Mathematics curricula have traditionally focused on content knowledge, often in the form of a scope and sequence of increasingly difficult mathematics. The importance of using and applying mathematics is recognised in the current Australian Curriculum Mathematics (AC: M) as 'proficiencies' that are intended to be integrated with the content. There…

This article offers a description of how empirical experiences through the use of procedural knowledge can serve as the stage for the development of hypothetical concepts using the learning cycle, an inquiry teaching and learning method with a long history in science education. The learning cycle brings a unique epistemology by way of using…

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.…

Presents an educational game on probability that can be the starting point for an open-ended statistical project. (ASK)

Analyzes the responses of pre- and in-service teachers (N=136) to a series of graded questions about average. Presents information in graphical form requiring respondents to compare datasets induced responses in iconic and concrete symbolic modes, demonstrating multimodal functioning. (Author/ASK)

Explores the development of understanding of the concept of average with students from grades 3 to 9 through interviews. Observed six levels of response based on an hierarchical model of cognitive functioning. Documents usage of ideas associated with the three standard measures of central tendency and representation as strategies for problem…

This book contains a set of versatile enrichment exercises that cover a very broad range of mathematical topics and applications in algebra from the Moebius strip to the googol. Several criteria have been used in developing the activities and selecting the topics that are included. All of them bear heavily and equally on concerns for curriculum…

Presents activity pages containing world population data for students to use to predict future population figures and Consumer Price Index (CPI) data to track changes in the costs of the goods. Includes answer key. (KHR)

Describes an activity that engages pupils in the whole statistical process from collecting data to interpreting the results. Discusses the importance of these activities in developing knowledge, skills, understanding, and ability in problem solving. (Author/ASK)

Potential uses for computers include: programing the solutions to problems; simulating situations in order to test hypotheses; gaming, as a study of probability and statistics; and practicing, testing, and tutoring. (MP)

Discusses Monte Carlo methods, powerful and useful techniques that rely on random numbers to solve deterministic problems whose solutions may be too difficult to obtain using conventional mathematics. Reviews two excellent candidates for the application of Monte Carlo methods. (ASK)

Discussed is one "quite general" attribute that can differentiate problem representations: the kinds of entities that are included -- the cognitive objects that the system can reason about in a relatively direct way, and that are included continuously in the representation. The ontology of a domain is significant for four reasons. First,…

The Colorado Model Content Standards for Mathematics were designed to serve as a guide for school districts as they define standards that will enable every Colorado student to develop the mathematical literacy needed for citizenship and employment in the 21st century. A new vision is provided of the content students should study in order to…

Reviews of relevant research on the application of operations research and statistics that appeared prior to 1980 are compared with those appearing in the early 1980s. In summary, both explicit and implicit users of mathematics in educational administration see it as a tool that essentially brings order and generalizability to administrative data.…

Five activity lessons are proposed to present applications of probability and to exhibit its use in conjunction with statistics as a major decision-making and problem-solving tool. (MP)