Background/purpose: In modern mathematical education, it is important to develop students' ability to understand the fundamental properties of geometric objects deeply. This makes it relevant to study the additivity of the area of triangles as a property inherent in various kinds of quantities and ways of representing it methodologically in the…

The purpose of this article is to present and discuss two recommended sequences of learning the areas of polygons, starting from the area of a rectangle. Exploring the algebraic derivations of the two sequences reveals that both are valid teaching progressions for introducing the area formula for various polygons. Further, it is suggested that…

The radius of curvature formula is usually introduced in a university calculus course. Its proof is not included in most high school calculus courses and even some first-year university calculus courses because many students find the calculus used difficult (see Larson, Hostetler and Edwards, 2007, pp. 870- 872). Fortunately, there is an easier…

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 use geometric transformations to find some interesting properties related with geometric loci. In particular, given a triangle or a cyclic quadrilateral, the locus generated by the centroid or by the orthocentre (for triangles) or by the anticentre (for cyclic quadrilaterals) when one vertex moves on the circumcircle of the…

One goal of a mathematics education is that students make significant connections among different branches of mathematics. Connections--such as those between arithmetic and algebra, between two-dimensional and three-dimensional geometry, between compass-and-straight-edge constructions and transformations, and between calculus and analytic…

This study reports the results of a study examining how easily students are able to transfer frequency solutions to conditional probability problems to novel situations. University students studied either a problem solved using the traditional Bayes formula format or using a natural frequency (tree diagram) format. In addition, the example problem…

This study focussed on the effect of grammar of Iwaidja, an indigenous Australian language, on mathematical conceptualisation. It investigated route description in Iwaidja. Spatial concepts such as direction, height and movement in relation to another object are briefly described using examples. Differences between English and Iwaidja are used to…

In 1859, on the occasion of being elected as a corresponding member of the Berlin Academy, Bernard Riemann (1826-66), a student of Carl Friedrich Gauss (1777-1855), presenteda lecture in which he presented a mathematics formula, derived from complex integration, which gave a precise count of the primes on the understanding that one of the terms in…

In this article, Ceyanes, Lockwood, and Gill use "The Geometer's Sketchpad" in a sequence of algebra lessons to introduce quadratic functions as the product of two linear functions. The lessons provide an enriched look at the creation of parabolas and allow students to experience the foundational idea that all functions are…

Automated theorem proving (ATP) for Propositional Classical Logic is an algorithm to check the validity of a formula. It is a very well-known problem which is decidable but co-NP-complete. There are many algorithms for this problem. In this paper, an educationally oriented implementation of Semantic Tableaux method is described. The program has…

In this paper we introduce a new collaborative technique in teaching and learning the epsilon-delta definition of a continuous function at the point from its domain, which connects mathematical logic, combinatorics and calculus. This collaborative approach provides an opportunity for mathematical high school students to engage in mathematical…

Mathematical teaching in Thai tertiary education still employs traditional methods of explanation and the use of rules, formulae, and theories in order for students to memorize and apply to their mathematical learning. This results in students' inability to concretely learn, fully comprehend and understand mathematical concepts and practice. In…

One of the main tasks in teaching mathematics to elementary students is to form calculating methods and techniques. The efforts of teachers and methodologists are aimed at solving this problem. Educational and psychological research is devoted to it. At the same time school teaching experience demonstrates some difficulties in learning methods of…

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…