Abstract
The fundamental question of whether preschool effects “fade” is hotly debated in arenas of theory, research, and policy. Few of these debates consider the role of transitions. Might it be that poor transitions are at least partly to blame? That is, if transitions are neglected, present educational contexts may be unintentionally aligned against the long-lasting impact of early interventions. We conducted a series of studies of an implementation of a scale-up model that evaluated the persistence of effects of a research-based model for scaling up. The largest of these research projects was explicitly based on the theory that fade-out of effects would be mitigated by attention to transitions. Results indicated that the intervention condition that included the model’s transition strategies maintained gains of the pre-K mathematics intervention better than the condition that did not include such strategies. However, more extensive and effective transition strategies should be developed and evaluated that expand on children’s learning in preschool and thereby completely close equity gaps in mathematics through the primary grades.
This research was supported by the Institute of Education Sciences, US Department of Education, through grants R305K05157 and R305A110188, and also by the National Science Foundation, through grants ESI-9730804 and REC-0228440. The opinions expressed are those of the authors and do not represent views of the IES or NSF. Although the research is concerned with the scale-up model, not particular curricula, a minor component of the intervention used in this research has been published by the authors, who thus could have a vested interest in the results. An external auditor oversaw the research design, data collection, and analysis, and other researchers independently confirmed findings and procedures. The authors wish to express appreciation to the school districts, teachers, and children who participated in this research. Address correspondence to Julie Sarama, University of Denver, Kennedy Institute and Educational Research, Policy & Practice Katherine A. Ruffatto Hall 224 1999 East Evans Avenue Denver CO 80208-1700.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
The reason for the quotation marks is that we believe there are ramifications of the use of the term “fade-out.” Although technically applied to the diminution of effect sizes, it is often interpreted as a loss of knowledge or skill or the evanescence of learning products or potential. This is consistent only with some theoretical interpretations and may be misinterpreted and misapplied to policy.
- 2.
The curricula used were an important component of the scale-up model and of the experiment, but this was a study of the TRIAD scale-up model, not only of a curriculum.
- 3.
To maintain focus, we do not describe all the ways that TRIAD’s guidelines were implemented, such as planning for the long term by starting with these schools for the research, but from the start scheduling counterfactual schools and any new teachers for professional development after the cohort of children had completed those grades.
References
ACF. (2010). Head Start impact study. Final report. Washington, DC: Office of Planning, Research and Evaluation, U.S. Department of Health and Human Services, Administration for Children and Families.
Agodini, R., & Harris, B. (2010). An experimental evaluation of four early elementary school math curricula. Journal of Research on Educational Effectiveness, 3, 199–253. https://doi.org/10.1080/19345741003770693
Akiba, M., LeTendre, G. K., & Scribner, J. P. (2007). Teacher quality, opportunity gap, and national achievement in 46 countries. Educational Researcher, 36, 369–387. https://doi.org/10.3102/0013189X07308739
Akkerman, S. F., & Baker, A. (2011). Boundary crossing and boundary objects. Review of Educational Research, 81(2), 132–169. https://doi.org/10.3102/0034654311404435
Atchison, B., Diffey, L., & Workman, E. (2016). K-3 policymakers' guide to action: Making the early years count. Retrieved from http://portal.criticalimpact.com/go.cfm?a=1&eid=0ed9acd27591255409e5cb74f1f037a9&c=25742&jid=0c3e88797c6eeaf6&d=45ba92c4d715b2443947229f28c3afba.
Aunola, K., Leskinen, E., Lerkkanen, M.-K., & Nurmi, J.-E. (2004). Developmental dynamics of math performance from pre-school to grade 2. Journal of Educational Psychology, 96, 699–713. https://doi.org/10.1037/0022-0663.96.4.699
Bailey, D. H., Watts, T. W., Littlefield, A. K., & Geary, D. C. (2014). State and trait effects on individual differences in children’s mathematical development. Psychological Science. https://doi.org/10.1177/0956797614547539
Ball, D. L., & Cohen, D. K. (1999). Instruction, capacity, and improvement. Philadelphia, PA: Consortium for Policy Research in Education, University of Pennsylvania.
