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…

In this proposal, I introduce a method for modeling the dynamics of a sixth-grade student's accommodation of his fractions scheme to include a disembedding operation (Steffe & Olive, 2010). I will describe a three-part approach consisting of a constructivist teaching experiment, retrospective analysis, and stochastic modeling of the student's…

We investigate the viability of a new approach to initial fraction instruction. We establish the need to empirically investigate whether the proposed approach shares the strengths of currently used approaches, specifically, whether students will (a) construe problems based on the proposed approach as experientially real, and (b) bring up ideas…

Interview and questionnaire responses of students in grades K-10 completing common and decimal fraction tasks suggested the existence of 2 sequential unistructural-multistructural-relational learning cycles within the concrete symbolic mode. (46 references) (MKR)

A study interviewed 6 grade-6 students after participation in 21 lessons on basic concepts of fractions and decimals to determine how different children construct rational number concepts. Discussed the formation of the key concept of equivalent fractions based on student responses to interview questions. (MDH)

Low ability sixth graders (n=19) participated in a teaching experiment involving fraction concepts. Results showed students were able to acquire and use semantic processes and transfer these processes to novel tasks. Semantic processing was positively associated with performance. (MKR)

Results of interviews with students regarding their conceptual understanding of fractions are discussed. Fewer than 10 percent had acquired an adequate conceptual base. (MP)

Considered is a conceptual analog of buggy algorithms and rule-based mathematical development. The investigations consider whether children's efforts to make conceptual sense of new mathematics instruction in terms of their available knowledge may sometimes lead them to make systematic errors. In particular, the possibility is explored that…

This paper describes student performance and beliefs regarding fractions resulting from a five-phase approach toward developing mathematical intuition via physical materials. Interviews with students using this approach and with students using a conventional textbook approach indicated significant differences in problem-solving abilities and…

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…

A teaching experiment with six third graders to analyze their ways of operating while solving fraction tasks. Children's quantitative reasoning with fractions was based on their quantitative reasoning with natural numbers. Presents the constructive itinerary of one of the most advanced children in the group. (Contains 44 references.) (Author/MDH)

Responses of students in grades K-10 (42 interviewed; 98 written) to 4 common fractions problems were analyzed for iconic mode processes in relationship to concrete symbolic mode development. Concludes that progress in the latter, without development of complementary iconic support, limits both understanding and flexibility in solving problems.…

This paper presents results from a study of 19 teacher education students' knowledge of mathematics and discusses an analytic framework for examing and appraising teachers' and prospective teachers' subject matter knowledge. Participants in the study were 10 elementary education majors and 9 mathematics majors or minors who were preparing to teach…