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Garcia, Stephan Ramon; Horn, Roger A. – PRIMUS, 2020

Linear algebra is best done with block matrices. As evidence in support of this thesis, we present numerous examples suitable for classroom presentation.

Descriptors: Mathematics Instruction, Algebra, Teaching Methods, Matrices

Oktaç, Asuman – ZDM: The International Journal on Mathematics Education, 2019

The aim of this paper is on the one hand to discuss from an APOS (Action-Process-Object-Schema) theory perspective the mental constructions involved in the learning of linear algebra, through examples concerning the linear transformation concept and related notions. On the other hand, methodological issues related to the design of research…

Descriptors: Algebra, Mathematics Instruction, Teaching Methods, Concept Formation

Herzinger, K.; Kunselman, C.; Pierce, I. – International Journal of Mathematical Education in Science and Technology, 2018

Theon's ladder is an ancient method for easily approximating "n"th roots of a real number "k." Previous work in this area has focused on modifying Theon's ladder to approximate roots of quadratic polynomials. We extend this work using techniques from linear algebra. We will show that a ladder associated to the quadratic…

Descriptors: Algebra, Mathematics Instruction, Mathematical Formulas, Mathematics

Rensaa, Ragnhild Johanne; Hogstad, Ninni Marie; Monaghan, John – Teaching Mathematics and Its Applications, 2020

This paper presents 'expert opinions' on what should be taught in a first-year linear algebra course at university; the aim is to gain a generic picture and general guiding principles for such a course. Drawing on a Delphi method, 14 university professors--called 'experts' in this study--addressed the following questions: What should be on a…

Descriptors: College Mathematics, Undergraduate Students, Algebra, Engineering Education

Stewart, Sepideh; Thomas, Michael O. J. – ZDM: The International Journal on Mathematics Education, 2019

Proof has a prominent place in the linear algebra curriculum, teaching and learning but in first-year courses it continues to be challenging for both instructors and students. While an introduction to new concepts through definitions and theorems adds to the complexity of the course, proof remains the number one hurdle for many students. How do…

Descriptors: Algebra, Advanced Courses, Mathematics Instruction, Mathematical Logic

Teixeira, Ricardo – Australian Senior Mathematics Journal, 2018

This article summarises activities that happened during the first three weeks of a fictitious high-school-level linear algebra section that used magic squares as a teaching tool to inspire students to further investigate the topics. The author has been working with students from high school and college levels for years, and although this situation…

Descriptors: Algebra, Secondary School Mathematics, Mathematics Instruction, Foreign Countries

Payton, Spencer – ZDM: The International Journal on Mathematics Education, 2019

Mathematical connections are widely considered an important aspect of learning linear algebra, particularly at the introductory level. One effective strategy for teaching mathematical connections in introductory linear algebra is through inquiry-based learning (IBL). The demands of IBL instruction can make it difficult to implement such strategies…

Descriptors: Algebra, Mathematics Instruction, Teaching Methods, Inquiry

Aytekin, Cahit; Kiymaz, Yasemin – Acta Didactica Napocensia, 2019

Linear algebra differs from other mathematics courses because of the special difficulties that students have in understanding the concepts. Teaching without concretizing the concepts of Linear Algebra encouraged students to memorize definitions of concepts and rules has been articulated. Many researches show that technology-supported teaching is…

Descriptors: Algebra, Mathematics Instruction, Computer Software, Educational Technology

Bianchini, Barbara Lutaif; de Lima, Gabriel Loureiro; Gomes, Eloiza – ZDM: The International Journal on Mathematics Education, 2019

The relevancy of linear algebra (LA) in different areas and also the difficulties faced by undergraduate engineering students studying this content are well known. Grounded on this premise, we aimed at articulating papers related to the teaching and learning of LA in engineering undergraduate programs through a mapping of the main investigations…

Descriptors: Mathematics Instruction, Advanced Courses, Undergraduate Students, Engineering Education

Rensaa, Ragnhild Johanne; Hogstad, Ninni Marie; Monaghan, John – International Journal of Mathematical Education in Science and Technology, 2021

This paper reports on themes that arose in an investigation of university lecturers' views on the teaching of linear algebra. This focus on themes was the initial part of a study concentrating on four areas: What is important to teach in a first course in linear algebra? Are there teaching methods which are particularly suited for such a course?…

Descriptors: Teaching Methods, Algebra, College Faculty, Advanced Courses

Talbert, Robert – PRIMUS, 2014

The inverted classroom is a course design model in which students' initial contact with new information takes place outside of class meetings, and students spend class time on high-level sense-making activities. The inverted classroom model is so called because it inverts or "flips" the usual classroom design where typically class…

Descriptors: Mathematics Instruction, Algebra, Teaching Methods, College Mathematics

Ramírez-Montes, Guillermo; Henriques, Ana; Carreira, Susana – Canadian Journal of Science, Mathematics and Technology Education, 2021

Mathematical modelling has acquired relevance at all educational levels in the last decades since integrating this activity in instruction provides significant contexts for improving students' learning, including in linear algebra courses that have a notable presence in many undergraduate courses from different fields, including engineering and…

Descriptors: Undergraduate Students, College Mathematics, Mathematics Instruction, Teaching Methods

Griffiths, Barry J.; Shionis, Samantha – Teaching Mathematics and Its Applications, 2021

In this study, we look at student perceptions of a first course in linear algebra, focusing on two specific aspects. The first is the statement by Carlson that a fog rolls in once abstract notions such as subspaces, span and linear independence are introduced, while the second investigates statements made by several authors regarding the negative…

Descriptors: Algebra, Mathematics Instruction, Student Attitudes, Mathematical Concepts

Schrier, Joshua – Journal of Chemical Education, 2021

Multicomponent solution calculations can be complicated for students and practiced chemists alike. This article describes how to simplify the calculations by representing a solution's composition as a point in a "concentration space," whose axes are the concentrations of each solute. The graphical representation of mixing processes in a…

Descriptors: Chemistry, Problem Solving, Computation, Visual Aids

Arnawa, I. Made; Yanita; Yerizon; Ginting, Bukti; Nita, Sri – International Journal of Instruction, 2021

The study examines the impact of APOS theory on students' achievement in Elementary Linear Algebra (ELA) in accordance with their adequate prior knowledge (APK) and inadequate prior knowledge (IAPK). The mixed methods were used to determine the problem-solving test in ELA. Data were obtained from 65 industrial engineering students at Andalas…

Descriptors: Constructivism (Learning), Educational Theories, Mathematics Achievement, Algebra