Bennett, N., Desforges, C., Cockburn, A., & Wilkinson, B. (1984). The quality of pupil learning experiences. Hillsdale, NJ: Erlbaum.
Berends, M., Kirby, S. N., Naftel, S., & McKelvey, C. (2001). Implementation and performance in New American Schools: Three years into scale-up. Santa Monica, CA: Rand Education.
Bitler, M. P., Domina, T., & Hoynes, H. W. (2012). Experimental evidence on distributional effects of Head Start. Berkeley, CA: University of California, Berkeley.
Bodilly, S. J. (1998). Lessons from New American Schools’ scale-up phase. Santa Monica, CA: RAND Education.
Borman, G. D. (2007). Designing field trials of educational interventions. In B. Schneider & S.-K. McDonald (Eds.), Scale-up in education: Issues in practice (Vol. II, pp. 41–67). Lanham, MD: Rowman & Littlefield.
Borman, G. D., Hewes, G. M., Overman, L. T., & Brown, S. (2003). Comprehensive school reform and achievement: A meta-analysis. Review of Educational Research, 73, 125–230. https://doi.org/10.3102/00346543073002125
Bornfreund, L., McCann, C., Williams, C., & Guernsey, L. (2014). Beyond subprime learning: Accelerating progress in early education. Washington, DC: New America.
Boser, U., Wilhelm, M., & Hanna, R. (2014). Power of the Pygmalion effect: Teachers’ expectations strongly predict college completion. Washington, DC: Center for American Progress.
Bright, G. W., Bowman, A. H., & Vacc, N. N. (1997). Teachers’ frameworks for understanding children’s mathematical thinking. In E. Pehkonen (Ed.), Proceedings of the 21st conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 105–112). Lahti, Finland: University of Helsinki.
Broberg, A. G., Wessels, H., Lamb, M. E., & Hwang, C. P. (1997). Effects of day care on the development of cognitive abilities in 8-year-olds: A longitudinal study. Developmental Psychology, 33, 62–69. https://doi.org/10.1037//0012-1649.33.1.62
Brooks-Gunn, J. (2003). Do you believe in magic? What we can expect from early childhood intervention programs. Social Policy Report, 17(1), 1; 3–14.
Brown, A. L., & Campione, J. C. (1996). Psychological theory and the design of innovative learning environments: On procedures, principles, and systems. In R. Glaser (Ed.), Innovations in learning: New environments for education (pp. 289–325). Mahwah, NJ: Erlbaum.
Bryk, A. S., Sebring, P. B., Allensworth, E., Suppescu, S., & Easton, J. Q. (2010). Organizing schools for improvement: Lessons from Chicago. Chicago, IL: University of Chicago Press.
Carneiro, P., & Heckman, J. J. (2003). Human capital policy. In A. B. Krueger & J. J. Heckman (Eds.), Inequality in American: What role for human capital policies? (pp. 77–239). Cambridge, MA: MIT Press.
Carpenter, T. P., Fennema, E. H., Peterson, P. L., & Carey, D. A. (1988). Teacher’s pedagogical content knowledge of students’ problem solving in elementary arithmetic. Journal for Research in Mathematics Education, 19, 385–401.
Case, R., Griffin, S., & Kelly, W. M. (1999). Socioeconomic gradients in mathematical ability and their responsiveness to intervention during early childhood. In D. P. Keating & C. Hertzman (Eds.), Developmental health and the wealth of nations (pp. 125–149). New York, NY: Guilford.
CCSSO/NGA. (2010). Common core state standards. Washington, DC: Council of Chief State School Officers and the National Governors Association Center for Best Practices.
Chernoff, J. J., Flanagan, K. D., McPhee, C., & Park, J. (2007). Preschool: First findings from the third follow-up of the early childhood longitudinal study, birth cohort (ECLS-B) (NCES 2008-025). Washington, DC: National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education.
