The importance of having children manipulate small objects that can be grouped, arranged, and counted is discussed. Learning activities for one-to-one correspondence, numerals, and the four operations are given. (MNS)

Results are reported from a study of the problem-solving abilities of Swedish children aged 12-13. Illustrative problems and conclusions are given to describe a method for defining and testing problem solving. (MNS)

A method is described for finding those numbers which are both triangular and square (named trisqy numbers). A program for a programmable calculator is given, as well as a proof. (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)

A method for finding logarithms is outlined. Four-function calculators are used to simplify the computation for those who enjoy experimenting with numbers. (MNS)

A procedure for helping students to calculate logarithms with any calculator that has a square root function is outlined. (MNS)

Models for division are discussed: counting, repeated subtraction, inverse of multiplication, sets, number line, balance beam, arrays, and cross product of sets. Expressing the remainder using various models is then presented, followed by comments on why all the models should be taught. (MNS)

Activities with triangular, square, pentagonal, hexagonal, and octagonal numbers are briefly discussed. (MNS)

Provided are some ideas on teaching elementary numerical methods to sixth-form students. Comments are included on the syllabus recently introduced at Advanced Level in Hong Kong. (MNS)

Subtractive magic triangles are discussed and questions raised for exploration with mathematics classes. Answers are also included. (MNS)

The relation between the area of a rectangle and its perimeter is clarified by looking at patterns. Several examples involving rectangles with integral sides are presented. (MNS)

The evolution of Archimedes' method is traced from its geometrical beginning as a means to approximate pi to its modern version as an analytical technique for evaluating inverse circular and hyperbolic functions. It is felt the web of old and new algorithms provides considerable instructional material, and ideas are offered. (MP)

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

Main objectives were to clarify the notion of numeration, to clarify understanding the concept, to develop a framework to evaluate understanding and teach numeration, and to single out children's main difficulties associated with this concept. Striking similarities between processes involved in numeration and measure were found. (MP)

A geometric model used to teach properties of rational numbers to college students is described. (MK)