Many of the difficulties that students have with mathematical symbolism seem to stem from the use of a horizontal form for an equation and a vertical form for computation. The differences between these two forms are discussed. (JT)

Some students can perform operations on fractions when using physical materials, but are unable to transfer this ability to operations with symbolic expressions. They seem to view the manipulative and paper-and-pencil problems as different and are not surprised to get different answers. (SD)

These worksheets will provide students with experiences in identifying largest and smallest single-digit numbers, in writing names for single-digit numbers, in tests of divisibility, and in writing number sentences. (MP)

How children can be guided to see and feel the power of thinking with and about mathematical symbols is discussed. A strategy to help them bridge the gap between manipulative models and symbols is detailed. (MNS)

Activities for the development of the association of number value and symbols using wooden numerals and pages are described. (MN)

Interpretation of rational numbers as fractions, ratios, percentages, and quotients of integers are discussed. Then coding conventions are noted, and equivalence classes are described. Finally, density and order are discussed. (MNS)

Activities are given for solving verbal subtraction problems. Take-away and comparison situations are described, and three levels of activities to model the situations are given: one involving concrete materials and verbal descriptions; the second with these plus written symbols; and the third encouraging mental images. (MNS)

Summarizes some student misconceptions concerning the concept of equality. Provides several ways to modify present instruction. Describes a way to model the relational view of equals using balances. (YP)