Claessens, A., & Garrett, R. (2014). The role of early childhood settings for 4–5 year old children in early academic skills and later achievement in Australia. Early Childhood Research Quarterly, 29(4), 550–561. https://doi.org/10.1016/j.ecresq.2014.06.006
Clarke, D. M., Cheeseman, J., Gervasoni, A., Gronn, D., Horne, M., McDonough, A.,… Rowley, G. (2002). Early Numeracy Research Project final report: Department of Education, Employment and Training, the Catholic Education Office (Melbourne), and the Association of Independent Schools Victoria.
Clements, D. H., & Sarama, J. (2004). Learning trajectories in mathematics education. Mathematical Thinking and Learning, 6, 81–89. https://doi.org/10.1207/s15327833mtl0602_1
Clements, D. H., & 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., & Sarama, J. (2007/2016). Building Blocks software [computer software]. Columbus, OH: McGraw-Hill Education.
Clements, D. H., & Sarama, J. (2008). Experimental evaluation of the effects of a research-based preschool mathematics curriculum. American Educational Research Journal, 45, 443–494. https://doi.org/10.3102/0002831207312908
Clements, D. H., & Sarama, J. (2009a). Learning and teaching early math: The learning trajectories approach. New York, NY: Routledge.
Clements, D. H., & Sarama, J. (2009b). Learning trajectories in early mathematics – Sequences of acquisition and teaching. In R. S. New & M. Cochran (Eds.), Encyclopedia of language and literacy development (pp. 1–6). London, ON: Canadian Language and Literacy Research Network.
Clements, D. H., & Sarama, J. (2011). Early childhood mathematics intervention. Science, 333(6045), 968–970. https://doi.org/10.1126/science.1204537
Clements, D. H., & Sarama, J. (2013). Building Blocks (Vol. 1 & 2). Columbus, OH: McGraw-Hill Education.
Clements, D. H., & Sarama, J. (2014). Learning and teaching early math: The learning trajectories approach (2nd ed.). New York, NY: Routledge.
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.
Clements, D. H., Sarama, J., Wolfe, C. B., & Spitler, M. E. (2013). Longitudinal evaluation of a scale-up model for teaching mathematics with trajectories and technologies: Persistence of effects in the third year. American Educational Research Journal, 50(4), 812–850. https://doi.org/10.3102/0002831212469270
Clements, D. H., Sarama, J., Wolfe, C. B., & Spitler, M. E. (2015). Sustainability of a scale-up intervention in early mathematics: Longitudinal evaluation of implementation fidelity. Early Education and Development, 26(3), 427–449. https://doi.org/10.1080/10409289.2015.968242
Clements, D. H., Sarama, J., Layzer, C., Unlu, F., Germeroth, C., & Fesler, L. (2018). Effects on executive function and mathematics learning of an early mathematics curriculum synthesized with scaffolded play designed to promote self-regulation versus the mathematics curriculum alone. Submitted for publication.
Clements, D. H., Fuson, K. C., & Sarama, J. (2017). The research-based balance in early childhood mathematics: A response to Common Core criticisms. Early Childhood Research Quarterly, 40, 150–162.
Cobb, P., McClain, K., de Silva, T., & Dean, C. (2003). Situating teachers’ instructional practices in the institutional setting of the school and district. Educational Researcher, 32(6), 13–24.
Coburn, C. E. (2003). Rethinking scale: Moving beyond numbers to deep and lasting change. Educational Researcher, 32(6), 3–12.
Cohen, D. K. (1996). Rewarding teachers for student performance. In S. H. Fuhrman & J. A. O'Day (Eds.), Rewards and reforms: Creating educational incentives that work (pp. 61–112). San Francisco, CA: Jossey Bass.
Cooper, H., Allen, A. B., Patall, E. A., & Dent, A. L. (2010). Effects of full-day kindergarten on academic achievement and social development. Review of Educational Research, 80(1), 34–70.
Darling-Hammond, L. (1996). Restructuring schools for high performance. In S. H. Fuhrman & J. A. O'Day (Eds.), Rewards and reform: Creating educational incentives that work (pp. 144–192). San Francisco: Jossey-Bass.
Darling-Hammond, L. (1997). The right to learn: A blueprint for creating schools that work. San Francisco: Jossey-Bass.
