We present an analysis of students' formal constructions in mathematics regarding to syntactic, semantic and pragmatic aspects. The analyzed tasks correspond to students of the Course of Mathematics for the admission to the university. Our study was qualitative, consisted in the identification, analysis and interpretation, focused in logic…

The 43rd meeting of Canadian Mathematics Education Study Group (CMESG) was held at St. Francis Xavier University in Antigonish, Nova Scotia (May 31-June 4, 2019). This meeting marked only the third time CMESG/GCEDM (Groupe Canadien d'Étude en Didactique des Mathématiques) had been held in Nova Scotia (1996, 2003), and the first time it had been…

Textbooks play a central role in US mathematics classrooms (Stein, Remillard, & Smith, 2007) and functions are a key topic in secondary mathematics (Carlson, Jacobs, Coe, Larsen, & Hsu, 2002). This study presents results from an analysis of this essential topic in the latest editions of three textbook series: the Glencoe Mathematics…

This student research project explores the properties of a family of matrices of zeros and ones that arises from the study of the diagonal lengths in a regular polygon. There is one family for each n greater than 2. A series of exercises guides the student to discover the eigenvalues and eigenvectors of the matrices, which leads in turn to…

Because the speed of light is finite, the further we look into space, the earlier we see. A galaxy seen 50 million light years away is 50 million years ago. How far out in space and how far back in time can we expect to see, and what should it look like? To a first approximation and ignoring local galactic interactions, the Hubble model of the…

The notion of an island has surfaced in recent algebra and coding theory research. Discrete versions provide interesting combinatorial problems. This paper presents the one-dimensional case with finitely many heights, a topic convenient for student research.

The systematic use of alternative normalization constants for 3j symbols can lead to a more natural expression of quantities, such as vector products and spherical tensor operators. The redefined coupling constants directly equate tensor products to the inner and outer products without any additional square roots. The approach is extended to…

The purpose of this paper is to provide an elementary introduction to the qualitative and quantitative results of velocity combination in special relativity, including the Wigner rotation and Thomas precession. We utilize only the most familiar tools of special relativity, in arguments presented at three differing levels: (1) utterly elementary,…

An agreement table with [n as an element of N is greater than or equal to] 3 ordered categories can be collapsed into n - 1 distinct 2 x 2 tables by combining adjacent categories. Vanbelle and Albert ("Stat. Methodol." 6:157-163, 2009c) showed that the components of Cohen's weighted kappa with linear weights can be obtained from these n - 1…

Fleming's right-hand rule and the right-flat-hand rule are generally applied for determining the direction of flow of induced emf/current in straight conductors. The right-hand-fingers rule is applied for coils only. The right-hand-thumb rule can be applied for either straight conductors or coils. Different rules have to be applied for different…

We describe composite Gauss-Legendre quadrature for determining definite integrals, including a means of controlling the approximation error. We compare the form and performance of the algorithm with standard Newton-Cotes quadrature. (Contains 1 table.)

This study examined the knowledge levels of prospective mathematics teachers about the concepts of degree and radian, which are among the angle measuring units that constitute the basis of trigonometry, and the relationships between those concepts. The study group consisted of 93 prospective mathematics teachers attending a state university in…

Mathematics teachers constantly encourage their students to think independently. The study of integration in calculus provides an excellent opportunity to encourage inventive investigation. In contrast to differentiation, which is predominately mechanical, integration is a more creative process. One such possibility is offered by the study of the…

Preservice Secondary Mathematics Teachers (PSMTs) were surveyed to identify if they could connect early-secondary mathematics content (Grades 7-9) in the Common Core State Standards for Mathematics (CCSSM) with mathematics content studied in content courses for certification in secondary teacher preparation programs. Respondents were asked to…

Within the "Australian Curriculum: Mathematics" the Understanding proficiency strand states, "Students build understanding when they connect related ideas, when they represent concepts in different ways, when they identify commonalities and differences between aspects of content, when they describe their thinking mathematically and…