Scaling Up TRIAD: Teaching Early Mathematics for Understanding with Trajectories and Technologies
Co-Principal Investigators: Sarama, Julie; Lee, J.; Lipsey, Mark; Farran, Dale
Purpose: In this project, the research team evaluated a large-scale implementation of the TRIAD mathematics intervention in both diverse geographical areas and student populations. Prior research showed that focused pre-K math interventions improved student learning in math under limited conditions, but no large-scale research had been done at the time of the project.
THE FOLLOWING CONTENT DESCRIBES THE PROJECT AT THE TIME OF FUNDING
Setting: One-hundred and twenty pre-K classes located in New York State, Boston, and Nashville. In New York State, 60 pre-K classes will be selected from 31 schools in 4 systems. These four selected preschool systems include both public and private pre-K programs. In Boston, the sample will include 41 pre-K sites. In Nashville, the sample will include 61 classrooms from 20 schools.
Sample: Participants will be 120 teachers and 1440 children in the New York, Boston, and Nashville area. From each pre-K classroom, 12 children who will soon be entering kindergarten will be randomly selected for assessment, and they will be followed through grade 1. The schools serve low-achieving populations, but their settings and racial/ethnic compositions are diverse. In the New York sites, approximately 83 percent of students are White and 17 percent minority. Free or reduced-price lunch rates range from 74 percent to 99 percent. In Boston, the sites serve mostly African-American (46 percent) and Hispanic (31 percent) children, about 1/3rd of whom have limited English proficiency and approximately 74 percent of whom receive public assistance.
Intervention: The TRIAD intervention is predicted to increase math achievement in young children, especially those at risk, by means of a high-quality implementation of the Building Blocks math curriculum, with all aspects of the curriculum based on a common core of learning trajectories through which children develop. Building Blocks is a research-based mathematics curriculum that addresses (a) geometric and spatial skills and (b) numeric and quantitative ideas and skills. The approach of Building Blocks is finding the mathematics in, and developing mathematics from, children's activity. Off-and on-computer activities are designed based on children's experiences and interests, with an emphasis on supporting the development of math activity. TRIAD not only provides these curriculum materials, but also professional development. Professional development includes distance education, an innovative TRIAD-website that supports teaching based on learning trajectories, and classroom coaching.
Research Design and Methods: The researchers will use a multisite cluster randomized experimental design that enables a formal test of the generalizability of TRIAD's impact over the varied settings in which it may ultimately be implemented. Schools will be randomly assigned within districts to one of three conditions: Control, experimental, and experimental with follow-through. In the follow-through experimental group, teachers in grades K and 1 will be taught about the preschool intervention and ways to build upon it. Teachers will participate in a credit-bearing professional development course with five components: (a) a 5-day institute in the summer and 2-day follow up after the winter break, (b) 3-hour classes after school once per month, (c) out of class assignments, (d) electronic communications, and (e) coaching and mentoring within each teacher's classroom. Fidelity of implementation will be assessed by means of two observational instruments.
Control Condition: Participants in the control condition will receive their existing classroom curriculum (practice-as-usual).
Key Measures: Standardized, experimenter-designed, and observational measures of children's mathematical knowledge, language development, and teacher classroom practices will be employed.
Data Analytic Strategy: Hierarchical linear models (HLMs) will be employed to examine the effects of the intervention on individual students' mathematics performance trajectories and account for possible variations of the effects among varied school/classroom settings.
Related IES Projects: Longitudinal Study of a Successful Scaling-Up Project: Extending TRIAD(R305A120813); Contributions to Mathematics Competency of At-Risk Students: The Impact of Executive Function,Approximate Number System, and Early Mathematics Skills(R305A140126); Evaluating the Efficacy of Learning Trajectories in Early Mathematics(R305A150243); The Evolution of Learning Strategies as Indicators of Intervention Efficacy(R305A200100); Integrated, Intelligent, and Interactive Technologies Building Young Children's Math Along Learning Trajectories(R305A220102)
ERIC Citations: Find available citations in ERIC for this award here.
Clements, D. H., & Sarama, J. (2008). Experimental evaluation of the effects of a research-based preschool mathematics curriculum. American educational research journal, 45(2), 443-494. [WWC Review]
Clements, D. H., Sarama, J., Spitler, M. E., Lange, A. A., & Wolfe, C. B. (2011). Mathematics learned by young children in an intervention based on learning trajectories: A large-scale cluster randomized trial. Journal for Research in Mathematics Education, 42(2), 127-166. [WWC Review]
Clements, D.H., and Sarama, J. (2009). Learning and Teaching Early Math: The Learning Trajectories Approach.New York: Routledge.
Clements, D.H. (2008). Linking Research and Curriculum Development. In L.D. English (Ed.), Handbook of International Research in Mathematics Education (2nd ed., pp. 589–625). New York: Taylor and Francis.
Clements, D.H., and Sarama, J. (2007). Curriculum, Technology. In R.S. New, and M. Cochran (Eds.), Early Childhood Education: An International Encyclopedia, Volume 1 (pp. 221–225). Westport, CT: Praeger.
Clements, D.H., and Sarama, J. (2007). Early Childhood Mathematics Learning. In F.K. Lester, Jr. (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 461–555). New York: Information Age Publishing.