Duncan, G. J., Claessens, A., & Engel, M. (2004). The contributions of hard skills and socio-emotional behavior to school readiness. Evanston, IL: Northwestern University.
Elmore, R. F. (1996a). Getting to scale with good educational practices. In S. H. Fuhrman & J. A. O'Day (Eds.), Rewards and reform: Creating educational incentives that work (pp. 294–329). San Francisco: Jossey-Bass.
Elmore, R. F. (1996b). Getting to scale with good educational practices. Harvard Educational Review, 66, 1–25.
Engel, M., Claessens, A., & Finch, M. A. (2013). Teaching students what they already know? The (mis)alignment between mathematics instructional content and student knowledge in kindergarten. Educational Evaluation and Policy Analysis, 35(2), 157–178. https://doi.org/10.3102/0162373712461850
Fish, R. (2007). Relationship between education intensity in kindergarten and grade 1 and the academic benefits of attending preschool (Doctoral dissertation). Buffalo, NY: University of Buffalo, State University of New York.
Fullan, M. G. (2000). The return of large-scale reform. Journal of Educational Change, 1, 5–28.
Galindo, C., & Sonnenschein, S. (2015). Decreasing the SES math achievement gap: Initial math proficiency and home learning environments. Contemporary Educational Psychology, 43, 25–38. https://doi.org/10.1016/j.cedpsych.2015.08.003
Giles, C., & Hargreaves, A. (2006). The sustainability of innovative schools as learning organizations and professional learning communities during standardized reform. Educational Administrative Quarterly, 42(1), 124–156.
Glennan, T. K., Jr., Bodilly, S. J., Galegher, J. R., & Kerr, K. A. (Eds.). (2004). Expanding the reach of education reforms: Perspectives from leaders in the scale-up of educational interventions. Santa Monica, CA: RAND Corporation.
Gray, S. W., Ramsey, B. K., & Klaus, R. A. (1983). The early training project 1962–1980. In Consortium for Longitudinal Studies (Ed.), As the twig is bent… Lasting effects of preschool programs (pp. 33–69). Mahwah, NJ: Erlbaum.
Griffin, S., & Case, R. (1997). Re-thinking the primary school math curriculum: An approach based on cognitive science. Issues in Education, 3, 1–49.
Guskey, T. R. (Ed.). (2000). Evaluating professional development. Thousand Oaks, CA: Corwin Press.
Hall, G. E., & Hord, S. M. (2001). Implementing change: Patterns, principles, and potholes. Boston, MA: Allyn and Bacon.
Heatly, M. C., Bachman, H. J., & Votruba-Drzal, E. (2015). Developmental patterns in the associations between instructional practices and children’s math trajectories in elementary school. Journal of Applied Developmental Psychology, 41(6), 46–59. https://doi.org/10.1016/j.appdev.2015.06.002
Higgins, J., & Parsons, R. (2011). Professional learning opportunities in the classroom: Implications for scaling up system-level professional development in mathematics. Mathematics Teacher Education and Development, 13(1), 54–76.
Hill, C. J., Gormley, J. W. T., & Adelstein, S. (2015). Do the short-term effects of a high-quality preschool program persist? Early Childhood Research Quarterly, 32, 60–79.
Huberman, M. (1992). Critical introduction. In M. G. Fullan (Ed.), Successful school improvement (pp. 1–20). Philadelphia, PA: Open University Press.
Institute of Medicine (IOM) and National Research Council (NRC). (2015). Transforming the workforce for children birth through age 8: A unifying foundation. Washington, DC: National Academy Press.
Jackson, K., Cobb, P., Wilson, J., Webster, M., Dunlap, C., & Appelgate, M. (2014). Investigating the development of mathematics leaders’ capacity to support teachers’ learning on a large scale. ZDM. https://doi.org/10.1007/s11858-014-0652-5
Jacobs, V. R., Franke, M. L., Carpenter, T. P., Levi, L., & Battey, D. (2001). Professional development focused on children's algebraic reasoning in elementary school. Journal for Research in Mathematics Education, 38, 258–288.
