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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

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

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

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

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)

Uygun, Tugba – Mathematics Education Research Journal, 2020

This study reports the classroom mathematical practices proposed in an instructional sequence grounding on the principles of inquiry-based learning (IBL) through the use of the dynamic geometry software (DGS) in learning to teach geometric transformations. A 5-week instructional sequence consisting of IBL activities that were guided by the…

Descriptors: Active Learning, Inquiry, Mathematics Instruction, Instructional Effectiveness

Boz-Yaman, Burçak; Yigit Koyunkaya, Melike – Acta Didactica Napocensia, 2019

Learning and teaching function transformation has a significant place since it provides new opportunities for learners to use, reflect and discover knowledge related to the concept of function. This study's main goals related to the importance of learning function transformation are to examine pre-service mathematics teachers' (PMTs) mental…

Descriptors: Preservice Teachers, Mathematics Education, Mathematics Teachers, Transformations (Mathematics)

Moses, Tim; Kim, YoungKoung – Journal of Educational Measurement, 2017

The focus of this article is on scale score transformations that can be used to stabilize conditional standard errors of measurement (CSEMs). Three transformations for stabilizing the estimated CSEMs are reviewed, including the traditional arcsine transformation, a recently developed general variance stabilization transformation, and a new method…

Descriptors: Error of Measurement, Scores, Comparative Analysis, Item Response Theory

Ramírez, José L.; Rubiano, Gustavo N. – International Journal of Mathematical Education in Science and Technology, 2017

In the present article, we introduce a generalization of the spherical inversion. In particular, we define an inversion with respect to an ellipsoid, and prove several properties of this new transformation. The inversion in an ellipsoid is the generalization of the elliptic inversion to the three-dimensional space. We also study the inverse images…

Descriptors: Generalization, Transformations (Mathematics), Geometric Concepts, Geometry