This paper introduces the reader to the concepts of binomial probability and simulation. A spreadsheet is used to illustrate these concepts. Random number generators are great technological tools for demonstrating the concepts of probability. Ideas of approximation, estimation, and mathematical usefulness provide numerous ways of learning…

The Purposeful Algebraic Activity Project is concerned with the development of algebraic activity in pupils in the early years of secondary schooling. Here we report on the different ways in which we have observed children articulating generalisations during semi-structured interviews which are being used to gain snap-shots of this development. We…

We explore the nature and consequences of teachers' problem solving through an example of a teacher's mathematical problem solving as it was occasioned by a student's mathematics. This illustration demonstrates the value of an interpretive framework that points to the mathematics of the classroom as a collective. Arising from this exploration is…

This unit of study for grades K-2 focuses on counting coins and coin equivalencies up to 50 cents, making use of a literature connection. The unit provides key words; recommends subject areas and approximate length of time; poses an essential question or problem; provides a unit introduction; notes four individual lessons ((1) For Sale!; (2)…

Fourteen third graders were given numerical computation and division-with-remainder (DWR) problems both before and after they were taught the division algorithm in classrooms. Their solutions were examined. The results show that students' initial acquisition of the division algorithm did improve their performance in numerical division computations…

Calculators are fast becoming accepted as needed household appliances. Certainly, children in school now will, as adults, look on calculators as being as necessary to everyday life as telephones. (Author)

In this first of two articles, computational algorithms for multiplication and division which encourage use of one operation at a time are proposed. (DT)

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)

Activities are provided for calculating speeds of celestial bodies. These focus on how fast earth rotates on its axis, how fast planets travel around the sun, and how fast the solar system is traveling with the Milky Way. (JN)

A strategy to make the transition from manipulative materials to a written algorithm for division is outlined in dialogue form. (MNS)

A method for computer grading pharmaceutical calculations exams in which students convert their answers into scientific notation and enter their solutions onto a mark sense form is described. A table is generated and then posted listing student identification numbers, exam grades, and which problems were missed. (Author/MLW)

Use of the commutativity, addition-subtraction complement, and N+1 progression principles was studied by interviewing 54 capable pupils in grades 1-3. Commutativity was used extensively at each grade, while the addition-subtraction principle to solve subtraction varied across grades, and the N+1 pattern was seldom used. (MNS)

Several ideas for questions and settings for interviews are presented. It is noted that although subtraction is used as an example in each case, most of the material can be easily adapted to the other basic operations. Many problems are noted with standard diagnostic tests and use of them is discouraged. (MP)

Suggests and illustrates ways in which systematic consideration of selected unary operations can be facilitated by using electronic calculators. Emphasis is placed upon unary operations suitable for exploration and investigation at the pre-algebra level, using calculation algorithms as a basis for generating examples and non-examples to develop…