Discussed is the meaning of the word "of" as is found in mathematical expressions that involve fractional numbers. The conceptual rather than numerical distinction is stressed. Teaching techniques regarding difficulties with this concept are suggested. (CW)

Presents two methods for solving equations. An asymmetric approach works backward from a number by reversing operations performed on a variable. A symmetric approach views the equation as a scale and performs inverse operations on both sides of the balance to solve for the variable. (MDH)

In Principles and Standards for School Mathematics (2000), the (U.S.) National Council of Teachers of Mathematics recommended that students communicate their mathematical thinking in a logical manner, and use the language of mathematics to express their thinking accurately and logically. Students should not only learn mathematics content, but…

Despite generally higher academic achievement, female students display lower academic self-confidence than males. Of particular interest to engineering educators is the difference in confidence in mathematical, scientific and problem-solving skills. Using a multi-method approach that utilizes the rich dataset of the Academic Pathways Study, the…

A number of cars drive along a narrow road that does not allow overtaking. Each driver has a certain maximum speed at which he or she will drive if alone on the road. As a result of slower cars ahead, many cars are forced to drive at speeds lower than their maximum ones. The average velocity in the queue offers a non-trivial example of a mean…

Conventional introduction to computer science presents individual algorithmic paradigms in the context of specific, prototypical problems. To complement this algorithm-centric instruction, this study additionally advocates problem-centric instruction. I present an original problem drawn from students' life that is simply stated but provides rich…

As in many other fields of science and technology, college students in computer engineering do not come into full contact with the key ideas and challenges of their chosen discipline until the third year of their studies. This situation poses a problem in terms of keeping the students motivated as they labor through their foundational, basic…

Recent research has revealed new information about how preschoolers develop an understanding of counting, and offers exciting new strategies for teaching. These new strategies encourage children to problem solve and use reasoning to understand quantities and how counting works rather than simply providing them practice with counting procedures.…

Sets of mathematics problems are generally arranged in 1 of 2 ways. With "blocked practice," all problems are drawn from the preceding lesson. With "mixed review," students encounter a mixture of problems drawn from different lessons. Mixed review has 2 features that distinguish it from blocked practice: Practice problems on…

Comparing and contrasting examples is a core cognitive process that supports learning in children and adults across a variety of topics. In this experimental study, we evaluated the benefits of supporting comparison in a classroom context for children learning about computational estimation. Fifth- and sixth-grade students (N = 157) learned about…

This yearbook includes four articles, one of which is written in German. The first article, "The Development of Mathematics Attitudes on the Upper Level of the Comprehensive School" (Olavi Karjalainen), examines the development of children's attitudes towards mathematics and the factors related to the development during the upper level…

The main purposes of the seminar were to examine the present status of school mathematics problem solving; to explore classroom practice and what is known about research; to compare the situations appearing in textbook word problems; and to make plans for cross-cultural research in both countries. A paper from each country was presented during the…

This three-part volume addresses topics and issues related to the education of secondary school mathematics teachers. The first part focuses on six contemporary trends in secondary school mathematics which bear heavily upon initial training. They include: the current concern for problem-solving; the influences of environmental change on…

When student achievement lags expectations, explanations are usually sought. One possibility is that the curriculum, as taught, is out of line with what is needed, and many feel that careful descriptions of the implemented curriculum are in short supply. Elementary school mathematics is used as a context for considering what can be learned from…

Investigates the development of concepts and processes associated with computational estimation. Twelve students at each of grades three, five, seven, and nine were interviewed. The older children understood better than the younger children what was asked but were uncomfortable with estimation processes and outcomes. (Author/YP)