There are many potential ways to represent arithmetical tasks, but students' choices may be limited by beliefs that only certain standardised representations are "legitimate" in school mathematics. Furthermore, concern for the quantity and speed of "work done" can override opportunities for meaningful engagement with the…

The purpose of this study was to examine adult developmental mathematics (ADM) students' knowledge of fraction addition and subtraction as it relates to their demonstrated fraction schemes and ability to disembed in multiplicative contexts with whole numbers. The study was conducted using a mixed methods sequential explanatory design. In the first…

This research aims to analyze ways of understanding of students with mathematics learning disabilities when learning fraction. The research was conducted in an Inclusive Junior High School in the West Java Province, Indonesia. This study is qualitative, with the single-case (holistic) designs. The case will focus on three students who suspected of…

This design study investigated the use of multiplication and division problems to help 5-year-old children develop an early understanding of multiplication and division. One teacher and her class of 15 5-year-old children were involved in a collaborative partnership with the researchers. The design study was conducted over two 4-week periods in…

This paper reports on 13 Grade 3 students' approaches to partitive and quotitive division word problems. Of particular interest was the extent to which students drew on their knowledge of multiplication to solve division problems. The findings suggest that developing a relationship between multiplication and division is more significant than…

This paper shares research from a pilot study in which young children were introduced to multiplication and division problems in their first year of school. The focus was on building children's conceptual understanding of the idea of "repeated groups" as a fundamental aspect of multiplication and its relation to division. The particular…

This study aimed at investigating the progress of students' learning on multiplication fractions with natural numbers through the five activity levels based on Realistic Mathematics Education (RME) approach proposed by Streefland. Design research was chosen to achieve this research goal. In design research, the Hypothetical Learning Trajectory…

Explores mathematical methods children use to find answers for themselves. Describes some methods used for multiplication and subtraction problems. (YP)

Discusses the development of multiplicative and divisional schemes within a constructivist framework. Illustrates child thinking and child methods relative to the meanings of these operations using interviews with children. Compares the constructivist perspective on the development of meanings of multiplication and division to what is found in…

Interviewed 59 2nd- and 44 3rd-year elementary school students concerning their solutions to arithmetic problems commensurate with their age and ability. The results indicate that as children progress through school, they continue to use counting as an important part of their problem-solving repertoire, combining counting skills in idiosyncratic…

Interviews with in-service elementary teachers (n=32) who were asked to solve multiplicative problems showed that teachers who solved problems relationally reasoned in terms of ratio and proportion concepts, whereas teachers who arrived at correct solutions without the concepts did so using a trial-and-error method. (24 references) (Author/MKR)

This paper looks at the issue of mathematics learning from a developmental perspective. It begins by focusing on the importance for teachers of understanding how mathematical thinking develops. The New Zealand Number Framework is used as an example of a developmental progression that is of particular relevance to the teaching of mathematics. The…