While representations of 3D shapes are used in the teaching of geometry in lower secondary school, it is known that such representations can provide difficulties for students. In this paper, we report findings from a classroom experiment in which Grade 7 students (aged 12-13) tackled a problem in 3D geometry that was, for them, quite challenging.…

Mathematical learning and teaching are increasingly seen as a multimodal experience involved in cultural and social semiotic registers and means, and as such social-cultural semiotic analysis is expected to shed light on learning and teaching processes occurring in the mathematics classroom. In this research, three social-cultural semiotic…

The purpose of mathematics competitions, and in our case the South African Mathematics Olympiad (SAMO), is to promote problem solving skills and strategies, to generate interest and enthusiasm for mathematics and to identify the most talented mathematical minds. SAMO is organised in two divisions--a junior and a senior division--over three rounds.…

Acid-base equilibrium is one of the most important and most challenging topics in a typical general chemistry course. This article introduces an alternative to the algebraic approach generally used in textbooks, the graphical log "C" method. Log "C" diagrams provide conceptual insight into the behavior of aqueous acid-base systems and allow…

This study analyzes six seventh grade Israeli mathematics textbooks, examining (1) the extent to which students are required to justify and explain their mathematical work, and (2) whether students are asked to justify a mathematical claim that is stated by the textbook or a mathematical claim that they themselves generated when solving a problem.…

Teacher education has become an area of considerable interest among policymakers in many countries over recent years. Teacher's knowledge and skills in qualified teaching is of great importance. The main purpose was to study the level and depth of the school mathematics and related teaching knowledge attained by prospective Ukrainian secondary…

Two problems from high school mathematics on finding minimum or maximum are discussed. The focus is on students' approaches and difficulties in identifying a correct solution and how dynamic geometry systems can help.

Over decades and across grade levels, deaf/hard-of-hearing (d/hh) student performance in mathematics has shown a gap in achievement. It is unclear, however, exactly when this gap begins to emerge and in what areas. This study describes preschool d/hh children's knowledge of early mathematics concepts. Both standardized and nonstandardized measures…

This paper presents the application of some concepts of Intelligent Tutoring Systems (ITS) to elaborate a conceptual framework that uses the remediation of errors with Multiple External Representations (MERs) in Learning Objects (LO). To this is demonstrated a development of LO for teaching the Pythagorean Theorem through this framework. This…

Designed for a broad audience, including educators, camp directors, afterschool coordinators, and preservice teachers, this investigation aims to help individuals experience mathematics in unconventional and exciting ways by engaging them in the physical activity of building geometric shapes using ropes. Through this engagement, the author…

This study examined how small groups of second-grade children developed understandings of the concept of congruence while collaboratively exploring and solving problems with dynamic representations of triangles using Sketchpad on the iPad. One case study is presented to illustrate how young learners can infer geometrical relationships between…

Two coordinate systems are related here, one defined by the earth's equator and north pole, the other by the orientation of a telescope at some location on the surface of the earth. Applying an interesting though somewhat obscure property of orthogonal matrices and using the cross-product simplifies this relationship, revealing that a surprisingly…

Various stakeholders in mathematics education have called for increasing the role of reasoning and proving in the school mathematics curriculum. There is some evidence that these recommendations have been taken seriously by mathematics educators and textbook developers. However, if we are truly to realize this goal, we must pose problems to…

The use of collaborative problem solving within mathematics education is imperative in this day and age of integrative science. The formation of interdisciplinary teams of mathematicians and scientists to investigate crucial problems is on the rise, as greater insight can be gained from an interdisciplinary perspective. Mathematical modelling, in…

Surveys were used to examine mathematics teachers (15) on their ability to solve similarity problems and on their likely implementation of lesson objectives for teaching similarity. All correctly solved a similarity problem requiring a traditional static perspective, but 7 out of 15 failed to correctly solve a problem that required a more…