The analysis of word problem types and schema-based diagrams are assumed useful for helping students and thus, important for preservice teachers to learn in their preparation programs. Drawing on pre-and post-assessments and videotaped demonstrations, this study analyzed elementary preservice teachers' understanding of addition and subtraction…

This submission contains the Proceedings of the 2015 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at the Université de Moncton in Moncton, New Brunswick. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of…

Changes in children's cognitive strategies for solving simple subtractions were studied by analyzing verbal reports given immediately after each problem. The development of children's cognitive processes involved a gradual shift from more primitive and less demanding memory strategies to reconstructive memory processes to retrieval processes.…

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…

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…

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…

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…

This study illustrates a process for selecting a preferred model in the validation of hierarchical learning scales. The test performance of 100 8-to 11-year-old children on subtraction tasks involving variations in borrowing are examined. Goodman's response scaling technique is illustrated. (Author/GDC)

The paragraph unit that constitutes an addition or subtraction word problem text is discussed and the logical conditions such problems must fulfill are formulated. An attempt is then made to formulate the semantic conditions which will define well-formed addition and subtraction texts. (MN)

Specific instruction in different contexts provide needed background for solving addition and subtraction problems. The categories of problems and relative difficulties are presented, followed by an explanation of a successful instructional sequence. (MNS)

Solution processes for simple arithmetic word problems are examined in three dimensions: the order of mention, the identity of the unknown, and the type of verb. The influence of mathematical and linguistic factors in these processes are discussed. (BJG)