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…

The experiment reported here investigated how verbalization of subtraction with regrouping operations influenced learning disabled students' self-efficacy and skillful performance, and also explored how effort attributional feedback affected these achievement behaviors. Learning disabled students (N=90) from grades 6 through 8 received training…

The notion of buggy procedures has played an important role in recent cognitive models of mathematical skills. Some earlier work on student modeling used artificial intelligence methods to automatically construct buggy models of student behavior. An alternate approach, proposed here, draws on insights from the rapidly developing field of machine…

Previous studies indicate that many early elementary school children have the misconception that whole number subtraction is a commutative operation. The degree and character of this subtraction error was investigated in this longitudinal study. Results obtained from three groups of students with different number abilities provided further…

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…

Young Filipino children are expected to solve mathematical word problems in English, which is not their mother tongue. Because of this, it is often assumed that Filipino children have difficulties in solving problems because they cannot read or comprehend what they have read. This study tested this assumption by determining whether presenting word…

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…

This is the second in a series of articles on using mathematical techniques from history to provide an interesting way for middle graders to practice math. (Editor)

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 paper proposes a semantic analysis in which meanings of word problems are structures that include class and order relations, and suggests a hypothesis of developmental levels that can account for children's performance of these problems at various ages. The different kinds of problems vary in the complexity of semantic structures and the…

Preschool children's problem-solving strategies on structured and unstructured number tasks were compared in this study. Participants were 20 four-years-olds and 20 five-year-olds. Each child was administered a number conservation, addition and subtraction, and division task. The addition and subtraction task contained trials which were designed…

This study investigated the effect of initial instruction on the processes children use to solve basic addition and subtraction verbal problems. Prior to instruction and following a 2-month introductory unit on addition and subtraction, 43 first-grade children were individually tested on verbal problems representing different models of addition…

Work by Dutch and Belgian researchers on arithmetic problems involving addition and subtraction is reviewed, especially word problems. It is an attempt to synthesize the research on the relationship between instruction in the part-whole line diagram and the solution of problems. Both logical and psychological interpretations are discussed. (MNS)

The effect of instruction in addition and subtraction concepts and skills on the processes first-grade pupils use to solve verbal problems was studied. Children represented solutions in individual interviews. Results indicated pupils shifted from a concrete direct modeling approach to a more unified conception that incorporated symbolic…