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…

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)

A learning and teaching approach using base-10 blocks to embody the English named-value system of number words and digit cards to embody the positional base-10 system of numeration is described. Examines the students' understanding and arithmetic skills on the multidigit arithmetic. (Author/YP)

The primary objective of this study was to provide an experimental model of children's representations of addition and subtraction concepts viewed as constructed schemes. How children with different counting schemes differ in their addition and subtraction concepts and how the types of problems children solve correlate with the addition and…

Refinements of work with calculator algorithms previously conducted by the author are reported. Work with "chaining" and the doing/undoing property in addition and subtraction was tested with 24 third-grade students. Results indicated the need for further instruction with both ideas. Students were able to manipulate the calculator keyboard, but…

Examined effects of problem size in mental addition among elementary children in China (n=104) and Missouri (n=105) and among undergraduates in China (n=26) and Missouri (n=35). For all Missouri subjects and Chinese through first grade, larger-valued numbers took longer and induced more errors. (Author/NBI)

Excerpts from interviews with pupils in grades 1, 2, 3, and 6 to ascertain their interpretations of mathematical sentences and symbols are presented. Children were found to consider the equal sign as an operator symbol ("do something") and not as a relational symbol. Implications for teaching are briefly discussed. (MS)

Another way to add and subtract, in which the mental regrouping strategy is applied to an original 10-structure, is presented. Pupils use a visual model, called "little person," to move from counting to visualization. Originally designed for use with pupils with learning disabilities, this method has wider applicability. (KR)

Students can learn to solve problems of qualitative integration and differentiation independently of their study of formal calculus or algebra. This exploratory study investigated the basic intuitions that elementary school children construct in their daily experience with physical and symbolic change. Elementary school children (n=18) were…

Five-frames are proposed as manipulative material to increase children's ability to identify the number of objects without direct counting. How to use frames and beansticks to construct basic facts without counting is discussed. (MNS)

Discusses the contributions in each chapter of the book, highlighting the textbook analyses for each arithmetic topic presented. (MDH)

Discussed is research which shows, in contrast to the dominant impression given by Piaget's work, that before the onset of schooling the young child possesses several kinds of fundamental "intuitions" concerning numbers. (Author/TG)

This paper reports the formative evaluation of six curriculum units related to initial number sentence writing. These units were used for a coordinated study carried out by the Mathematics Work Group of the Wisconsin Research and Development Center for Individualized Schooling. The units were tried during the 1977-78 and 1978-79 school years at a…

A discussion is presented concerning variables associated with children's representation of certain addition and subtraction problems. Problem components are classified as physical, pictorial, sensual, verbal-spoken, verbal-written, symbolic, or internal. Problems are discussed as abstract (symbolic) or nonsymbolic. Three problem components are…

Presents a method for demonstrating addition and subtraction of integers on the number line in a way that distinguishes between subtraction and negative numbers. The model depicts the sign of the number by forward or backward movement on the number line. Subtraction is illustrated by a turning around movement. (MDH)