mathematics teachers. They have studied solid geometry during one…

Descriptors: Preservice Teachers, Mathematics Instruction, Mathematics Teachers, Spatial Ability

Yan, Xiaoheng; Mason, John; Hanna, Gila – International Journal of Mathematical Education in Science and Technology, 2019

This study investigates an exploratory teaching style used in an undergraduate geometry course to help students identify an ellipse. We attempt to probe beneath the surface of exploration to understand how the actions of teachers can contribute to developing students' competence in justifying an ellipse. We analyse the complex interactions between…

Descriptors: Mathematics Instruction, Teaching Methods, Geometry, Geometric Concepts

Palatnik, Alik; Sigler, Avi – International Journal of Mathematical Education in Science and Technology, 2019

The introduction of auxiliary elements as a method of solving problems in high-school geometry is considered here from two perspectives: first, to elicit recalling some known result or concretizing a definition and, second, as a means of shifting the focus and structure of the students' attention. We present and compare various examples of how…

Descriptors: Geometric Concepts, Geometry, Secondary School Mathematics, High School Students

Wares, Arsalan – International Journal of Mathematical Education in Science and Technology, 2019

These notes discuss several related propositions in geometry that can be explored in a dynamic geometry environment. The propositions involve an unexpected property of quadrilaterals.

Descriptors: Geometry, Geometric Concepts, Secondary School Mathematics, High School Students

Dolores-Flores, Crisólogo; Rivera-López, Martha Iris; García-García, Javier – International Journal of Mathematical Education in Science and Technology, 2019

This paper reports the results of a research exploring the mathematical connections of pre-university students while they solving tasks which involving rates of change. We assume mathematical connections as a cognitive process through which a person finds real relationships between two or more ideas, concepts, definitions, theorems, procedures,…

Descriptors: Mathematics Instruction, Mathematical Concepts, Foreign Countries, Arithmetic

Gilboa, Nava; Kidron, Ivy; Dreyfus, Tommy – International Journal of Mathematical Education in Science and Technology, 2019

We analyze the process of constructing a definition within the theoretical framework of "Abstraction in Context." Pairs of students were engaged in a task designed to engender a need for a definition of a tangent to a graph at a given point, and lead to constructing a definition following that need. The results of our analysis point to…

Descriptors: Mathematics Instruction, Definitions, Mathematics Teachers, High School Students

Kandil, Semanur; Isiksal-Bostan, Mine – International Journal of Mathematical Education in Science and Technology, 2019

The purpose of the study was to investigate the effect of inquiry-based instruction enriched with origami activities on 7th grade students' achievement in reflection symmetry and self-efficacy in geometry. Two classes, instructed by the first author of the paper, were randomly assigned as experimental and control groups. In order to gather data,…

Descriptors: Mathematics Instruction, Teaching Methods, Manipulative Materials, Mathematics Achievement

Wares, Arsalan – International Journal of Mathematical Education in Science and Technology, 2019

The purpose of this note is to discuss how paper folding can be used to find the exact trigonometric ratios of the following four angles: 22.5°, 67.5°, 27°, and 63°.

Descriptors: Mathematics Instruction, Teaching Methods, Manipulative Materials, Mathematical Concepts

Verzosa, Debbie Marie B.; De Las Peñas, Ma. Louise Antonette N.; Aberin, Maria Alva Q.; Garces, Len Patrick Dominic M. – International Journal of Mathematical Education in Science and Technology, 2019

This paper presents apps designed to assist students in understanding and developing proofs in geometric theorems. These technologies focus on triangle congruence, triangle similarity and properties of parallelograms. Focus group discussions and initial testing of the apps revealed that the apps offered a more engaging medium for learning proving…

Descriptors: Computer Oriented Programs, Mathematics Instruction, Scaffolding (Teaching Technique), Mathematical Logic

Wares, Arsalan; Elstak, Iwan – International Journal of Mathematical Education in Science and Technology, 2019

The purpose of these notes is to provide examples of large-scale geometry problems that have the potential to promote "constructive struggling" in high-school geometry classrooms. These problems are suitable for being explored in a dynamic geometry environment. The notes also contain brief sketches of solutions to the two problems.

Descriptors: Mathematics Instruction, Geometry, Problem Solving, High School Students

Akhtyamov, Azamat; Amram, Meirav; Mouftakhov, Artour – International Journal of Mathematical Education in Science and Technology, 2018

In this paper, we reconstruct matrices from their minors, and give explicit formulas for the reconstruction of matrices of orders 2 × 3, 2 × 4, 2 × n, 3 × 6 and m × n. We also formulate the Plücker relations, which are the conditions of the existence of a matrix related to its given minors.

Descriptors: Matrices, Algebra, Mathematics Instruction, Mathematical Models

Horzum, Tugba; Ertekin, Erhan – International Journal of Mathematical Education in Science and Technology, 2018

The purpose of this study is to analyze what kind of conceptions prospective mathematics teachers (PMTs) have about the base concept (BC). One-hundred and thirty-nine PMTs participated in the study. In this qualitative research, data were obtained through open-ended questions, the semi-structured interviews and pictures of geometric figures drawn…

Descriptors: Preservice Teachers, Mathematics Teachers, Mathematics Education, Foreign Countries

Moreno-Armella, Luis; Brady, Corey; Elizondo-Ramirez, Rubén – International Journal of Mathematical Education in Science and Technology, 2018

This paper explores a deep transformation in mathematical epistemology and its consequences for teaching and learning. With the advent of non-Euclidean geometries, direct, iconic correspondences between physical space and the deductive structures of mathematical inquiry were broken. For non-Euclidean ideas even to become "thinkable" the…

Descriptors: Geometry, Mathematics, Mathematics Instruction, Geometric Concepts

Ponce Campuzano, Juan Carlos; Matthews, Kelly E.; Adams, Peter – International Journal of Mathematical Education in Science and Technology, 2018

In this paper, we report on an experimental activity for discussing the concepts of speed, instantaneous speed and acceleration, generally introduced in first year university courses of calculus or physics. Rather than developing the ideas of calculus and using them to explain these basic concepts for the study of motion, we led 82 first year…

Descriptors: Mathematics, History, College Freshmen, College Science