The column presents activities for grades K-8 focusing on the concept of equality. A geometric-puzzle motif is used, with basic number facts reviewed for the lower grades and equivalent fractions for the upper levels. Four worksheets and a problem poster are included. (DT)

Mathematical worksheets are presented for use in the elementary school classroom. The sheets deal with arithmetic and number patterns, one being for the primary grades, the other for grades 4 to 8. (RS)

What is meant by "normal science" is described, the first three steps in the "route to normal science" are outlined, and an example is given in which the trend toward research consensus is apparent. This involves current work on learning addition and subtraction. (MNS)

Use of the commutativity, addition-subtraction complement, and N+1 progression principles was studied by interviewing 54 capable pupils in grades 1-3. Commutativity was used extensively at each grade, while the addition-subtraction principle to solve subtraction varied across grades, and the N+1 pattern was seldom used. (MNS)

This report illustrates a simple, short, yet relatively little known partial check on addition that elementary school pupils can be lead to discover, and later taught to understand. The process can also be used for subtraction and is viewed as more useful than the traditional check of casting out nines. (MP)

Problems are discussed in which addition facts are presented using words instead of numbers. The letters are then replaced by numbers that will make the addition problems correct. (MP)

This article focuses on the aspect of mental arithmetic that uses thinking strategies that are effective with large numbers as well as basic facts. Two activities are suggested for lack of the four operations. (MK)

A teacher discusses his attempt to analyze his pupil's difficulties with arithmetic by looking at the component parts of each operation. (MP)

Describes how a 2nd grade class learned to add and subtract effectively by packing and unpacking "Aunt Mary's candies." (KHR)

A learning and teaching approach using base-10 blocks to embody the English named-value system of number words and digit cards to embody the positional base-10 system of numeration is described. Examines the students' understanding and arithmetic skills on the multidigit arithmetic. (Author/YP)

Reviews research using diagrams, number sentences, and algorithms to help students learn to add and subtract; poses questions on the relationship of instruction to children's knowledge construction; and proposes a research agenda in this area. (86 references) (MKR)

Presents exercises that analyze the additive property of energy. Concludes that if a body has more than one component of energy depending on the same physical quantity, the body's total energy will be the algebraic sum of the components if a linear relationship exists between the energy components and that physical quantity. (JRH)

Eight students with Down's syndrome, aged 11 through 13, were taught to add by counting-on in a 5-day teaching program. Teaching included instruction in component skills and use of precision teaching techniques. All students continued to use the technique six months later and generalized the technique to other materials. (Author/DB)

Investigates 10-year-old children's abilities to reason by analogy in solving addition and subtraction comparison problems involving unknown compare sets and unknown reference sets. Children responded in a consistent manner to the tasks involving the basic addition problems, indicating substantial relational knowledge of these but responded in an…