This paper discusses the role of uncertainty during the early stages of problem solving. It is argued that students start the problem solving activity with some degree of uncertainty that may vary from high to low. This degree of uncertainty may affect students' decisions at early stages of the problem solving process. It may be suggested that an…

Algebra and calculus students have difficulties to express themselves in a statement of mathematical symbols and to comment on written mathematical statements to end with equivalent mathematical symbols statement. In this study, the reasons behind the meaning students load to the mathematical symbols and written mathematical statements was…

A teacher in a large suburban elementary school in East Tennessee found that her fourth grade students had poor number sense and relied almost solely upon algorithmic procedure to solve math problems. Therefore, mental math was difficult for these students, so the daily number talks method was employed to strengthen number sense. However, no…

This collection of stories from a teacher's classroom highlights the problem-solving potential of very young students if they are engaged and challenged from the beginning. Arranged by month of the school year, each of these 10 stories is a suggestion for a classroom lesson. Together the stories provide a comprehensive picture of what can be…

The fundamental opposition of two types of discourse, mathematical proof and argumentation to the problem of validation in mathematics is explored. The naturalistic study of interaction in classrooms suggests the possibility of a mathematical argumentation to which students have access by the practice of discussions ruled by socio-mathematical…

The approximate nature of measurement is stressed, with examples given of elementary school mathematics problems which confuse reality with its mathematical model. Examples relating measurement to mathematical structure are given. (DT)

Examined were differential performances among categories of first graders when solving arithmetical workd problems of eight types under two distinct conditions. The categories were based on various types of quantitative comparisons which children are known to make. Several statistically significant results were obtained involving differences…

A method of using vector analysis is presented that is an application of calculus that helps to find the best angle for tacking a boat into the wind. While the discussion is theoretical, it is seen as a good illustration of mathematical investigation of a given situation. (MP)

A structural arithmetic curriculum is designed to help students develop their own powers of thought. (Author/MLF)

Presents 21 ideas for helping children learn to do story problems in math. (SJL)

Results of the second mathematics assessment show that students are alarmingly weak in problem-solving ability. (Author)