The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. By using the Infona portal the user accepts automatic saving and using this information for portal operation purposes. More information on the subject can be found in the Privacy Policy and Terms of Service. By closing this window the user confirms that they have read the information on cookie usage, and they accept the privacy policy and the way cookies are used by the portal. You can change the cookie settings in your browser.
The aim of this research is to analyse students’ sense-making regarding matrix representation of geometric transformations in a dynamic geometry environment (DGE) within the perspective of semiotic mediation. In particular, the focus is on students’ reasoning on the transition from the notion of function to transformation and to matrix representation of geometric transformations in $${{\mathbb{R}}^2}$$...
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 students view proof in linear algebra? Do they distinguish...
In this study, I examined seven first-year linear algebra students’ linear independence schemas. Data came from participants’ interview responses to a set of nine questions. The analysis focused on the identification of concepts and connections pertaining to plans and activations. Overall, the findings revealed the existence of routinized plans, each containing one of six most frequently expressed...
There is relatively little research specifically about student understanding of basis. Our ongoing work addresses student understanding of basis from an anti-deficit perspective, which focuses on the resources that students have to make sense of basis using everyday ideas. Using data from a group of women of color in the United States, we previously developed an analytical framework to describe student...
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 on the teaching and learning of LA carried out since...
Learning is a complex phenomenon. Analyzing its development can provide knowledge about regularities and differences in students’ progress, which is needed to better understand learning. The aim of this study is to examine the development of students’ Linear Algebra Schema through an introductory one semester course. For that purpose, Action Process Object Schema (APOS) theory’s notions of Schema...
Reflection is an important part of teaching and needs to be considered carefully. In this study, we examined a mathematics instructor’s reflections on teaching linear algebra. The research team employed Tall’s (How humans learn to think mathematically: exploring the three worlds of mathematics. Cambridge University Press, Cambridge, 2013) framework to track the instructor’s movements between the three...
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 instruments and implementation of didactic interviews are...
In this survey paper, we describe the state of the field on linear algebra research. We synthesize themes, questions, results, and perspectives emphasized in the papers that appear in this issue, as well as a selection of those published between 2008 and 2017. We highlight the extensive base of empirical research detailing how students reason about a variety of topic areas in linear algebra, as well...
The purpose of this research study was to understand how linear algebra students in a university in the United States make sense of subspaces of vector spaces in a series of in-depth qualitative interviews in a technology-assisted learning environment. Fourteen mathematics majors came up with a diversity of innovative and creative ways in which they coordinated visual and analytic approaches in the...
Geometry is used in different ways in the teaching of linear algebra. In this paper, I offer a typology of these ways, which I call varieties, and address three central questions. The first question is, What varieties of use of geometry in the teaching of linear algebra exist? This question is addressed through an analysis of six linear algebra textbooks, republished in multiple editions in the last...
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 in courses in which the instructor faces various constraints...
Solving systems of linear equations is of central importance in linear algebra and many related applications, yet there is limited literature examining the symbolizing processes students use as they work to solve systems of linear equations. In this paper, we examine this issue by analyzing final exam data from 68 students in an introductory undergraduate linear algebra course at a large public research...
Many studies provide insights into students’ conceptions of various linear algebra topics and difficulties they face with multiple modes of thinking needed for conceptualization. While it is important to understand students’ initial conceptions, students’ transfer of learning of these conceptions to subsequent courses can provide additional information to structure meaningful curricular materials...
To contribute to the sparse educational research on student understanding of eigenspace, we investigated how students reason about linear combinations of eigenvectors. We present results from student reasoning on two written multiple-choice questions with open-ended justifications involving linear combinations of eigenvectors in which the resultant vector is or is not an eigenvector of the matrix...
International comparative studies of education have shown that the increase in mathematical attainment differs significantly among students in relation to the different school types in which their mathematical foundations were acquired. In tertiary education, the same differences are observed with respect to simple tasks that relate to the subject matter of secondary education. Therefore, we investigate...
This paper examines proof constructions in group work in the field of linear algebra teaching at the university level. Studies have shown that students at tertiary level have difficulties in understanding different kinds of quantifiers, which are fundamental in linear algebra proof constructions. This study investigates how two student groups, with a tutor involved in one of the groups, construed...
Set the date range to filter the displayed results. You can set a starting date, ending date or both. You can enter the dates manually or choose them from the calendar.