In this article, we explore how the solving of linear equations is represented in English­-language algebra text books from the early nineteenth century when schooling was becoming institutionalized, and then survey contemporary teachers. In the text books, we identify the increasing presence of a prescribed order of steps (a canonical method) for…

Drawing on a review of recent work conducted in the area of pattern generalization (PG), this paper makes a case for a distributed view of PG, which basically situates processing ability in terms of convergences among several different factors that influence PG. Consequently, the distributed nature leads to different types of PG that depend on the…

Although lecture is the traditional method of university mathematics instruction, there has been little empirical research that describes the structure of lectures. In this paper, we apply ideas from narrative analysis to an upper-level mathematics lecture. We develop a framework that enables us to conceptualize the lecture as consisting of…

In abstract algebra, the study of concrete groups is fundamentally important to beginners. Most commonly used groups as examples are integer addition modulo n, real number addition and multiplication, permutation groups, and groups of symmetry. The last two examples are finite non-abelian groups and can be investigated with the aid of concrete…

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…

Whole number arithmetic is the foundation of higher mathematics and a core part of elementary mathematics. Awareness of pattern and underlying problem structure promote the learning of whole number arithmetic. A growing consensus has emerged on the necessity to provide students with the opportunity to engage in algebraic reasoning earlier in their…

In this article, the author, a ninth grade teacher at a Title I high school, describes how she began her algebra classes with an open-ended research project, entitled Why Math? This project offered opportunities for students to reflect on why mathematics is important and to determine its relevance to them as individuals, that is, why…

The development of proofs and argumentation is one of the major standards for mathematical practices in K-12 education that researchers and practitioners alike are continuing to improve. Further, the use of discourse is considered essential in the learning of mathematical concepts at these levels. However, K-12 educators continue to confound how…

This study aims to know the characteristics of mathematical communication of pre-service primary school teachers. The material used as the object of research is geometry. It requires the ability of algebra and spatial skills. The area of trapezoid is selected as the topic since it is perceived as the most complex of all plane shapes studied in…

Even though basketry is an age old occupation in Ghana and the world over, it appears mathematics tasks and activities involving the designs and structures have remained unnoticed and inadequately tapped for early school instructions. This qualitative survey therefore, purposively sampled four teachers, two basket artisans and six pupils in the…

Students with learning disabilities often struggle with the academic demands presented in secondary mathematics curricula. To combat these students' struggles, researchers have studied various pedagogical practices and classroom technologies for teaching standards covered in subjects such as algebra and geometry. However, as the role of computer-…

The author shares the lesson that he used to introduce the quadratic unit to students in an extended second-year algebra class, demonstrate why it was appropriate for his struggling learners, and discuss possible future modifications to this lesson.

Middle-grades mathematics prospective teachers (PSTs) participated in three iterations of a design experiment that explored their current conceptualizations of integer and binomial multiplication; this study analyzed whether that knowledge changed after engaging in a series of scaffolded tasks while using area models as concrete manipulatives.…

The implementation of the Pennsylvania Algebra 1 Keystone Exam brought many changes to the mathematics classroom for both teachers and students. The purpose of this case study will be to explore how teachers at a charter school respond to testing requirements through adjustments in how and what they teach and to understand and explain the…

The purpose of this study was to determine if there was a correlation between the implementation of standards-based grading (SBG) and a rise in student achievement as indicated by the evaluation of end-of-course exam data from the four core subject areas in secondary schools--English, Algebra, Government, and Biology. This mixed methods study…