A focus on mathematical understanding and problem solving in math education has developed a need to implement alternate ways of testing to better assess the students' understanding and problem solving skills. The seventh national school curriculum (MOE, 1997) for mathematics in Korea was revised to the current curriculum (MOEHRD, 2007) to…

In this chapter, the authors illustrate on mathematical problem-solving activities within families how the functions and structures of their mathematics at home are dependent on values, and how interacting values during problem situations came to shape what counted as solutions. These values examples from family math illustrate the complex…

Collaborative learning is being used extensively by educators at all levels. Peer-led team learning in a version of collaborative learning that has shown consistent success in science, technology, engineering and mathematics disciplines. Using a multi-phase research study we describe the development of an observation instrument that can be used to…

Teaching math problem solving has been a challenge for many educators, especially in Title I schools. Textbooks provided by the district under study were the primary source of math instructional material. Moreover, the instruction of computation was the method used for preparing students for success with later problem solving lessons. The lack of…

Symbolic circuit analysis is a cornerstone of electrical engineering education. Solving a suitable set of selected problems is essential to developing professional skills in the field. A new method is presented for automatic validation of circuit equations representing a student's intermediate steps in the solving process. Providing this immediate…

These conference proceedings include two invited lectures, four working group reports, seven reports from topic groups, one ad hoc presentation paper, a list of participants and a list of previous proceedings. The invited lectures were: "Mathematics Education and Technology" (Christine Keital); and "All One System" (Lynn A.…

Presented is an account of a day-and-a-half seminar which was held for selected mathematics educators from six states. It was sponsored by the Regional Exchange (RX), a National Institute of Education (NIE) dissemination project headquartered at the Southwest Educational Development Laboratory (SEDL). The seminar had two important purposes: (1) to…

The second phase of a new national survey conducted among college instructors and employers shows that 78% of college faculty and 62% of employers believe that public high schools are not doing enough to prepare students for the expectations they will face in college and the working world. Only roughly one in four recent high school grads report…

This paper, part of a series of working papers published to provide documentation of research and development efforts associated with the Indigenous Mathematics Project of Papua New Guinea, discusses the role of problem solving in the mathematics curriculum and types and characteristics of good problems, with illustrations. Reasoning by analysis…

Suggestions are provided for activities involving the construction of mathematical models to solve "real-life" problems. (SD)

After describing desirable characteristics of a student's first encounter with proof, and listing skills prerequisite for the proposed lesson (knowledge of some operational systems), the author describes in detail an introductory session in which students prove consequences of commutativity and associativity for a system supposedly encountered on…

This paper proposes a semantic analysis in which meanings of word problems are structures that include class and order relations, and suggests a hypothesis of developmental levels that can account for children's performance of these problems at various ages. The different kinds of problems vary in the complexity of semantic structures and the…

This is one of a series that is a collection of translations from the extensive Soviet literature of the past 25 years on research in the psychology of mathematics instruction. It also includes works on methods of teaching mathematics directly influenced by the psychological research. Selected papers and books considered to be of value to the…

This paper describes a study in which 14 linguistic variables were used to determine which variables would account for a significant amount of the observed variance in the error rate in verbal arithmetic problems. Three forms of verbal problem sets in which the number of words in the problem statement were systematically varied were administered…