This article is based on a project that investigated teachers' knowledge in teaching an important aspect of algebra in the middle years of schooling--functions, relations and joint variation. As part of the project, 105 upper primary teachers were surveyed during their participation in Contemporary Teaching and Learning of Mathematics, a research…

In this study, we explored the relationship between prospective teachers' algebraic thinking and the questions they posed during one-on-one diagnostic interviews that focused on investigating the algebraic thinking of middle school students. To do so, we evaluated prospective teachers' algebraic thinking proficiency across 125…

This research investigates the influence that gender, single-sex and co-educational schooling can have on students' mathematics education in second-level Irish classrooms. Although gender differences in mathematics education have been the subject of research for many years, recent results from PISA (Programme for International Student Assessment)…

This paper deals with the modern development of matrices, linear transformations, quadratic forms and their applications to geometry and mechanics, eigenvalues, eigenvectors and characteristic equations with applications. Included are the representations of real and complex numbers, and quaternions by matrices, and isomorphism in order to show…

The purpose of this correlational study is to understand the relationship between end-of-course grades as assigned by teachers and standardized end-of-course scores earned by students in Algebra, Geometry, Biology, Physical Science, and U.S. History courses at one virtual charter school in the State of Georgia. Pearson Product-Moment Correlation…

This study used a randomized controlled trial to determine whether students, assessed by their community colleges as needing an elementary algebra (remedial) mathematics course, could instead succeed at least as well in a college-level, credit-bearing introductory statistics course with extra support (a weekly workshop). Researchers randomly…

The purpose of this quantitative study was to determine if a relationship existed between Algebra I passing rates and graduation rates, and if gender, ethnicity, and/or economic status influenced the relationship, particularly for African-American urban high school students in Texas. Participant data included 16,372 first-time ninth grade high…

Historically, what people can learn is co-determined by the "representational infrastructure" for knowledge building. When Latin was the required medium of knowledge building, few could engage in scholarly activities; without the change to the vernacular, nearly universal access to higher education would not be possible. The highly…

Of the "big four", division is likely to regarded by many learners as "the odd one out", "the difficult one", "the one that is complicated", or "the scary one". It seems to have been that way "for ever", in the perception of many who have trodden the learning pathways through the world of…

Southern Illinois University Edwardsville (SIUE) is a postbaccalaureate comprehensive university in the Midwest. In 2005, SIUE embarked on a challenging journey of general education reform. A review of the current general education program revealed that it is possible for a student to graduate from SIUE without taking a quantitative course. Hence,…

It is proved that an integer n [greater than or equal] 2 is a prime (resp., composite) number if and only if there exists exactly one (resp., more than one) nth-degree monic polynomial f with coefficients in Z[subscript n], the ring of integers modulo n, such that each element of Z[subscript n] is a root of f. This classroom note could find use in…

Students' struggles in learning reasoning and proof (RP) in mathematics are well known. Despite the instantiation of RP opportunities in mathematics textbooks in the USA and the important role that textbooks play in teachers' instructional decisions, little research has been conducted on analyzing student textbook tasks and narrative sections of…

The MiGen project is designing and developing an intelligent exploratory environment to support 11-14-year-old students in their learning of algebraic generalization. Deployed within the classroom, the system also provides tools to assist teachers in monitoring students' activities and progress. This paper describes the design of these Teacher…

This study introduced various nonlinear growth models, including the quadratic conventional polynomial model, the fractional polynomial model, the Sigmoid model, the growth model with negative exponential functions, the multidimensional scaling technique, and the unstructured growth curve model. It investigated which growth models effectively…

This article could be of interest to teachers of applied mathematics as well as to people who are interested in applications of linear algebra. We give a comprehensive study of linear systems from an application point of view. Specifically, we give an overview of linear systems and problems that can occur with the computed solution when the…