Certain mathematical concepts were not introduced to solve a specific open problem but rather to solve different problems with the same tools in an economic formal way or to unify several approaches: such concepts, as some of those of linear algebra, are presumably difficult to introduce to students as they are potentially interwoven with many…

Examples are believed to be very important in developing conceptual understanding of mathematical ideas, useful both in mathematics research and instruction (Bills & Watson in "Educational Studies in Mathematics" 69:77-79, 2008; Mason & Watson, 2008; Bills & Tall, 1998; Tall & Vinner, 1981). In this study, we draw on the…

Ninety-seven education students majoring or minoring in mathematics had their math homework examined in a Number Theory or Abstract Algebra course. Each student's homework was observed for the purpose of identifying common errors and misconceptions when writing mathematical proofs. The results showed that students collectively made four…

Like many commodities, the price of gasoline continues to rise, and these price changes are readily observed in gas stations' signage. Moreover, algebraic methods are well suited to model price change and answer the student's question. Over the course of one ninety-minute block or two forty-five-minute classes, students build functions…

This paper deals with the ancient origin of matrices, and the system of linear equations. Included are algebraic properties of matrices, determinants, linear transformations, and Cramer's Rule for solving the system of algebraic equations. Special attention is given to some special matrices, including matrices in graph theory and electrical…

An analysis of one-step equations from a cognitive load theory perspective uncovers variation within one-step equations. The complexity of one-step equations arises from the element interactivity across the operational and relational lines. The higher the number of operational and relational lines, the greater the complexity of the equations.…

This paper presents study that investigates brain activity (using ERP methodology) of male adolescents when solving short problems in algebra and geometry. The study design links mathematics education research with neuro-cognitive studies. We performed a comparative analysis of brain activity associated with the translation from visual to symbolic…

This research project involved teaching linear algebra to second year undergraduates. Using Tall's three worlds of mathematical thinking as a theoretical framework, students were taught fundamental linear algebra concepts using each of the embodied, symbolic and formal dimensions. By varying the order in which these approaches were used in each…

This study aims to determine the ability of algebra students who have 3 levels van Hiele levels. Follow its framework Dindyal framework (2007). Students are required to do 10 algebra shaped multiple choice, then students work 15 about the geometry of the van Hiele level in the form of multiple choice questions. The question has been tested levels…

How can educators encourage and better prepare students to pursue science, technology, engineering, and mathematics (STEM)-based fields? To start, students are more likely to pursue these fields if they enjoy and perceive themselves to be good at them. This means introducing relevant concepts and skills at an early age and embedding them…

Algebraic reasoning is an essential habit of mind for building conceptual knowledge in K-12 mathematics, yet little is known about how middle school mathematics teachers think about algebraic reasoning. In this article we describe a research project examining how algebraic reasoning was considered by grades 6, 7, or 8 mathematics teachers in a…

The Common Core State Standards (CCSSI 2010) and NCTM's (2014) "Principles to Actions" agree that "for meaningful learning of mathematics, tools and technology must be indispensable features of the classroom . . . that support students in exploring mathematics as well as in making sense of concepts and procedures and engaging in…

About half of students attending community colleges leave school before finishing their intended goals. To increase students' retention and to prevent the multiple-repeater problem, Queensborough Community College (QCC) offered a short-term workshop for remedial-mathematics students. This was another chance to exit remediation instead of repeating…

The work described in this report is the second phase of a project to provide easy-to-use tools for authoring and rendering secondary-school algebra-level math expressions in synthesized speech that is useful for students with blindness or low vision. This report describes the development and results of the second feedback study performed for our…

Between 2003 and 2013, the proportion of California eighth graders enrolled in algebra or a more advanced course nearly doubled to 65%. In this article, we consider the organizational processes that accompanied this curricular intensification. Facing a complex set of accountability, institutional, technical/functional, and internal political…