This paper describes the authors' journey in designing a linear representation that aligns mathematics and music to support fractional reasoning. The three authors, guided by the theoretical framing of realistic mathematics education, engaged in a task design process over a 12-month period to develop integrated resources. Data were collected in…

Pedagogical content knowledge forms the core of teachers' professional knowledge; it refers to knowledge about making subject matter accessible to students. Thus, the formation of pedagogical content knowledge constitutes a crucial issue for educational research and practice. We investigated the contributions of content knowledge and pedagogical…

Interviews of fifth and sixth graders (n=120) found that they approached a task perceptually instead of reasoning with equivalent fractions, which they had studied in school. (Author/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)

Investigates validity of scores derived from the measurement procedure involving number lines by assessing its unique contributions to performance differences in criterion measures of rational number knowledge and skills, including fraction computation, application, and explanation. States that 205 fifth-grade and 208 sixth-grade students…

Describes an attempt to encourage fifth- and sixth-graders to invent their own ways of solving problems involving division with fractions. Emphasizes the importance of social interaction in Piaget's constructivism and explains why debate and verification are important for children's construction of logico-mathematical knowledge. (22 references)…

Two experiments explored the relationship between conceptual and procedural knowledge. Results revealed that fourth and sixth graders made computational errors even though they possessed conceptual knowledge. Fifth graders mastered conceptual knowledge before procedural knowledge. Results support the dynamic interaction theory. (BC)

This document is part 1 of the workbook for grade 6 pupils in the Comprehensive Instructional Management System, a unified mathematics curriculum for kindergarten through grade 7. Each objective is developed by a variety of strategies, with mastery of objectives diagnosed through a testing component. The activities in the student workbook are…

This document is part 2 of the workbook for grade 6 pupils in the Comprehensive Instructional Management System, a unified mathematics curriculum for kindergarten through grade 7. Each objective is developed by a variety of strategies, with mastery of objectives diagnosed through a testing component. The activities in the student workbook are…

This is part two of a two-part SMSG elementary school text for sixth-grade students. The content is aimed at the development of some of the fundamental concepts of mathematics such as number, numeration, the operations of arithmetic, and intuitive geometry. Chapter topics include division of rational numbers, volume, organizing and describing…

Examines the development of students' understandings about fractions during six weeks of instruction. Reports that all students possessed informal knowledge disconnected from their knowledge of fraction symbols and procedures and that knowledge of rote procedures often interfered with students' attempts to build on their informal knowledge.…

This is the teacher's manual to accompany part 1 of the workbook for grade 6 pupils in the Comprehensive Instructional Management System, a teacher-designed unified mathematics curriculum for kindergarten through grade 7. It is composed of a curriculum, a testing component, and a computer-managed reporting system. The curriculum is organized into…

This is the teacher's manual to accompany part 2 of the workbook for grade 6 pupils in the Comprehensive Instructional Management System, a teacher-designed unified mathematics curriculum for kindergarten through grade 7. It is composed of a curriculum, a testing component, and a computer-managed reporting system. The curriculum is organized into…

Presented is a detailed discussion of the performance pattern of third- and sixth-grade pupils in the Los Angeles Unified School District (LAUSD) for the skill area of fractional numbers. The report begins with a brief and general introduction regarding minimum competencies and continues with tables showing the performance levels of non-English…

These are some of the individual materials needed by students using the Comprehensive School Mathematics Program for the Intermediate Grades, Part VI. The book of "Worksheets" contains materials that are labeled with the same letter and number as the lessons with which they are to be used. The six "Collage of Problems" booklets…