Revisits and discusses the polar bear problem that was published in the March 1997 issue. The problem concerns a riddle: If you walk one mile south, one mile east, and one mile north, and end up in the same spot as you started, what kind of bear would you see? (ASK)

Describes simple experiments to explore the variables and links to a theoretical approach. Using genuine data, develops an application to the drive mechanism for a lift in a deep mine shaft; poses follow-up questions. (ASK)

Provides an example of the modeling power of Mathematics, demonstrated in a piece of A-Level student coursework which was undertaken as part of the MEI Structured Mathematics scheme. A system of two masses and two springs oscillating in one dimension is found to be accurately modeled by a system of linear differential equations. (Author/ASK)

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…

Reviews a number of interesting sites on the Internet for mathematics education and considers the different ways in which the information available can be used as a teaching resource. Provides practical guidance on how teachers might take information in text, graphic, and file formats and use it either for themselves or with pupils. (Author/ASK)

Computer algebra systems have great potential uses, but learning the basic concepts of algebra is itself a mathematical activity. Explores theoretical concepts that may be seen as essential enabling skills for computer algebra systems users. (Author/ASK)

Errant mathematical views are widely found among teachers, their students, and authors of applied mathematics texts. Suggests classroom experimentation, both to confirm the occurrence of these errors, and to apply the appropriate corrective teaching. (Author/ASK)

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)

Investigates the basic mechanics of cycling with a simple reckoning of how much effort is needed from the cyclist. The work done by the cyclist is quantified when the ride is on the flat and also when pedaling uphill. Proves that by making use of the available gears on a mountain bike, cycling uphill can be accomplished without pain. (Author/ASK)

Examines the gear system of a mountain bike to discover any redundancy in the many gear settings available to the cyclist. Suggests a best strategy for changing up through the gears on a typical 21-gear system and an adjustment to the available gears that would result in a smoother change. (Author/ASK)

Reviews the historic relationship between logic and the mathematics curriculum. Proposes a list of logical elements for modern school mathematics. Checks the current national curriculum against this list and finds it to be deficient, especially in relation to the development of ideas of proof. Presents arguments for reform. (Contains 29…

Presents a game in which if player is playing a match of this game with an opponent, at each step in the game he has to decide whether to continue or to stop. Helps students to develop a strategy for making such a decision based on the expected gain and related probabilities. (Author/ASK)

Presents activities to model dynamic systems using graphing calculators and calculator based laboratories. (Author/ASK)

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…

Argues that teachers and lecturers need to identify essential skills which are technology-independent and need to determine the most effective use of new technology in the classroom. Examines prospects for change using the newer technology of graphing calculators for mathematics courses. Contains 15 references. (ASK)