By the time they reach middle school, all students have been taught to add fractions. However, not all have "learned" to add fractions. The common mistake in adding fractions is to report that a/b + c/d is equal to (a + c)/(b + d). It is certainly necessary to correct this mistake when a student makes it. However, this occasion also…

"How Students Learn: Mathematics in the Classroom" builds on the discoveries detailed in the best-selling "How People Learn." Now these findings are presented in a way that teachers can use immediately, to revitalize their work in the classroom for even greater effectiveness. This book shows how to overcome the difficulties in teaching math to…

Some pedagogical problems in Chinese numeration are described. They involve the teaching and learning of how to speak numerals with fluency in Chinese, using Hindu-Arabic written numbers. An alternative approach which stresses regularity is proposed. (MNS)

Describes a pattern which emerged from an examination of the digits of the squares of numbers. Provides eight examples having the pattern at the units or tens digit of the number. (YP)

Discusses figurate number learning activities using patterns and manipulative models. Provides examples of square numbers, triangular numbers, pentagonal numbers, hexagonal numbers, and oblong numbers. (YP)

As students translate number words into the language of mathematics they explore number composition, equivalent expressions, and patterns in numbers and words. (MKR)

A method of identification of pigs used by farmers is described as an application of a base three numeration system. (MP)

The concepts of number sense and numeration, operations, and whole-number computations and their importance are discussed. Activities cover developing concepts of operations, exploring patterns and relationships, and building an understanding of mathematical structure. (KR)

The content of the standards focusing on numbers and numeration for grades K-8 are discussed. Several activities for developing number concepts and skills are described. (YP)

Describes four activities designed to discover numerical patterns using a calculator or paper and pencil. Provides tables and figures for the activities. (YP)

Presents two practice-discovery activities to furnish computational review in a nonroutine setting. Provides a worksheet for the activities. (YP)

Suggests that good number sense is fundamental for success in estimation, approximation, and problem solving. Further, large-number concepts are appropriate for development in upper elementary school, high school, and beyond. Presents examples to enhance a sense of large numbers in middle and high school students. (PK)

Provides methods of teaching negative number operations, including addition, subtraction, and multiplication. Presents examples and activities for the operations. (YP)

Described is an activity in which students develop their own number system. This activity allow students to examine the structure and history of number systems and to discover the power and respectable efficiency of the number system used today. (KR)

This document provides a listing of the revised sequence of mathematics skills to be taught in grades K-6 in the Lancaster (Pennsylvania) School District. For each level the individual skills are grouped into categories, listed in sequence, and cross-referenced to specific pages in three mathematics textbook series. The categories of skills relate…