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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

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

Glassmeyer, David; Brakoniecki, Aaron; Amador, Julie M. – International Journal of Mathematical Education in Science and Technology, 2019

Including opportunities for students to experience uncertainty in solving mathematical tasks can prompt learners to resolve the uncertainty, leading to mathematical understanding. In this article, we examine how preservice secondary mathematics teachers' thinking about a trigonometric relationship was impacted by a series of tasks that prompted…

Descriptors: Mathematics Instruction, Problem Solving, Concept Formation, Preservice Teachers

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

Hoban, Richard A. – International Journal of Mathematical Education in Science and Technology, 2019

Many students do not have a deep understanding of the integral concept. This article defines what a deep understanding of the integral is in respect to integration involving one independent variable; briefly discusses factors which may inhibit such an understanding; and then describes the design of a mathematical resource for introducing students…

Descriptors: Mathematics Instruction, Mathematical Concepts, Concept Formation, Calculus

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

Cunningham, Daniel W. – International Journal of Mathematical Education in Science and Technology, 2018

Modern calculus textbooks carefully illustrate how to perform integration by trigonometric substitution. Unfortunately, most of these books do not adequately justify this powerful technique of integration. In this article, we present an accessible proof that establishes the validity of integration by trigonometric substitution. The proof offers…

Descriptors: Mathematics Education, Trigonometry, Calculus, Mathematical Concepts

de Camargo, André Pierro – International Journal of Mathematical Education in Science and Technology, 2018

In a previous article published in the "American Mathematical Monthly," Tucker ("Amer Math Monthly." 1997; 104(3): 231-240) made severe criticism on the Mean Value Theorem and, unfortunately, the majority of calculus textbooks also do not help to improve its reputation. The standard argument for proving it seems to be applying…

Descriptors: Mathematics Education, Calculus, Mathematical Logic, Equations (Mathematics)

Zeynivandnezhad, Fereshteh; Bates, Rachel – International Journal of Mathematical Education in Science and Technology, 2018

The importance of developing students' mathematical thinking is frequently highlighted in literature regarding the teaching and learning of mathematics. Despite this importance, most curricula and instructional activities for undergraduate mathematics fail to bring the learner beyond the mathematics. The purpose of this study was to enhance…

Descriptors: Mathematics Instruction, Equations (Mathematics), Computer Uses in Education, Educational Technology

Ghergu, Marius – International Journal of Mathematical Education in Science and Technology, 2018

We explore the connection between the notion of critical point for a function of one variable and various inequalities for iterated exponentials defined on the positive semiline of real numbers.

Descriptors: Mathematics, Mathematics Instruction, Mathematical Concepts, Numbers

Dobbs, David E. – International Journal of Mathematical Education in Science and Technology, 2018

For a function "f": [real numbers set][superscript n]\{(0,…,0)}[right arrow][real numbers set] with continuous first partial derivatives, a theorem of Euler characterizes when "f" is a homogeneous function. This note determines whether the conclusion of Euler's theorem holds if the smoothness of "f" is not assumed. An…

Descriptors: Mathematical Logic, Validity, Mathematics Instruction, Calculus

Buchbinder, Orly – International Journal of Mathematical Education in Science and Technology, 2018

The nine-point circle theorem is one of the most beautiful and surprising theorems in Euclidean geometry. It establishes an existence of a circle passing through nine points, all of which are related to a single triangle. This paper describes a set of instructional activities that can help students discover the nine-point circle theorem through…

Descriptors: Mathematical Logic, Validity, Geometry, Geometric Concepts

Wares, Arsalan – International Journal of Mathematical Education in Science and Technology, 2018

The purpose of this paper is to provide examples of "non-traditional" proof-related activities that can explored in a dynamic geometry environment by university and high school students of mathematics. These propositions were encountered in the dynamic geometry environment. The author believes that teachers can ask their students to…

Descriptors: Teaching Methods, Validity, Mathematical Logic, High School Students