Discussed are the concepts of intuition, the general properties of an intuitive knowledge, and the classification of intuitions as problem solving of affirmative. An example of intuition using multiplication and division is described in some detail. (MNS)

A brief survey of models in dealing with various types of understanding is given. Then a hybrid model, which proved inadequate for describing understanding, is outlined. Finally, four levels of understanding are discussed: intuitive, procedural, abstract, and formal. The concept of number is used to illustrate these levels. (MNS)

The theorem is seen as the foundation for large-sample statistical inferences, and is usually difficult for students to understand because one expects to take only one sample from a population. A description of how a table of random numbers readily available to students could be used is provided. (MP)

Recent trends in mathematics education, including instruction, curriculum, and defining the basic skills in mathematics are reviewed. Also reviewed is research addressed to whether mathematics achievement is declining. The authors conclude that computation remains a primary focus of curricula and that most teachers continue to teach as they were…

Teaching suggestions for graphing the function y=sin 1/x and the greatest integer function are given. (MK)

The need to define what concepts are is viewed as a necessary first step in shifting the teaching focus from skills. A call for the development of conceptual instruction that unites separate strands of research is made, and a seven-step plan is suggested. (MP)

The history of formal mathematical proofs is sketched out, starting with the Greeks. Included in this document is a chronological guide to mathematics and the world, highlighting major events in the world and important mathematicians in corresponding times. (MP)

The concept of equivalence is shown to be an elusive one that provides difficulty for preschoolers through college students. The idea persists that the equal sign is a "do something," or operator symbol, rather than a symbol for an equivalence relation. (MP)

A concept of infinity is described which extrapolates the measuring rather than counting aspects of number. Various theorems are proved in detail to show that "false" properties of infinity in a cardinal sense are "true" in a measuring sense. (MP)

There were 120 pupils in years 1 to 5 from two schools which were interviewed using specially prepared tasks to study the variety of interpretations given to letters by adolescents. Results indicate that two distinct conceptual understandings of the role played by a letter in relation to geometrical data exist in pupil's thinking. (Author/TG)

An activity for generating approximations of pi is described. (MK)

The author discusses the use of calculators in calculus classes and difficulties caused by roundoff errors. References for advanced follow-up topics are given. (Author/MK)

ENTER: History, geography, consumerism, science facts. COMPUTE: Totals, averages, percentages, etc. READ OUT: Enriched, integrated learning. (Editor)

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)

Presents a problem drawn from real life that addresses finding a way to cross all seven bridges of Konigsberg, Russia. Illustrates a set of simple examples and an instructional approach in order for students to make sense of a seemingly impossible problem. (ASK)