Learning mathematical thinking and reasoning is a main goal in mathematical education. Instructional tasks have an important role in fostering this learning. We introduce a learning sequence to approach the topic of integrals in secondary education to support students mathematical reasoning while participating in collaborative dialogue about the…

In this paper, we examine the ways the history of mathematics is integrated in the national textbooks of Cyprus and Greece. Our data-driven analyses suggest that the references identified can be clustered in four categories: (a) biographical references about mathematicians or historical references regarding the origins of a mathematical concept…

Access to advanced study in mathematics, in general, and to calculus, in particular, depends in part on the conceptual architecture of these knowledge domains. In this paper, we outline an alternative conceptual architecture for elementary calculus. Our general strategy is to separate basic concepts from the particular advanced techniques used in…

Exploring and deriving proofs of closed-form expressions for series can be fun for students. However, for some students, a physical representation of such problems is more meaningful. Various approaches have been designed to help students visualize squares of sums and sums of squares; these approaches may be arithmetic-algebraic or combinatorial…

Reports four new readability formulas which account for a higher percentage of variance than the Coleman formulas and which can also be used for readers below college level.

There is growing concern in Europe that some students are not well-equipped to start a Bachelor's or Master's programme, especially when the programme has a strong mathematical focus. In particular, attention is drawn to problems with mathematics in the transition from secondary to higher education. Higher education expects a certain level of…

Comparisons are made between the errors obtained when approximating the integral with the midpoint rule, the trapezoidal rule, and Simpson's rule. (MP)

The purpose of this study was to investigate the degree to which various selected test item discrimination indices reflect a common factor. The indices used include the point-biserial, biserial, phi and tetrachoric coefficients, Flanagan's approximation of the product-moment correlation, Gulliksen's item reliability index, and Findley's difference…

A detailed proof is given of a theorem that characterizes the vertex sequence of any convex polyhedron and establishes the existence of only 13 Archimedean solids. (MP)

Demonstrates the logical relationship between percentage composition and an empirical formula using a technique that depends on determining a minimum molar mass for the compound based on the mass percent of each element. (DDR)

Results of operations on the Pythagorean formula are interpreted pictorially to yield interesting art forms. (MP)

A coordinate system is imposed on a geoboard to form a table that leads to the discovery of the formula n[(n+1)(n+1)] (n+2)/12. Proof is by induction. (MP)

Problems which can be solved or partially solved by the Gregory Interpolation Formula are presented. The formula is explained and applied to three problems. (MNS)

A human interest account of the discovery of a mathematical formula is given. (Author/MK)

An algorithm for multiplying natural numbers is described. The algorithm provides a chance for some unusual drill and might serve as an enrichment topic. (MK)