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Margherita Piroi – Educational Studies in Mathematics, 2025
This study aims at elaborating a well-established theoretical framework that distinguishes three modes of thinking in linear algebra: the analytic-arithmetic, the synthetic-geometric, and the analytic-structural mode. It describes and analyzes the bundle of signs produced by an engineering student during an interview, where she was asked to recall…
Descriptors: Undergraduate Students, Engineering Education, Case Studies, Algebra
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Ruhama Even; Boaz Silverman – International Journal of Science and Mathematics Education, 2024
When justifying a mathematical statement, textbooks often interweave several instances of justification, creating, what we term, "paths of justification." This study aims to characterize the paths of justification of mathematical statements that are offered in eight 7th grade Israeli mathematics textbooks. The study attended to context…
Descriptors: Foreign Countries, Mathematics Instruction, Grade 7, Textbooks
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Miškovic, Vladimir – Australian Mathematics Education Journal, 2021
In the third of a series, the author describes how symmetrical quintic functions can be expressed in three equivalent formats--like other symmetrical functions. Quadratic functions have a line of symmetry through their vertex and cubic functions have 1800 rotational symmetry around their point of inflection. However, polynomial functions of degree…
Descriptors: Mathematics Instruction, Teaching Methods, Algebra, Geometry
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Hortensia Soto; Leonardo Abbrescia; Adam Castillo; Laura Colmenarejo; Anthony Sanchez; Rosaura Uscanga – ZDM: Mathematics Education, 2024
In this case study we explored how a mathematician's teaching of the Cauchy-Riemann (CR) equations actualized the virtual aspects of the equations. Using videotaped classroom data, we found that in a three-day period, this mathematician used embodiment to animate and bind formal aspects of the CR equations (including conformality), metaphors,…
Descriptors: Mathematics Teachers, Mathematics Instruction, Teaching Methods, Mathematical Concepts
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Bach, Cecilie Carlsen – Digital Experiences in Mathematics Education, 2023
Previously defined profiles for using a computer algebra system (CAS) describe prototypical uses of such a tool. When students use a dynamic geometry environment (DGE), however, new opportunities arise for transitions within and beyond the DGE. In this article, CAS profiles are used to explore students' uses of a DGE. Four cases of students, all…
Descriptors: Computer Uses in Education, Computer Assisted Instruction, Computer Software, Mathematics Instruction
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Bhesh Mainali; Ali Sabri Ipek – International Journal for Mathematics Teaching and Learning, 2025
Textbook is one of the most tangible resources for teaching and learning mathematics, offering valuable opportunities for both teachers and students. This study compared the mathematical tasks in 6th-grade textbooks from the United States and Turkey, focusing on three dimensions of the tasks: representation, contextual features, and cognitive…
Descriptors: Foreign Countries, Mathematics Instruction, Textbooks, Textbook Content
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Ramírez, Rafael; Cañadas, María C.; Damián, Alba – ZDM: Mathematics Education, 2022
This study lies within the field of early-age algebraic thinking and focuses on describing the functional thinking exhibited by six sixth-graders (11- to 12-year-olds) enrolled in a curricular enhancement program. To accomplish the goals of this research, the structures the students established and the representations they used to express the…
Descriptors: Algebra, Grade 6, Mathematics Instruction, Geometry
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Dyah Worowirastri Ekowati; Toto Nusantara; Makbul Muksar; Dwi Agus Sudjimat – Pegem Journal of Education and Instruction, 2024
In learning mathematics in the 21st century and after the COVID-19 pandemic, a multimodal role in the process of drawing conclusions involving mathematical symbols or signs is very much needed. This process is called multimodal semiotic reasoning. This research aims to study the literature on multimodal semiotic reasoning research articles. Until…
Descriptors: Semiotics, Mathematics Instruction, Mathematics Skills, Databases
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Hans Bila; Kgaladi Maphutha; Paul Mutodi – Pythagoras, 2024
In this article, we explored Grade 11 learners' algebraic and geometric connections when solving Euclidean geometry riders. A qualitative interpretive case study design was followed. Thirty Grade 11 learners from a non-fee-paying secondary school in the Capricorn North district of South Africa were conveniently sampled to participate in this…
Descriptors: Grade 11, Algebra, Geometry, Mathematics Instruction
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Elizabeth Huffaker; Sarah Novicoff; Thomas S. Dee – Educational Researcher, 2025
A controversial, equity-focused mathematics reform in the San Francisco Unified School District (SFUSD) featured delaying Algebra I until ninth grade for all students. This study examines student-level longitudinal data on mathematics course-taking across successive cohorts of SFUSD students who spanned the reform's implementation. We observe…
Descriptors: Educational Change, Mathematics Education, Mathematics Instruction, Algebra
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Andriunas, R.; Boyle, B.; Lazowski, A. – PRIMUS, 2022
This paper discusses a project for linear algebra instructors interested in a concrete, geometric application of matrix diagonalization. The project provides a theorem concerning a nested sequence of tetrahedrons and scaffolded questions for students to work through a proof. Along the way students learn content from three-dimensional geometry and…
Descriptors: Algebra, Geometry, Matrices, Mathematics Instruction
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Terri L. Kurz; Mi Yeon Lee – School Science and Mathematics, 2024
Recognizing, building, describing, extending, and analyzing patterns are key components of algebraic reasoning. Oftentimes pattern-based instruction is used to support the understanding of functions and variables. In this study, elementary preservice teachers (n = 23) were asked to explore, extend, explain, create equations for, and analyze…
Descriptors: Elementary School Teachers, Preservice Teachers, Numbers, Error Patterns
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Oxman, Victor; Sigler, Avi – International Journal of Mathematical Education in Science and Technology, 2021
In this article we consider two triangles: one inscribed in another. We prove that the area of the central triangle is at least the harmonic mean of the areas of corner triangles. We give two proofs of this theorem. One is based on Rigby inequality and the other is based on the known algebraic inequality, to which we bring a new, geometric, proof.…
Descriptors: Geometry, Mathematics Instruction, Validity, Mathematical Logic
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de la Rosa, Félix Martínez – International Journal of Mathematical Education in Science and Technology, 2021
The goal of this note is to obtain the area enclosed between a parabola and two tangent lines using visual arguments. The first step that we have to follow, in order to do that, is noticing that the area between a parabola and a tangent line only depends on the leading coefficient of the quadratic function of the parabola. Finally, the…
Descriptors: Mathematics Instruction, Mathematical Concepts, Secondary School Mathematics, Algebra
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Thierry Noah Dana-Picard; Sara Hershkovitz – International Journal for Technology in Mathematics Education, 2023
Relying on the students' cultural background to teach mathematics may be a strong incitement for the learning process. This background can include artistic creations, items from the news, among others. Because of the strong presence of space related news (in particular the almost simultaneous launching of three spacecrafts towards Mars), we…
Descriptors: Visual Arts, Astronomy, Mathematics Activities, Mathematics Instruction
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