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…

Asserts that findings on whether young infants look longer at incorrect addition and subtraction have been inconsistent or negative. Hypothesizes that imprecise ordinal calculating with very small numbers of objects develops in late infancy and that precise calculating develops in early childhood. (Author/KB)

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 this paper we discuss a study that looks at the kinds of practices that Latino parents use to support their children's learning of mathematics. Some of our findings reveal that parents react to their children's mathematics education looking back to their own experiences as students. Thus, in some cases, they are faced with pedagogical…

This document plus diskette product provides nine interactive puzzles and games that both teach and provide practice with simple addition and subtraction concepts. The activities address these skills through carrying in addition and regrouping in subtraction. The activities address cognitive skills such as problem solving, planning, visual pattern…

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…

The study investigated whether the pre-arrangement of math facts in spaced repetitions redundancy would increase the acquisition rate of a second grader with poor mathematics achievement. Baseline data were provided by observation of in-class math performance of addition sums zero through 18. In the experimental phase, worksheet problems were…

This paper is concerned with the role of meaning and understanding in the acquisition of computational skill in subtraction. Evidence on the syntactic nature of subtraction errors is reviewed, with common "bugs" described. Then, data collected from interviews with four children are summarized in terms of their semantics of concrete…

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…