Clements, D.H., and Sarama, J. (2007). Fool's Gold? Critical Remarks About the Critics From the Alliance for Childhood (Gold Der Narren?—Fools's Gold?—Kritische Bemerkungen Zur Kritik Der Alliance for Childhood Et Al.). In H. Mitzlaff (Ed.), Internationales Handbuch: Computer (ICT), Grundschule, Kindeergarten and Neue Lernkultur, Volume 2 (pp. 740–748). Baltmannsweiler, Germany: Schneider Verlag Hohengehren.
Clements, D.H., and Sarama, J. (2007). Mathematics. In R.S. New, and M. Cochran (Eds.), Early Childhood Education: An International Encyclopedia, Volume 2 (pp. 502–509). Westport, CT: Praeger.
Clements, D.H., and Sarama, J. (2007). The Role of Computers in American Kindergartens and Primary Schools: The Building Blocks for Early Childhood Mathematics Project. In H. Mitzlaff (Ed.), Internationales Handbuch: Computer (ICT), Grundschule, Kindeergarten and Neue Lernkultur, Volume 2 (pp. 538–546). Baltmannsweiler, Germany: Schneider Verlag Hohengehren.
Clements, D.H., and Sarama, J. (2007). Using Computers in American Kindergartens and Primary Schools: An Interim Report (Einsatz Von Computern in Amerikanischen Vor- Und Grundschulen — En Zwischenbericht). In H. Mitzlaff (Ed.), Internationales Handbuch: Computer (ICT), Grundschule, Kindeergarten and Neue Lernkultur, Volume 1 (pp. 251–259). Baltmannsweiler, Germany: Schneider Verlag Hohengehren.
Clements, D.H., and Sarama, J. (2008). Mathematics and Technology: Supporting Learning for Students and Teachers. In O.N. Saracho, and B. Spodek (Eds.), Contemporary Perspectives on Science and Technology in Early Childhood Education (pp. 127–147). Charlotte, NC: Information Age Publishing, Inc.
Clements, D.H., Sarama, J., Yelland, N.J., and Glass, B. (2008). Learning and Teaching Geometry With Computers in the Elementary and Middle School. In M.K. Heid, and G.W. Blume (Eds.), Research on Technology and the Teaching and Learning of Mathematics: Volume 1: Research Syntheses (pp. 109–154). New York: Information Age Publishing, Inc.
Brown, C.S., Sarama, J., and Clements, D.H. (2007). Thinking About Learning Trajectories in Preschool. Teaching Children Mathematics, 14(3): 178–181.
Clements, D.H. (2007). Curriculum Research: Toward a Framework for 'Research-Based Curricula'. Journal for Research in Mathematics Education, 38(1): 35–70.
Clements, D.H., and Sarama, J. (2007). Effects of a Preschool Mathematics Curriculum: Summative Research on the Building Blocks Project. Journal for Research in Mathematics Education, 38(2): 136–163.
Clements, D.H., and Sarama, J. (2008). Experimental Evaluation of the Effects of a Research-Based Preschool Mathematics Curriculum. American Educational Research Journal, 45(2): 443–
Clements, D.H., and Sarama, J. (2011). Early Childhood Teacher Education: The Case of Geometry. Journal of Mathematics Teacher Education, 14(2): 133–148.
Clements, D.H., and Sarama, J. (2011). Early Childhood Mathematics Intervention. Science, 333(6045): 968–970.
Clements, D.H., Sarama, J., and Liu, X. (2008). Development of a Measure of Early Mathematics Achievement Using the Rasch Model: The Research-Based Early Maths Assessment. Educational Psychology, 28(4): 457–482.
Clements, D.H., Sarama, J., Spitler, M.E., Lange, A.A., and Wolfe, C.B. (2011). Mathematics Learned by Young Children in an Intervention Based on Learning Trajectories: A Large-Scale Cluster Randomized Trial. Journal for Research in Mathematics Education, 42(2): 127–166.
Sarama, J., and Clements, D.H. (2006). Mathematics, Young Students, and Computers: Software, Teaching Strategies and Professional Development. Mathematics Educator, 9(2): 112–134.
Sarama, J., and Clements, D.H. (2008). Building Blocks and Cognitive Building Blocks; Playing to Know the World Mathematically. American Journal of Play, 1: 313–337.
Sarama, J., and Clements, D.H. (2009). Teaching Math in the Primary Grades: The Learning Trajectories Approach. Young Children, 64(2): 63–65.
Sarama, J., Clements, D.H., Lange, A., and Wolfe, C.B. (2012). The Impacts of an Early Mathematics Curriculum on Oral Language and Literacy. Early Childhood Research Quarterly, 27(3): 489–502.
Sarama, J., Clements, D.H., Wolfe, C.B., and Spitler, M.E. (2012). Longitudinal Evaluation of a Scale-Up Model for Teaching Mathematics With Trajectories and Technologies. Journal of Research on Educational Effectiveness, 5(2): 105–135.
Weiland, C., Wolfe, C.B., Hurwitz, M.D., Clements, D.H., Sarama, J., and Yoshikawae, H. (2012). Early Mathematics Assessment: Validation of the Short Form of a Pre-Kindergarten and Kindergarten Mathematics Measure. Educational Psychology, 32(3): 311–333.