Examines 250 sixth-grade students' understanding of arithmetic average by assessing their understanding of the computational algorithm. Results indicate that the majority of the students knew the "add-them-all-up-and-divide" averaging algorithm, but only half of the students were able to correctly apply the algorithm to solve a…

The hypothesis investigated is that understanding of the long division algorithm requires a higher cognitive level than understanding of fundamental division concepts. Sixth-grade children were tested on performance and understanding of a given algorithm and concepts of division. (MP)

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)…

This study investigated the relationship between the level of conservation of displaced volume and the degree to which sixth graders learn the volume algorithm of a cuboid, i.e., volume = length x width x height (v = l x w x h). The problem is a consequence of an apparent discrepancy between the present school programs and the theory of Piaget…

Two questions were investigated in this study: (1) How did the computational proficiency of sixth graders who had one year's experience with Developing Mathematical Processes (DMP) materials compare with an equivalent group of students who used the usual textbook program; and (2) What occurs when sixth graders study algorithms as sequences of rule…

The "modern mathematics" curriculum places considerably more emphasis on the use of precise terminology when referring to properties of whole numbers than did previous curricula. The relationship between the ability to make these verbal associations and other aspects of mathematics achievement of sixth graders is investigated in this study A…

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…

This two-volume teacher's guide is to be used with a second-semester, sixth-grade mathematics program. The manner of presentation and the pedagogical ideas and tools are based on the works of Georges and Frederique Papy. They are recognized as having introduced colored arrow drawings ("papygrams") and models of our numeration system (the…

This study was designed to investigate the relationship between the level of conservation of displaced volume and the degree to which sixth-grade children learn the volume algorithm of a cuboid, namely, volume equals weight times length times height. The problem chosen is based on an apparent discrepancy between the present school programs and…