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Wha-Suck Lee – International Journal of Mathematical Education in Science and Technology, 2024

We view the (real) Laplace transform through the lens of linear algebra as a continuous analogue of the power series by a negative exponential transformation that switches the basis of power functions to the basis of exponential functions. This approach immediately points to how the complex Laplace transform is a generalisation of the Fourier…

Descriptors: Numbers, Algebra, Equations (Mathematics), Mathematical Concepts

Muhamat Hidayatul Ridho; Endang Cahya Mulyaning A.; Jarnawi Afgani Dahlan – International Society for Technology, Education, and Science, 2023

Mathematical representation includes the process of transforming problems or ideas into new forms, including changing pictures or physical models into symbols, words, or sentences that can facilitate students in solving mathematical problems. Pythagorean Theorem material is widely used in analytic geometry, so this material becomes important for…

Descriptors: Foreign Countries, Junior High School Students, Geometric Concepts, Plane Geometry

Sani Sahara; Maarten Dolk; Agus Hendriyanto; Tri Atmojo Kusmayadi; Laila Fitriana – Journal on Mathematics Education, 2024

Learning Transformation Geometry (TG) needs a more informal approach to concern situational problems. This study aims to develop actionable knowledge of TG in the form of design related to context and yet general enough to use digital manipulative activities in new situations. We propose such knowledge in the form of conjectured Local…

Descriptors: Transformations (Mathematics), Mathematics Instruction, Geometric Concepts, Grade 11

Basu, Marina; Koellner, Karen; Jacobs, Jennifer K.; Seago, Nanette – Mathematics Teacher: Learning and Teaching PK-12, 2022

This article discusses a set of tasks that introduce dilations using nonstandard figures, incorporating snippets of classroom conversations as students try to make sense of the specified tasks, to show how they progress in their understanding. The authors provide a theoretical foundation for the tasks and discuss the pedagogical implications for…

Descriptors: Mathematics Instruction, Teaching Methods, Geometric Concepts, Problem Solving

Nokwanda Mbusi; Kakoma Luneta – SAGE Open, 2023

Active learning strategies are purported to be effective in enhancing students' understanding of concepts that would otherwise be difficult to master through other strategies of mediating learning. This study forms part of a bigger study where pre-service teachers' errors and misconceptions in transformation geometry were identified, analyzed and…

Descriptors: Student Teachers, Active Learning, Transformations (Mathematics), Geometry

Hollebrands, Karen; McCulloch, Allison W.; Okumus, Samet – Digital Experiences in Mathematics Education, 2021

Although geometric transformations are functions, few studies have examined students' reasoning about these two important concepts. The purpose of this study was to examine the various ways students reasoned about functions in the context of pre-constructed, dynamic sketches of geometric transformations. We found that, regardless of prior…

Descriptors: High School Students, Student Characteristics, Transformations (Mathematics), Geometric Concepts

Turgut, Melih – International Journal of Science and Mathematics Education, 2022

This paper reports the multimodal resources that attached to students' reasoning in the reinvention of specific geometric linear transformations (like reflections according to the axes, projections onto axes and composition of reflections) in a dynamic geometry environment. Following the design heuristics of Realistic Mathematics Education, we…

Descriptors: Geometry, Algebra, Mathematical Concepts, Mathematics Education

Kieran, Carolyn; Martínez-Hernández, Cesar – ZDM: Mathematics Education, 2022

"They are the same" is a phrase that teachers often hear from their students in arithmetic and algebra. But what do students mean when they say this? The present paper researches the notion of sameness within algebraic thinking in the context of generating equivalent numerical equalities. A group of Grade 6 Mexican students (10- to…

Descriptors: Mathematical Concepts, Algebra, Equations (Mathematics), Arithmetic

Harrow, Christopher; Merchant, Nurfatimah – Mathematics Teacher: Learning and Teaching PK-12, 2020

Sinusoidal functions are difficult for students: Periodicity is a new concept, transferring information from the unit circle can be confusing, and computations with multiple solutions can be overwhelming. Many struggle with both the unfamiliar "waviness" of sinusoidal graphs and their transformations (translations, dilations, and…

Descriptors: Graphs, Mathematics, Transformations (Mathematics), Computer Uses in Education

Palmér, Hanna; van Bommel, Jorryt – ZDM: The International Journal on Mathematics Education, 2020

This paper focuses on problem solving and problem posing in mathematics education with 6-year-olds. After working on a problem-solving activity, the young students were asked to pose a "similar" task to a friend. This article explores how the students interpret the notion of "similar." To be able to pose a problem-solving task…

Descriptors: Preschool Children, Preschool Education, Mathematics Education, Mathematics Skills

Ferrarello, Daniela; Mammana, Maria Flavia; Pennisi, Mario – International Journal of Mathematical Education in Science and Technology, 2018

In this paper, we show some properties of centroids of geometric figures, such as triangles, quadrilaterals and tetrahedra. In particular, we will prove the properties by means of geometric transformations and by introducing extensions of triangles and quadrilaterals, i.e. by adding one, two or three new vertices to the figure. The study of these…

Descriptors: Geometric Concepts, Transformations (Mathematics), Secondary School Mathematics, Mathematics Instruction

Wiles, Peter; Lemon, Travis; King, Alessandra – Mathematics Teaching in the Middle School, 2019

Middle school students are faced with a number of mathematical concepts that require new forms of reasoning. Although the shifts toward proportional and algebraic reasoning are often emphasized in middle school curricula, changes in the nature of geometric reasoning are not always given the same weight. As highlighted in "Catalyzing Change in…

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

Sevgi, Sedef; Erduran, Ayten – Acta Didactica Napocensia, 2020

The purpose of this study is to investigate how students' in senior grade of the high school participate in and interpret the transformational geometry activities integrated with cultural context. 5 students in senior grade participated in this study, all of whom live in Aydin district of Turkey. The main design of the study is qualitative.…

Descriptors: Culturally Relevant Education, Geometric Concepts, Transformations (Mathematics), Mathematics Education

Aydin-Güç, Funda; Hacisalihoglu-Karadeniz, Mihriban – Acta Didactica Napocensia, 2020

The purpose of this study was to investigate the tessellation performance of 8th-grade students and factors affecting their performance. Student performances have been examined in two dimensions: identification and completion of tessellation. In this context, a diagnostic test containing two main questions with the content of determining whether…

Descriptors: Geometric Concepts, Pattern Recognition, Mathematics Skills, Mathematics Achievement

de Villiers, Michael – International Journal of Mathematical Education in Science and Technology, 2017

This paper discusses an interesting, classic problem that provides a nice classroom investigation for dynamic geometry, and which can easily be explained (proved) with transformation geometry. The deductive explanation (proof) provides insight into why it is true, leading to an immediate generalization, thus illustrating the discovery function of…

Descriptors: Geometry, Mathematical Logic, Validity, Transformations (Mathematics)