Reasoning about graphical representations representing dynamic data (e.g., distance changing over time), including interpreting, creating, changing, combining, and comparing graphs, can be considered a domain-specific operationalization of the general twenty-first century skills of creative, critical thinking and solving problems. This paper…

This paper presents the results of a literature review focusing on the use and potential of Fermi problems (FPs) in the STEM disciplines. We identify different usages and roles given to FPs in each of the STEM disciplines and highlight their potential to promote modeling of real phenomena and situations as well as learning about the estimation of…

Teachers are increasingly being called upon to teach in ways that develop 21st century learning skills in their students. Various frameworks for 21st century learning have been proposed and while they differ, all agree on four components for development--creativity, collaboration, communication and critical thinking. Both individually and…

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…

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)…

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…

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,…

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…

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…

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…

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…

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…

This paper is centred around a framework for studying teaching--Mediating Primary Mathematics (MPM)--developed in the context of the teaching of Whole Number Arithmetic (WNA) in South Africa. Findings from the analysis of four WNA lessons are used to illustrate how the application of the MPM framework can measure nuanced differences in the…

Teachers and mathematicians hold different perspectives on the teaching and learning of whole number arithmetic. Though these perspectives may be complementary, sharing them across communities is challenging. An unusual professional development course for primary school teachers, initiated and taught by research mathematicians, provided a setting…

This study investigates the teaching and learning of single-digit whole number multiplication in China. Analysis of data from documents, classroom teaching, and semi-structured interviews revealed three salient characteristics of emphasizing "oral calculation," "calculation speed," and "understanding" across…