Describes the Six Circle problem which consists of the numbers 1-6, six circles, and asks whether it is possible to put the numbers in the circles--which are configured in a triangle--so that the sums of the three numbers on either side are the same. (NB)

Recommends a change in the way mathematics is taught to engineers and scientists. Espouses a shift away from traditional methods to an approach that makes significant use of algebra packages. Suggests that teaching the language comprised of the notation and grammar of mathematics would be of more use and more accessible than focusing entirely on…

Shows how integer-sided triangles can be nested, each nest having a single enclosing isosceles triangle. Brings to light what can be seen as a relatively simple generalization of Pythagoras' theorem, a result that should be readily accessible to many secondary school pupils. (Author/KHR)

Investigates the use of mathematical modeling tasks in 11- and 12-year-old students and the development of mathematical thinking skills using practical modeling activities. Analyzes the development of students' mathematical thinking with interviews of a form of dynamic assessment. Reports that some students proved to be naturally mindful and…

Considers the impact of the introduction of graphic calculators into assessment within the International Baccalaureate Diploma. Discusses difficulties that arise in the development of practice questions, how these difficulties were resolved in the questions that appeared on the examinations, and problems of different calculator syntax. (Author/KHR)

Investigates the introduction of mathematical modeling into the mathematics assessment program of the International Baccalaureate Diploma. Considers structured and open modeling in the pre-university mathematics program. Discusses influences of the use of hand-held technology on mathematical modeling and teacher and assessor beliefs about modeling…

Reports on the observed actions of prospective Swedish secondary mathematics teachers as they were working in a modeling situation. Discusses the way the students tackled the modeling situation and their strategies and attitudes as well as the difficulties in assessing mathematical modeling performance. (KHR)

Explains an application of mathematical modeling within a school setting as well as progressive use of graphing calculators in mathematical modeling. Analyzes students' performances in the process of problem-solving using the problem of baton-passing in relay races. Discusses students' use of their mathematical knowledge and ideas when they used…

Considers educational aspects of the development of ratio and proportion focusing on the arithmetization undergone by these concepts in light of the relationship between mathematics and music. Investigates the instructional aspects of compounding ratios. Points out features of the differences between identity and proportion which can be…

Carries out a survey of schools and colleges on problems associated with the new Advanced Subsidiary (AS) award introduced in 2000. Reports on teachers' views of the content of the specifications and examinations, entry patterns, changes that teachers want to see to the current system, progression to A2, and the benefits/disadvantages of the…

Discusses certain transferable skills and a strategy for developing them via an intensive short course on mathematical modeling. Includes student reactions and comments on the course. Suggests that this course developed modeling as well as generic skills through teaching, learning, and assessment style. (Author/KHR)

The number of students studying for A and AS level Further Mathematics has fallen dramatically since the early 1980s. Explains this decline and why it is vital that Further Mathematics be saved. Outlines the Gatsby-funded MEI project 'Enabling Access to Further Mathematics' which aims to show that distance learning using modern technology can…

Explores the derivation of empirical models for the stopping distance of a car being driven at a range of speeds. Indicates that the calculation of stopping distances makes an excellent example of empirical modeling because it is a situation that is readily understood and particularly relevant to many first-year undergraduates who are learning or…

Observes the application of probability theory to a game between two players. Shows how basic techniques such as tree diagrams can be used to demonstrate optimum strategies, how the art of bluffing can be quantified, and how this might be applied to a game of poker. (Author/ASK)

Observes four groups of mathematics undergraduates carrying out a mathematical modeling exercise of a familiar physical process (the cooling of a cup of hot water). Indicates that students neither took the time to reflect upon the physical process nor to reflect on the appropriateness of the model they produced. Recommends that classroom…