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Douglas H. Clements, Julie Sarama and Ann-Marie DiBiase

NCTM's Principles and Standards for School Mathematics (2000) addresses preschool mathematics education, which is a first for the NCTM's Standards documents. We celebrate this initial coverage but wonder whether Principles and Standards has enough detail for early childhood teachers and caregivers. We are concerned that although the document offers a good start, it might not provide sufficient guidelines. Without these guidelines, we face the danger that a wide variety of incoherent standards will be produced, some of which may be developmentally inappropriate. A lack of consistency across various standards and guidelines will continue to result in “mile wide and inch deep” curricula (National Center for Education Statistics 1996) as publishers struggle to meet a variety of different content standards and guidelines. Because we believe in the importance of supporting early communication and coordinating efforts among educational leaders and agencies, we held a national Conference on Standards for Preschool and Kindergarten Mathematics Education in May 2000, in Arlington, Virginia.

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Candace Joswick, Douglas H. Clements, Julie Sarama, Holland W. Banse and Crystal A. Day-Hess

Modify activities according to these principles and suggestions.

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Matthew E. Foster, Jason L. Anthony, Doug H. Clements, Julie Sarama and Jeffrey M. Williams

This study evaluated the effects of a mathematics software program, the Building Blocks software suite, on young children's mathematics performance. Participants included 247 Kindergartners from 37 classrooms in 9 schools located in low-income communities. Children within classrooms were randomly assigned to receive 21 weeks of computer-assisted instruction (CAI) in mathematics with Building Blocks or in literacy with Earobics Step 1. Children in the Building Blocks condition evidenced higher posttest scores on tests of numeracy and Applied Problems after controlling for beginning-of-year numeracy scores and classroom nesting. These findings, together with a review of earlier CAI, provide guidance for future work on CAI aiming to improve mathematics performance of children from low-income backgrounds.

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Douglas H. Clements, Michael T. Battista, Julie Sarama, Sudha Swaminathan and Sue McMillen

We investigated the development of linear measure concepts within an instructional unit on paths and lengths of paths, part of a large-scale curriculum development project funded by the National Science Foundation (NSF). We also studied the role of noncomputer and computer interactions in that development. Data from paper-and-pencil assessments, interviews, and case studies were collected within the context of a pilot test of this unit with 4 third graders and field tests with 2 thirdgrade classrooms. Three levels of strategies for solving length problems were observed: (a) apply general strategies such as visual guessing of measures and naive guessing of numbers or arithmetic operations; (b) draw hatch marks, dots, or line segments to partition lengths to serve as perceptible units to quantify the length; (c) no physical partitioning—use an abstract unit of length, a “conceptual ruler,” to project onto unsegmented objects. Those students who had connected numeric and spatial representations evinced different and more powerful problem-solving strategies in geometric situations than those who had forged fewer such connections.

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Douglas H. Clements, Julie Sarama, Mary Elaine Spitler, Alissa A. Lange and Christopher B. Wolfe

This study employed a cluster randomized trial design to evaluate the effectiveness of a research-based intervention for improving the mathematics education of very young children. This intervention includes the Building Blocks mathematics curriculum, which is structured in research-based learning trajectories, and congruous professional development emphasizing teaching for understanding via learning trajectories and technology. A total of 42 schools serving low-resource communities were randomly selected and randomly assigned to 3 treatment groups using a randomized block design involving 1,375 preschoolers in 106 classrooms. Teachers implemented the intervention with adequate fidelity. Pre- to posttest scores revealed that the children in the Building Blocks group learned more mathematics than the children in the control group (effect size, g = 0.72). Specific components of a measure of the quantity and quality of classroom mathematics environments and teaching partially mediated the treatment effect.

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Amanda L. Cullen, Cheryl L. Eames, Craig J. Cullen, Jeffrey E. Barrett, Julie Sarama, Douglas H. Clements and Douglas W. Van Dine

We examine the effects of 3 interventions designed to support Grades 2–5 children's growth in measuring rectangular regions in different ways. We employed the microgenetic method to observe and describe conceptual transitions and investigate how they may have been prompted by the interventions. We compared the interventions with respect to children's learning and then examined patterns in observable behaviors before and after transitions to more sophisticated levels of thinking according to a learning trajectory for area measurement. Our findings indicate that creating a complete record of the structure of the 2-dimensional array—by drawing organized rows and columns of equal-sized unit squares—best supported children in conceptualizing how units were built, organized, and coordinated, leading to improved performance.