Kaser, J. S., Bourexis, P. S., Loucks-Horsley, S., & Raizen, S. A. (1999). Enhancing program quality in science and mathematics. Thousand Oaks, CA: Corwin Press.
Klein, A., Starkey, P., Clements, D. H., Sarama, J., & Iyer, R. (2008). Effects of a pre-kindergarten mathematics intervention: A randomized experiment. Journal of Research on Educational Effectiveness, 1, 155–178.
Klingner, J. K., Ahwee, S., Pilonieta, P., & Menendez, R. (2003). Barriers and facilitators in scaling up research-based practices. Exceptional Children, 69, 411–429.
Leak, J., Duncan, G. J., Li, W., Magnuson, K., Schindler, H., & Yoshikawa, H. (2012). Is timing everything? How early childhood education program cognitive and achievement impacts vary by starting age, program duration and time since the end of the program. Irvine, CA: University of California, Irvine Department of Education.
Magnuson, K. A., & Waldfogel, J. (2005). Early childhood care and education: Effects on ethnic and racial gaps in school readiness. The Future of Children, 15, 169–196.
Magnuson, K. A., Meyers, M. K., Ruhm, C. J., & Waldfogel, J. (2004). Inequality in preschool education and school readiness. American Educational Research Journal, 41, 115–157.
Maloney, A. P., Confrey, J., & Nguyen, K. H. (Eds.). (2014). Learning over time: Learning trajectories in mathematics education. New York, NY: Information Age Publishing.
McDonald, S.-K., Keesler, V. A., Kauffman, N. J., & Schneider, B. (2006). Scaling-up exemplary interventions. Educational Researcher, 35(3), 15–24.
Moller, S., Stearns, E., Mickelson, R. A., Bottia, M. C., & Banerjee, N. (2014). Is academic engagement the panacea for achievement in mathematics across racial/ethnic groups? Assessing the role of teacher culture. Social Forces. https://doi.org/10.1093/sf/sou018
Mononen, R. (2014). Early mathematics interventions: Supporting young children with low performance in mathematics. Helsinki, Finland: University of Helsinki.
Montie, J. E., Xiang, Z., & Schweinhart, L. J. (2006). Preschool experience in 10 countries: Cognitive and language performance at age 7. Early Childhood Research Quarterly, 21, 313–331.
National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston, VA: Author.
National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, DC: U.S. Department of Education, Office of Planning, Evaluation and Policy Development.
National Research Council. (2001). Eager to learn: Educating our preschoolers. Washington, DC: National Academy Press.
National Research Council. (2009). Mathematics learning in early childhood: Paths toward excellence and equity. Washington, DC: National Academy Press.
Natriello, G., McDill, E. L., & Pallas, A. M. (1990). Schooling disadvantaged children: Racing against catastrophe. New York, NY: Teachers College Press.
Nyhan, P. (2015). The power of a good idea: How the San Francisco school district is building a prek – 3rd grade bridge. Washington, DC: New America.
O’Day, J. A., & Smith, M. S. (2016). Quality and equality in American education: Systemic problems, systemic solutions. In I. Kirsch & H. Braun (Eds.), The dynamics of opportunity in America (pp. 297–358).
Paris, S. G., Morrison, F. J., & Miller, K. F. (2006). Academic pathways from preschool through elementary school. In P. Alexander & P. Winne (Eds.), Handbook of research in educational psychology (pp. 61–85). Mahwah, NJ: Erlbaum.
Pellegrino, J. W. (2007). From early reading to high school mathematics: Matching case studies of four educational innovations against principles for effective scale up. In B. Schneider & S.-K. McDonald (Eds.), Scale up in practice (pp. 131–139). Lanham, MD: Rowman and Littlefield.
Phillips, D. A., Gormley, W. T., & Anderson, S. (2016). The effects of Tulsa's CAP Head Start program on middle-school academic outcomes and progress. Developmental Psychology, 52(8), 1247–1261. https://doi.org/10.1037/dev0000151
Pianta, R. C., Belsky, J., Vadergrift, N., Houts, R., & Morrison, F. J. (2008). Classroom effects on children’s achievement trajectories in elementary school. American Educational Research Journal, 45, 365–397.
