This document presents the executive summary of the National Assessment of Educational Progress (NAEP) 1992 mathematics assessment. It included nearly 250,000 fourth, eighth, and twelfth grade students attending approximately 10,000 schools across the United States. The results from the assessment indicate that student performance is improving…

An investigation was conducted to determine the effectiveness of utilizing analogies to effect conceptual change in mathematics. Forty-one high school seniors participated in a knowledge reconstruction process regarding their beliefs about everyday probability situations such as sports events or lotteries. These mathematics students were given…

This study investigated six students' understandings of and difficulties with qualitative and numerical methods for analyzing differential equations. From an individual cognitive perspective, the obstacles found to influence the development of students' understandings included the function dilemma, the tendency to overgeneralize, interference from…

This study assessed estimation skills on both static and transformation (conservation) tasks on numerosities ranging from 3 to 16, and included addition and subtraction trials to control for response bias. A total of 148 four- and five-year-old children estimated the number of balls of yarn sewn on elastic straps, and participated in 1 addition, 1…

Mathematical concepts presented within disciplines outside mathematics are either assumed to be already familiar to the students, or else, they are regarded as being peripheral to the appreciation of the content of the nonmathematical lesson. Because it is routinely included without regard for possible students' interpretations, the mathematical…

In a series of activities involving map coloring, students can discover various combinatorial theorems including Euler's formula. (SD)

Mathematical concepts and experiences are recalled and organized in a flow chart format. The power of unifying ideas in mathematics often causes this sequence to be forgotten or assigned less importance than it should be. (SD)

Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…

This is the second edition of a curriculum guide for elementary school mathematics. It is one of a series intended to serve as a model for Alaskan school districts as they develop and review their curriculum documents. Listed are topics and concepts, learning outcomes and objectives, and sample learning activities. The learning activities are…

Reported are studies which investigate children's understandings of concepts of symmetry and topology, area measure, limit and function, and logical inference. In each case, the mathematical concepts are analyzed in terms of their conceptual foundations. Tasks were created or adapted for testing the subconcepts at appropriate grade levels from K…