Using R. S. Siegler's retrieval-required task, 19 male and 22 female third graders were examined before they had been introduced to multiplication in school. Examination of error patterns suggests that the basic assumptions of the distribution-of-associations model need to be tested directly and that the retrieval-required task confounds retrieved…

Describes four activities to analyze drinking water for its pH, hardness, turbidity, and conductivity. (MDH)

Eighty-seven elementary students in grades four, five, and six, were administered a 30-item multiplication instrument to assess performance in computation across grade levels. An interpretation of student performance using error ratio analysis is provided and the use of this method with groups of students for instructional decision making is…

Discusses important lessons on the mathematics of manufacturing and how curriculum content and teaching can prepare students for working. Features concepts such as the importance of spatial and geometric reasoning, problem solving, numbers and computation, and measurement. (ASK)

Presents ideas for an assessment that reflects the curriculum standards set forth by the National Council of Teachers of Mathematics (NCTM). Discusses how assessment tasks are created to support instruction that values a mastery of the basics, mental mathematics, mathematical vocabulary, problem solving and writing in mathematics, calculator…

Introduces a unit on data analysis which would not only satisfy elementary statistics requirements but also involve students in a long-term mathematics project in a meaningful and relevant way. Addresses the mathematical concepts of measurement, graphing, and computation. (ASK)

Presents a problem for grades 3-6 on number concepts and computation. Also provides guidelines for teachers to improve problem-solving practices in their classrooms. (ASK)

Presents results of a study of the development of early mathematical competence related to counting among young poor arithmetic achievers in the four- to seven-year age group. An Additional Early Mathematics program was offered to students scoring below a criterium with either guiding instruction or structured instruction. (Author/LRW)

Describes a fifth grade social studies unit on the concept of time. Explains that the unit focused on teaching about the terms century and millennium in order to help students understand that the true date of the new millennium is January 1, 2001. (CMK)

Two experiments investigated infants' sensitivity to amount of continuous quantity and to changes in amount of continuous quantity. Found that 6-month-olds looked significantly longer at a novel quantity than at the familiar quantity. Nine-month-olds looked significantly longer at an impossible event than at a possible event. Findings question…

This study investigated the developmental dynamics of mathematical performance during children's transition from preschool to Grade 2 and the cognitive antecedents of this development. 194 Finnish children were examined 6 times according to their math performance, twice during each year across a 3-year period. Cognitive antecedents, that is,…

This article extends and strengthens the knowledge in pieces perspective (diSessa, 1988, 1993) by applying core components to analyze how 5th-grade students with computational knowledge of whole-number multiplication and connections between multiplication and discrete arrays constructed understandings of area and ways of using representations to…

The authors extend the standard education production function and student time allocation analysis to focus on the interactions between student effort and performance over the semester. The purged instrumental variable technique is used to obtain consistent estimators of the structural parameters of the model using data from intermediate…

Three pieces of literature are used to launch mathematical investigations. The tasks provide opportunities for students to apply proportional reasoning skills, explore linear relationships, calculate a unit rate, and find the relationship between the volume of a cylinder and a cone. A poem, a short story, and a young adult novel are discussed.…

Spatial visualization is an important skill that deserves instructional attention. Strong evidence supports the claim that "measures of mathematical ability tend to be strongly correlated with spatial ability" (Anderson 2000). Thus, there is every reason to believe that time spent helping students develop their spatial visualization skills will…