Scaling Up the Implementation of a Pre-Kindergarten Mathematics Curriculum: Teaching for Understanding With Trajectories and Technologies

Abstract This study used a randomized field trial design to evaluate the efficacy of a research-based model for scaling up an intervention focused on preschool mathematics. Although the successes of research-based educational practices have been documented, equally well known is the paucity of successful efforts to bring these practices to scale. The same research corpus provides guidelines to scale up successful interventions. We designed an intervention model based on that research, including mathematics curricula with an emphasis on teaching for understanding following developmental guidelines, or learning trajectories, and using technology at multiple levels. We then implemented that model and evaluated the implementation with a limited scale up study. Within a design involving 25 classrooms serving children at risk for later school failure, we examined the impact of the model, using measures of fidelity of implementation, classroom observations of mathematics environment and teaching, and child outcomes. High levels of fidelity of implementation resulted in consistently higher scores in the intervention, compared to control, classes on the observation instrument and significantly and substantially greater gains in children's mathematics achievement in the intervention, compared to the control, children (effect size = .62).

[1]  L. Grossman,et al.  Eager to Learn: Educating Our Preschoolers , 2001 .

[2]  Leslie Rescorla,et al.  Academic Instruction in Early Childhood: Challenge or Pressure? , 1991 .

[3]  Liora Bresler,et al.  Implementation of Computer-Based Innovation: A Case Study. , 1990 .

[4]  Belinda Blevins-Knabe,et al.  Number Use at Home by Children and Their Parents and Its Relationship to Early Mathematical Performance , 1996 .

[5]  Julie Sarama.  Listening to Teachers: Planning for Professional Development , 2002 .

[6]  Diane Trister Dodge,et al.  The creative curriculum for early childhood , 1988 .

[7]  D. Clements.  Computers in Early Childhood Mathematics , 2002 .

[8]  Robert Balfanz,et al.  The Implementation and Impact of Evidence-Based Mathematics Reforms in High-Poverty Middle Schools: A Multi-Site, Multi-Year Study. , 2006 .

[9]  David Tyack,et al.  The “Grammar” of Schooling: Why Has it Been so Hard to Change? , 1994 .

[10]  M. Burchinal,et al.  Family and classroom correlates of head start children's developmental outcomes , 1994 .

[11]  L. Darling-Hammond.  The Right To Learn: A Blueprint for Creating Schools That Work. The Jossey-Bass Education Series. , 1997 .

[12]  K. Fuson,et al.  Advancing children's mathematical thinking in everyday mathematics classrooms , 1999 .

[13]  Joyce Kaser,et al.  Enhancing Program Quality in Science and Mathematics , 1999 .

[14]  R. Elmore.  Getting to Scale with Good Educational Practice , 1996 .

[15]  Michael Kalinowski,et al.  National Association for the Education of Young Children , 1991 .

[16]  J. Sarama,et al.  Effects of a Preschool Mathematics Curriculum: Summative Research on the Building Blocks Project , 2007 .

[17]  S. Raudenbush.  Statistical analysis and optimal design for cluster randomized trials , 1997 .

[18]  C. Ramey,et al.  Early intervention and early experience. , 1998, The American psychologist.

[19]  Herbert J. Walberg,et al.  Schooling Disadvantaged Children: Racing Against Catastrophe. , 1991 .

[20]  T. P. Carpenter,et al.  Using Knowledge of Children’s Mathematics Thinking in Classroom Teaching: An Experimental Study , 1989 .

[21]  Donna Hinkle,et al.  School Involvement in Early Childhood. , 2000 .

[22]  N. Vaidya,et al.  Science Teaching for the 21st Century , 2002 .

[23]  Alan Ginsburg,et al.  Reassessing U.S. International Mathematics Performance: New Findings from the 2003 TIMSS and PISA. , 2005 .

[24]  Robbie Case,et al.  Teaching for understanding: The importance of the central conceptual structures in the elementary mathematics curriculum. , 1995 .

[25]  Sheila Nataraj Kirby,et al.  Implementation and Performance in New American Schools: Three Years into Scale Up , 2001 .

[26]  Harold L. Schoen,et al.  Teacher Variables That Relate to Student Achievement When Using a Standards-Based Curriculum. , 2003 .

[27]  Julie Sarama,et al.  Network of Influences in an Implementation of a Mathematics Curriculum Innovation , 1998, Int. J. Comput. Math. Learn..

[28]  G. Resnick,et al.  Head Start FACES: Longitudinal Findings on Program Performance. Third Progress Report. , 2001 .

[29]  Douglas H. Clements,et al.  Linking research and curriculum development , 2008 .

[30]  Barbara Clarke,et al.  Mathematics teaching in grades K-2: painting a picture of challenging, supportive, and effective classrooms , 2004 .

[31]  Jacob Cohen.  Statistical Power Analysis for the Behavioral Sciences , 1969, The SAGE Encyclopedia of Research Design.

[32]  Geoffrey B. Saxe,et al.  Social processes in early number development. , 1987 .

[33]  Edwin W. Schreiber.  The National Council of Teachers of Mathematics , 1936 .

[34]  A. Sockloff,et al.  Statistical power analysis for the behavioral sciences: (revised edition), by Jacob Cohen. New York: Academic Press, 1977, xv + 474 pp., $24.50. , 1978 .

[35]  Ralph L. Rosnow,et al.  Essentials of Behavioral Research: Methods and Data Analysis , 1984 .

[36]  Douglas H. Clements,et al.  Development of a measure of early mathematics achievement using the Rasch model: the Research‐Based Early Maths Assessment , 2008 .

[37]  Arthur J. Baroody,et al.  Fostering Children's Mathematical Power: An Investigative Approach To K-8 Mathematics Instruction , 1998 .

[38]  Douglas H. Clements.  Training Effects on the Development and Generalization of Piagetian Logical Operations and Knowledge of Number , 1984 .

[39]  Douglas H. Clements,et al.  Design of Microworlds in Mathematics and Science Education , 2002 .

[40]  J. Hiebert.  Relationships between research and the NCTM standards , 1999 .

[41]  Susan C. Levine,et al.  Differential calculation abilities in young children from middle- and low-income families. , 1992 .

[42]  John W. Moore.  Teaching for Understanding , 2002 .

[43]  Karen C. Fuson,et al.  A Design Framework for Teaching, Learning Activities Supporting Latino First Graders' Ten-Structured Thinking in Urban Classrooms , 1996, ICLS.

[44]  B. Fuller,et al.  What is “appropriate practice” at home and in child care?: Low-income mothers' views on preparing their children for school☆ , 1995 .

[45]  Donald P. Ely,et al.  Conditions That Facilitate the Implementation of Educational Technology Innovations , 1990 .

[46]  Susanna W. Purnell,et al.  Lessons From New American Schools' Scale-Up Phase , 1998 .

[47]  Shirley M. Hord,et al.  Taking Charge of Change , 1987 .

[48]  Walter G. Secada.  Race, ethnicity, social class, language, and achievement in mathematics. , 1992 .

[49]  Geoffrey D. Borman,et al.  Comprehensive School Reform and Achievement: A Meta-Analysis , 2003 .

[50]  J. Sarama,et al.  Learning Trajectories in Mathematics Education , 2004 .

[51]  Michael Fullan,et al.  The Return of Large-Scale Reform , 2000 .

[52]  Herbert P. Ginsburg,et al.  Social Class and Racial Influences on Early Mathematical Thinking. , 1981 .