The problem-solving skills of logical thinking, critical thinking, visualization, and communication skills are linked with some activities for students. Sample activities with logic, strategies and patterns, breaking fixed notions, open-minded problems, spatial visualization, and communication are described. (MNS)

A National Assessment of Educational Progress study was conducted on students to assess the dependence of high school mathematics learning on the amount and level of course work as well as other productive factors. Achievement appears to depend on number and level of courses, traditional teaching methods, home environment, and ethnicity.…

Contending that the recommendations of the Commission on Excellence in Education cannot apply to all schools, the author argues against requirements including computer science, foreign language, and additional mathematics and science courses for all students. The quality of United States education is concluded to be higher than recent publicity…

The pros and cons of using calculators in the arithmetic classroom were discussed in an English seminar for teachers. (SD)

Worksheets are provided for an activity involving the use of the calculator in discovering patterns when a number is divided by 9, 99, or 999. (DT)

It is generally considered that diagram use aids efficacy of math word problem solving. While understanding diagrams is considered important in both New Zealand and Japanese secondary schools, there is an additional emphasis in New Zealand schools for students to appreciate their use as tools for problem solving and communication. This study…

Data reported in this paper is part of a larger study which explored form five (14 to 16 year olds) students' ideas in probability and statistics. This paper presents and discusses the ways in which students made sense of task involving independence construct obtained from the individual interviews. The findings revealed that many of the students…

We examine a prospective high school teacher's instructional representations of rate of change and right triangle trigonometry to investigate his interpretation and understanding in relation to the development of proportional reasoning. Despite a constant effort by the subject to resort to "real life" examples in order to give meaning to his…

The various difficulties and cognitive obstacles that students face when they are introduced to algebra are well documented and described in the relevant bibliography. If it is possible, in order to avoid these difficulties, we have adopted the functional approach widening the meaning of algebraic thinking. In this paper, which is part of wider…

Two of the greatest problems of research on affective factors, and in particular, research on beliefs, is "what" and "how" we observe. The first difficulty is due to the lack of a clear terminology; but even once it has been clearly decided what to observe, it is not easy to put this into practice. This report describes from a…

In this paper we report on some patterns of reasoning, which emerged during an activity of proving a mathematical statement performed by nine grade and university mathematics students. The statement in question involves drawing figures, working in arithmetic and in algebra. As for secondary students we detected fluency, flexibility and ability of…

The report describes a mathematical modelling activity of a natural phenomenon (transmission of hereditary characters in a codominance case) using the concept of model as a theoretical instrument. The chosen tool enables us to show how the construction of a link between reality and a model is related to the evolution of the graphical…

The use of student aides to help implement andstaff a mathematics laboratory is discussed. The actual types of help given are presented as well as the effect the program had on the aides themselves as they were able to demonstrate acceptance of responsibility and gain self-confidence from the experience. (LS)

Projects for teachers which stress the use of multisensory aids, provide for experimentation, and encourage exchange of ideas and experiences are described. The goal of these recommended programs is the establishment of a purposeful, creative, self-directive learning environment. (LS)