This textbook is a course in elementary arithmetic. It stresses mental as well as written exercises. Addition and subtraction are first presented together, and later multiplication and division.

Using various aspects of mathematical structure as unifying concepts is stressed. Specific examples are given based on the concept of equivalent fractions and on the addition property of equality. (LS)

A problem about minimum distance travelled on a route through ten cities is used as a means for giving students practice in addition and with problem-solving skills. (DT)

Four levels of quantitative comparisons based on Piagetian task analysis and three IQ levels were used to partition a population of 341 first grade children. Each child was then tested on a set of addition facts and a set of addition problems which varied according to the use of aids or transformation. (JG)

Presented are two self-contained worksheets and teacher guides for open-ended experiences in recording and reading data which require the use of basic addition facts. One is for grades 1-3; the other for grades 4-8. (CT)

Discusses a tally device using discs on a paper diagram. Instructions given for number representation, negative values, games, addition and subtraction. (RS)

Three experiments evaluated performance on a mental multiplication task and the adequacy of several different models of mental addition as extended to multiplication. Results are discussed in terms of a network-retrieval approach to mental arithmetic, the commonalities between addition and multiplication, and rule- versus retrieval-based…

Four activities concerning addition and subtraction are described. They range in appropriate grade level from K-2 (crossing out objects) to 6-8 (solving decimal inequalities). Masters for worksheets are provided. (SD)

Describes second graders' responses to finding the sum of the numbers from 1 through 10 after reading the book, Ten Black Dots. Includes student work demonstrating their problem solving. (MKR)

Proposes a four-category classification of semantic structures of one-step word problems involving multiplication and division: forming the n-th multiple of measures, combinatorial multiplication, composition of operators, and multiplication by formula. This classification is compatible with semantic structures of addition and subtraction word…

Comprehension and development of the commutative law of addition by children were studied through commutative tasks completed by 72 children aged 5 to 8 years in Madrid (Spain). Results show that children focus mainly on addends in judging equivalence of commuted pairs. A five-level model of understanding of commutativity is proposed. (SLD)

Investigates the question of how a set of examples for adding natural numbers can be extended in a unique manner ad infinitum using the framework of a neural network model. Discusses Wittgenstein's remarks on the foundations of mathematics. (Contains 11 references.) (MDH)

Presents an activity involving students in a research project with pictures like those commonly found in elementary school mathematics textbooks and workbooks to sharpen student appreciation of the need for standardized methods of data collection. Illustrates that several different interpretations of the operations of addition and subtraction are…