Powell, S. R., Fuchs, L. S., & Fuchs, D. (2013). Reaching the mountaintop: Addressing the Common Core standards in mathematics for students with mathematical disabilities. Learning Disabilities Research & Practice, 28(1), 38–48. https://doi.org/10.1111/ldrp.12001
Preschool Curriculum Evaluation Research Consortium. (2008). Effects of preschool curriculum programs on school readiness (NCER 2008–2009). Retrieved from Washington, DC: http://ncer.ed.gov/.
Puma, M. J., Bell, S., Cook, R., Heid, C., Broene, P., Jenkins, F., … Downer, J. T. (2012). Third grade follow-up to the Head Start impact study final report, OPRE report # 2012-45. Washington, DC: Office of Planning, Research and Evaluation, Administration for Children and Families, U.S. Department of Health and Human Services.
Ramey, C. T., & Ramey, S. L. (1998). Early intervention and early experience. American Psychologist, 53, 109–120.
Raudenbush, S. W. (2008). Advancing educational policy by advancing research on instruction. American Educational Research Journal, 45, 206–230.
Raudenbush, S. W. (2009). The Brown legacy and the O’Connor challenge: Transforming schools in the images of children's potential. Educational Researcher, 38(3), 169–180.
Robertson, J. (2015, November 7). In Tulsa, a hot spot for early childhood education, the grade is ‘incomplete’. The Kansas City Star. Retrieved from http://www.kansascity.com/news/local/article43613463.html - storylink=cpy.
Rogers, E. M. (2003). Diffusion of innovations (5th ed.). New York, NY: The Free Press.
Salaschek, M., Zeuch, N., & Souvignier, E. (2014). Mathematics growth trajectories in first grade: Cumulative vs. compensatory patterns and the role of number sense. Learning and Individual Differences, 35, 103–112. https://doi.org/10.1016/j.lindif.2014.06.009
Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. New York, NY: Routledge.
Sarama, J., & DiBiase, A.-M. (2004). The professional development challenge in preschool mathematics. In D. H. Clements, J. Sarama, & A.-M. DiBiase (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education (pp. 415–446). Mahwah, NJ: Erlbaum.
Sarama, J., Clements, D. H., & Henry, J. J. (1998). Network of influences in an implementation of a mathematics curriculum innovation. International Journal of Computers for Mathematical Learning, 3, 113–148.
Sarama, J., Clements, D. H., Starkey, P., Klein, A., & Wakeley, A. (2008). Scaling up the implementation of a pre-kindergarten mathematics curriculum: Teaching for understanding with trajectories and technologies. Journal of Research on Educational Effectiveness, 1, 89–119. https://doi.org/10.1080/19345740801941332
Sarama, J., Clements, D. H., Wolfe, C. B., & 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. https://doi.org/10.1080/19345747.2011.627980
Schmidt, W. H., Wang, H. C., & McKnight, C. C. (2005). Curriculum coherence: An examination of US mathematics and science content standards from an international perspective. Journal of Curriculum Studies, 37(5), 525–559.
Schoen, H. L., Cebulla, K. J., Finn, K. F., & Fi, C. (2003). Teacher variables that relate to student achievement when using a standards-based curriculum. Journal for Research in Mathematics Education, 34(3), 228–259.
Showers, B., Joyce, B., & Bennett, B. (1987). Synthesis of research on staff development: A framework for future study and a state-of-the-art analysis. Educational Leadership, 45(3), 77–87.
Snipes, J., Doolittle, F., & Herlihy, C. (2002). Foundations for success: Case studies of how urban school systems improve student achievement. Washington, DC: Council of the Great City Schools.
Sowder, J. T. (2007). The mathematical education and development of teachers. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 1, pp. 157–223). New York, NY: Information Age Publishing.
Starkey, P., Klein, A., & Wakeley, A. (2004). Enhancing young children’s mathematical knowledge through a pre-kindergarten mathematics intervention. Early Childhood Research Quarterly, 19, 99–120.
