This study: (1) documented the spontaneous derived facts strategies (DGSs) that second-grade children (N=23) used; (2) investigated how training in use of DFSs influenced the solution strategies children used to solve addition and subtraction problems; and (3) examined the role of DFSs in the transition to recall of number facts. (JN)

Described is a procedure for teaching children to learn to count on with finger patterns after they have learned to count with objects. The technique has been found to be successful with children of all ability levels at grades one and two. (RH)

Presents results from an Australian study examining whether children who use cognitive strategies in solving simple addition questions develop greater proficiency in addition than children who do not use such strategies. Describes the subjects, instruments, procedure, and instructional treatment. Concludes that the development of cognitive…

This study documented the spontaneously derived strategies that children use which may play a key role in the transition from counting to recall of number facts. For these strategies, the child uses a small set of known number facts to derive the solution to unknown number facts. How training in the use of derived strategies influences the…

Eight sixth-grade students received individualized instruction on the addition and subtraction of fractions in a one-to-one setting for 6 weeks. Instruction was specifically designed to build upon the student's prior knowledge of fractions. It was determined that all students possessed a rich store of prior knowledge about parts of wholes in real…

Three factors associated with arithmetical processes (sequence skills, arithmetical strategies, and information processing capacity) were measured in individual interviews with 35 first-grade pupils, aged 7.6 to 8.6, in one Finnish school. Mathematics achievement was determined from information supplied by teachers. Attitudes were assessed twice,…

Eight sixth-grade students received individualized instruction on the addition and subtraction of fractions in a one-to-one setting for 6 weeks. Instruction was specifically designed to build upon the student's prior knowledge of fraction ideas and to emphasize estimation. It was determined that all students possessed a rich store of prior…

Describes a study designed to investigate the relationship between students' learning of the standard double-digit addition algorithm and basic fact mastery or numeration concepts. Results suggest basic fact mastery and knowledge of numeration concepts may not be as necessary as previously assumed to learning multidigit addition. (PK)

Determined whether 11 third-grade children, differing in cognitive processing capacity, solve addition and subtraction word problems differently. Results, among others, show that children who differ in cognitive processing capacity also differ in strategies they use to solve the same verbal problems and differ in their success in finding correct…

Described is a study in which three instructional approaches were applied in second grade classes. Discussed are proportional materials, nonproportional materials, nonproportional materials with pictorial models. Findings, results, and recommendations are presented. (CW)

The study investigated which addition facts children and preservice teachers view as being difficult, whether it is possible to determine facts which are difficult for all children, and whether children and adults agree on which facts are difficult. Results indicated that children and adults disagree about the difficulty of facts. (PK)

This study compared the effectiveness of teaching multidigit addition of whole numbers without regrouping prior to teaching it with regrouping to teaching multidigit addition with and without regrouping simultaneously. Pretest/posttest-delayed posttest results of second grade students (n=151) from seven randomly assigned classrooms indicated no…

An editorial and abstracts for 12 research reports are contained in this issue. The editorial by Robert E. Reys focuses on the dangers of publishing poor research. The abstracts, each with a critique, concern research on a game for logical reasoning, wait-time and sex differences, vocabulary instruction on ratio and proportion, male-female…