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…

In this article we present a didactic proposal for teaching linear algebra based on two compatible theoretical models: emergent models and mathematical modelling. This proposal begins with a problematic situation related to the creation and use of secure passwords, which leads students toward the construction of the concepts of spanning set and…

The findings reported in this paper were generated from a case study of teacher leaders at a state-level mathematics conference. Investigation focused on how participants viewed the mathematical processes of communication, connections, representations, problem solving, and reasoning and proof. Purposeful sampling was employed to select nine…

The article introduces a software application (MATH) supporting an education of Applied Mathematics, with focus on Numerical Mathematics. The MATH is an easy to use tool supporting various numerical methods calculations with graphical user interface and integrated plotting tool for graphical representation written in Qt with extensive use of Qwt…

Algebra is often considered as difficult and mysterious doctrine due to numerous symbols that represent mathematical notions. Results of the research on students' interpretation of literal expressions show that only a small number of students are ready to accept that a letter can represent a variable. The aim of this research with students of the…

This study examined whether college students are better able to apply knowledge of simple mathematical concepts when they are taught the concepts using abstract symbols or concrete examples. The research described in this article is consistent with What Works Clearinghouse (WWC) evidence standards. Strengths: The study is a well implemented…

Simon's (1995) development of the construct of hypothetical learning trajectory (HLT) offered a description of key aspects of planning mathematics lessons. An HLT consists of the goal for the students' learning, the mathematical tasks that will be used to promote student learning, and hypotheses about the process of the students' learning.…

Describes a laboratory-type activity, liquid assets, used to illustrate, develop, or reinforce central concepts in first-year algebra. These include linear function, slope, intercept, and dependent and independent variables. Presents a group activity for collecting data, transition from group to individual activity in plotting data points, and…

Elementary combinatorial problems may be classified into three different combinatorial models: (1) selection; (2) partition; and (3) distribution. The main goal of this research was to determine the effect of the implicit combinatorial model on pupils' combinatorial reasoning before and after instruction. Gives an analysis of variance of the…

This paper describes three methods that can be utilized in teaching for meaning in mathematics. These three methods are based on learning theories. Although there may not be consensus of what constitutes meaningful learning in the study of mathematics, there are problems with meaningless mathematics that are widely agreed upon by educators.…

Discusses the principle elements for understanding and using mathematics, particularly arithmetic. Three aspects of arithmetic are considered: Understanding the concepts underlying a mathematical process, techniques or algorithms of arithmetic, and applications of the techniques to real situations. (SH)

Describes an investigation of polygons and their properties in which students apply very basic understandings of geometric properties. (KHR)

The ways in which students in grades five and six solve problems is the focus of this paper, which provides background for the staff of the Skills Essential to Learning Television Project, (a multi-level series of video and print resources for classroom use). It considers the problem-solving process categories of understanding, transformation, and…

This paper proposes a theory that can account for differences between everyday and formal mathematics knowledge and a set of processes by which informal knowledge is transformed into formal mathematics. After an introduction, the paper is developed in five sections. The first section lays out the nature of informal, everyday mathematics knowledge.…

Studies whether students' stated preferences for flowcharts or pseudocodes match their actual behaviors. Provides a review of the literature on flowchart utility. Reports that students preferred flowcharts to pseudocodes. Lists an example of both a flowchart and pseudocode. (MVL)