Examined the relationship between 6- to 8-year olds' conceptual understanding of additive composition, commutativity, and associativity principles and addition problem-solving procedures. Results revealed that conceptual understanding was related to using order-indifferent, decomposition, and retrieval strategies and speed and accuracy in solving…

A teacher in a large suburban elementary school in East Tennessee found that her fourth grade students had poor number sense and relied almost solely upon algorithmic procedure to solve math problems. Therefore, mental math was difficult for these students, so the daily number talks method was employed to strengthen number sense. However, no…

A number of models are considered that specify how children and adults solve single-digit addition problems. (Authors)

Presents some results of a study on teaching negative numbers. Focuses on the identification of addition and subtraction, the use of the number line, additive problem solving, and the possibility of following several sequences of numerical extensions. Indicates the importance of previous ideas on positive numbers and how these ideas influence the…

Eighteen college students solved addition problems using the Hutchings Low Fatigue Addition Algorithm, which requires a written record of running sums, and the standard algorithm, which does not. Students using the Hutchings algorithm had significantly higher reaction times to a tone, indicating that the Hutchings method requires less cognitive…

Three models have been proposed to account for the relationship between the principle of commutativity and the development of more economical addition strategies, which disregard addend order. In the first and second models, it has been proposed that either discovery or assumption of commutativity is a necessary condition for the invention of…

Is there a better way to help your first-grade students with addition? Author offers suggestions. (Editor/RK)

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)

Analyzes a didactical sequence for the teaching of addition and subtraction procedures and algorithms. Uses didactical procedures by children in problem solving activities in order to gain a better understanding of the interaction between numbers, numeration, and operations knowledge which are involved in the construction of addition and…

In the Hypothesis-Experiment-Instruction (HEI) method students are presented with a problem with three or four answer alternatives, which leads them later to recognize the distribution of choices, discuss a variety of ideas among them, and integrate distributed pieces of information. This study examined the effects of presenting a problem with or…

Simple and complex addition problems were presented for true/false verification to 30 undergraduate students to test a general model for cognitive addition. Problems were presented on a microcomputer, with reaction time (RT) and response accuracy recorded. Models for addition were fit to average RT data using multiple regression techniques. These…

This study involved the development and experimental tryout of 22 lessons designed to teach 23 primary grade children a set of specific procedures, focusing on the drawing of meaningful diagrams, for analyzing and solving arithmetic story problems. Major dependent variables studied were gain on (1) a 20-item test on stories of the eight types…

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)

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)