Stevenson, H. W., & Newman, R. S. (1986). Long-term prediction of achievement and attitudes in mathematics and reading. Child Development, 57, 646–659.
Sztajn, P., Confrey, J., Wilson, P. H., & Edgington, C. (2012). Learning trajectory based instruction: Toward a theory of teaching. Educational Researcher, 41, 147–156. https://doi.org/10.3102/0013189X12442801
TERC. (2008). Investigations in number, data, and space (2nd ed.). Upper Saddle River, NJ: Pearson Scott Foresman.
Thomas, B. (1982). An abstract of kindergarten teachers’ elicitation and utilization of children's prior knowledge in the teaching of shape concepts: Unpublished manuscript, School of Education, Health, Nursing, and Arts Professions, New York University.
Turner, R. C., & Ritter, G. W. (2004, April). Does the impact of preschool childcare on cognition and behavior persist throughout the elementary years? Paper presented at the American Educational Research Association, San Diego, CA.
Turner, R. C., Ritter, G. W., Robertson, A. H., & Featherston, L. (2006, April). Does the impact of preschool child care on cognition and behavior persist throughout the elementary years? Paper presented at the American Educational Research Association, San Francisco, CA.
U.S. Department of Education. (2016). Case studies of schools implementing early elementary strategies: Preschool through third grade alignment and differentiated instruction. Retrieved from Washington, DC: http://www2.ed.gov/rschstat/eval/implementing-early-strategies/report.pdf?utm_content=&utm_medium=email&utm_name=&utm_source=govdelivery&utm_term=.
Westat, & Policy Studies Associates. (2001). The longitudinal evaluation of school change and performance (LESCP) in Title I schools: Final report. Washington, DC: U.S. Department of Education, Office of the Deputy Secretary, Planning and Evaluation Service.
Wilson, P. H., Mojica, G. F., & Confrey, J. (2013). Learning trajectories in teacher education: Supporting teachers’ understandings of students’ mathematical thinking. The Journal of Mathematical Behavior, 32(2), 103–121. https://doi.org/10.1016/j.jmathb.2012.12.003
Wilson, P. H., Sztajn, P., Edgington, C., & Myers, M. (2015). Teachers’ uses of a learning trajectory in student-centered instructional practices. Journal of Teacher Education, 66(3), 227–244. https://doi.org/10.1177/0022487115574104
Wood, K., & Frid, S. (2005). Early childhood numeracy in a multiage setting. Mathematics Education Research Journal, 16(3), 80–99.
Wright, R. J., Martland, J., Stafford, A. K., & Stanger, G. (2002). Teaching number: Advancing children’s skills and strategies. London, ON: Paul Chapman/Russell Sage.
Yuzawa, M., Bart, W. M., Kinne, L. J., Sukemune, S., & Kataoka, M. (1999). The effects of “origami” practice on size comparison strategy among young Japanese and American children. Journal of Research in Childhood Education, 13(2), 133–143. https://doi.org/10.1080/02568549909594734
Zaslow, M. J., Tout, K., Halle, T. G., Vick, J., & Lavelle, B. (2010). Towards the identification of features of effective professional development for early childhood educators: A review of the literature. Retrieved from Washington, DC: http://www2.ed.gov/rschstat/eval/professional-development/literature-review.pdf.
Zhai, F., Raver, C. C., & Jones, S. M. (2012). Academic performance of subsequent schools and impacts of early interventions: Evidence from a randomized controlled trial in Head Start settings. Children and Youth Services Review, 34(5), 946–954.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Sarama, J., Clements, D.H. (2018). Promoting Positive Transitions Through Coherent Instruction, Assessment, and Professional Development: The TRIAD Scale-Up Model. In: Mashburn, A., LoCasale-Crouch, J., Pears, K. (eds) Kindergarten Transition and Readiness . Springer, Cham. https://doi.org/10.1007/978-3-319-90200-5_15
Download citation
DOI: https://doi.org/10.1007/978-3-319-90200-5_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-90199-2
Online ISBN: 978-3-319-90200-5
eBook Packages: Behavioral Science and PsychologyBehavioral Science and Psychology (R0)