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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
Shiv Krishna Madi Reddy; Meng Guo; Long Cai; Ralph E. White – Chemical Engineering Education, 2024
A method is presented which can be used to obtain analytical solutions for boundary value problems (BVPs) using the matrix exponential and Maple. Systems of second order, linear differential equations are expressed as two or more first order equations in matrix form, and their solutions are obtained using the matrix exponential, matrix…
Descriptors: Chemical Engineering, Engineering Education, Computer Software, Mathematics Instruction
Amenda N. Chow; Peter D. Harrington; Fok-Shuen Leung – Teaching Mathematics and Its Applications, 2024
Physical experiments in classrooms have many benefits for student learning, including increased student interest, participation and knowledge retention. While experiments are common in engineering and physics classes, they are seldom used in first-year calculus, where the focus is on solving problems analytically and, occasionally, numerically. In…
Descriptors: Mathematics Instruction, Calculus, Computer Software, Programming
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
Manuel Santos-Trigo; Matías Camacho-Machín; Fernando Barrera-Mora – ZDM: Mathematics Education, 2024
The aim of this paper is to review recently calculus curriculum reforms and research studies that document what types of understanding students develop in their precalculus courses. We argue that it is important to characterize what difficulties students experience to solve tasks that include the use of foundational calculus concepts and to look…
Descriptors: Mathematics Instruction, Calculus, Barriers, Problem Solving
Renata Teófilo de Sousa; Francisco Régis Vieira Alves; Helena Maria Barros de Campos – Pedagogical Research, 2024
This work is the result of a master's investigation in Brazil, which discusses the teaching of the parabola in the initial training of mathematics teachers. Our theoretical framework addresses the relationship between intuition and the dialectics of the theory of didactic situations, which supports the analysis of the results of this study Its…
Descriptors: Foreign Countries, Preservice Teacher Education, Mathematics Teachers, Mathematics Instruction
Wahid Yunianto; Guillermo Bautista Jr.; Bungkus Dias Prasetyo; Zsolt Lavicza – International Journal for Technology in Mathematics Education, 2024
As computational thinking (CT) is new to teachers, they need support on how CT integration will work. This study examines the use of a hypothetical learning trajectory (HLT) to support teachers in integrating computational thinking into mathematics lessons utilizing GeoGebra. By employing the educational design research (EDR) methodology, the…
Descriptors: Computer Software, Mental Computation, Mathematics Instruction, Educational Technology
José Vidarte; Nancy Chachapoyas – International Journal of Mathematical Education in Science and Technology, 2023
Jordan canonical form (JCF) is one of the most important, and useful, concepts in linear algebra. Mathematics, physics, biology, science and engineering undergraduates often find the first application of real JCF in the discipline of differential equations (continuous models) to solving systems of differential equations. In this work, we apply…
Descriptors: Biochemistry, Mathematics Instruction, Advanced Courses, Problem Solving
Mehmet Demir; Yilmaz Zengin – International Journal of Mathematical Education in Science and Technology, 2025
The aim of this study is to show how the GeoGebra software-supported collaborative learning environment contributes to a group of students using multiple representations and reaching generalisations while solving problems collectively. Blending individual and collaborative learning activities were carried out with a learning method called ACODESA…
Descriptors: Computer Software, Geometry, Cooperative Learning, Grade 8
Victor Oxman; Moshe Stupel – International Journal of Mathematical Education in Science and Technology, 2024
We present an investigation of the infinite sequences of numbers formed by calculating the pairwise averages of three given numbers. The problem has an interesting geometric interpretation related to the sequence of triangles with equal perimeters which tend to an equilateral triangle. Investigative activities of the problem are carried out in…
Descriptors: Mathematics Instruction, Geometry, Problem Solving, Preservice Teachers
Alonso Ogueda-Oliva; Padmanabhan Seshaiyer – International Journal of Mathematical Education in Science and Technology, 2024
In this paper, we introduce novel instructional approaches to engage students in using modelling with data to motivate and teach differential equations. Specifically, we introduce a pedagogical framework that will execute instructional modules to teach different solution techniques for differential equations through repositories and notebook…
Descriptors: Mathematical Models, Equations (Mathematics), Mathematics Instruction, Learning Modules
Tim Erickson – Australian Mathematics Education Journal, 2023
This is the first of four columns by Tim Erikson which introduces us to the Common Online Data Analysis Platform (CODAP). CODAP is a free, web-based software tool that your students can use for many types of tasks. This first column shows how CODAP can be used for mathematical modelling and where it might fit with the "Australian Curriculum:…
Descriptors: Mathematics Instruction, Teaching Methods, Computer Software, Data Analysis
Bülbül, Buket Özüm; Güler, Mustafa – E-Learning and Digital Media, 2023
Geometric habits of mind (GHoM) are the approaches that individuals use to solve geometry problems. This study aimed to determine the effect of dynamic geometry software (DGS) in activating the GHoM of pre-service mathematics teachers. The study was conducted with six teacher candidates who were enrolled in a semester-long course titled…
Descriptors: Cognitive Processes, Problem Solving, Geometry, Computer Software
Belma Alihodžic; Tatjana Atanasova-Pachemska; Sanela Nesimovic – International Electronic Journal of Mathematics Education, 2024
Teaching is a process for which its plan should contain reflection onto previous experience. With that in mind, teaching situations should be continuously researched and improved in accordance with the research results. Led by this thought and the fact that students are uncritically using visualization to solve mathematical problems, we defined…
Descriptors: High School Students, Mathematics Instruction, Student Attitudes, Problem Solving
Yan, Xiaoheng; Zazkis, Rina – International Journal of Mathematical Education in Science and Technology, 2022
Windmill images and shapes have a long history in geometry and can be found in problems in different mathematical contexts. In this paper, we share and discuss various problems involving windmill shapes and solutions from geometry, algebra, to elementary number theory. These problems can be used, separately or together, for students to explore…
Descriptors: Mathematics Instruction, Teaching Methods, Geometry, Algebra