Skip to main content
SpringerLink
Log in
Book cover

Mathematics and Transition to School pp 153–169Cite as

Scaling Up Early Mathematics Interventions: Transitioning with Trajectories and Technologies

  • Chapter
  • First Online:

Part of the book series: Early Mathematics Learning and Development ((EMLD))

Abstract

Transitions in the early years have substantial effects on children’s success in school. Moreover, lack of consideration of continuity and alignment may mislead both researchers and politicians to assume preschool effects ‘fade’, when it may be that poor transitions to primary school are to blame. We hypothesise that most present educational contexts are unintentionally and perversely aligned against early interventions. For example, primary curricula assume little mathematical competence, so only low-level skills are taught. Most teachers are required to follow such curricula rigidly and remain unaware that some of their students have already mastered the material they are about to ‘teach’. Teachers may be held accountable for getting the largest number of students to pass minimal competency assessments, engendering the belief that higher performing students are ‘doing fine’. In this way, we believe the present U.S. educational system unintentionally but insidiously re-opens the gap between students from low- and higher-resource communities. We conducted a large cluster randomised trial of an intervention that evaluated the persistence of effects of a research-based model for scaling up educational interventions, with one control and two intervention conditions. Only the intervention condition that included a follow-through treatment to support the transition to the primary grades maintained substantial gains of the pre-K mathematics curriculum.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

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.

    Google Scholar 

  • Alexander, K. L., & Entwisle, D. R. (1988). Achievement in the first 2 years of school: Patterns and processes. Monographs of the Society for Research in Child Development, 53(2, Serial No. 157), 1–157.

    Article  Google Scholar 

  • 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. doi:10.1037/0022-0663.96.4.699.

    Article  Google Scholar 

  • Bennett, N., Desforges, C., Cockburn, A., & Wilkinson, B. (1984). The quality of pupil learning experiences. Hillsdale: Erlbaum.

    Google Scholar 

  • Berends, M., Kirby, S. N., Naftel, S., & McKelvey, C. (2001). Implementation and performance in New American Schools: Three years into scale-up. Santa Monica: RAND Education.

    Google Scholar 

  • Bobis, J., Clarke, B. A., Clarke, D. M., Gould, P., Thomas, G., Wright, R., & Young-Loveridge, J. (2005). Supporting teachers in the development of young children’s mathematical thinking: Three large scale cases. Mathematics Education Research Journal, 16(3), 27–57.

    Article  Google Scholar 

  • Bodilly, S. J. (1998). Lessons from New American Schools’ scale-up phase. Santa Monica: RAND Education.

    Google Scholar 

  • 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. doi:10.3102/00346543073002125.

    Article  Google Scholar 

  • 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: Erlbaum.

    Google Scholar 

  • Bryk, A. S., Sebring, P. B., Allensworth, E., Suppescu, S., & Easton, J. Q. (2010). Organizing schools for improvement: Lessons from Chicago. Chicago: University of Chicago Press.

    Google Scholar 

  • 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.

    Google Scholar 

  • Clarke, D. (1994). Ten key principles from research for the professional development of mathematics teachers. In D. B. Aichele & A. F. Coxford (Eds.), Professional development for teachers of mathematics (pp. 37–48). Reston: National Council of Teachers of Mathematics.

    Google Scholar 

  • Clarke, D., Cheeseman, J., Gervasoni, A., Gronn, D., Horne, M., McDonough, A., Montgomery, P., Roche, A., Sullivan, P., Clarke, B., & Rowley, G. (2002). Early numeracy research project final report. Melbourne: Mathematics Teaching and Learning Centre, Australian Catholic University.

    Google Scholar 

  • Clements, D. H. (2007). Curriculum research: Toward a framework for ‘research-based curricula’. Journal for Research in Mathematics Education, 38, 35–70.

    Google Scholar 

  • Clements, D. H., & Sarama, J. (2004). Learning trajectories in mathematics education. Mathematical Thinking and Learning, 6, 81–89. doi:10.1207/s15327833mtl0602_1.

    Article  Google Scholar 

  • 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, 136–163.

    Google Scholar 

  • Clements, D. H., & Sarama, J. (2007/2012). Building blocks software. Columbus: SRA/McGraw-Hill.

    Google Scholar 

  • Clements, D. H., & Sarama, J. (2013). Building blocks (Vols. 1 and 2). Columbus: McGraw-Hill.

    Google Scholar 

  • Clements, D. H., & Sarama, J. (2014). Learning and teaching early math: The learning trajectories approach (2nd ed.). New York: Routledge.

    Google Scholar 

  • Clements, D. H., Sarama, J., & DiBiase, A.-M. (2004). Engaging young children in mathematics: Standards for early childhood mathematics education. Mahwah: Erlbaum.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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. doi:10.3102/0002831212469270.

    Article  Google Scholar 

  • Duncan, G. J., Claessens, A., & Engel, M. (2004). The contributions of hard skills and socio-emotional behavior to school readiness. Evanston: Northwestern University

    Google Scholar 

  • Duncan, G. J., & Magnuson, K. (2011). The nature and impact of early achievement skills, attention skills, and behavior problems. In G. J. Duncan & R. Murnane (Eds.), Whither opportunity? Rising inequality and the uncertain life chances of low-income children (pp. 47–70). New York: Russell Sage.

    Google Scholar 

  • Elmore, R. F. (1996). Getting to scale with good educational practices. Harvard Educational Review, 66, 1–25.

    Google Scholar 

  • Engel, M., Claessens, A., & Finch, M. (in press). Teaching students what they already know? The misalignment between mathematics instructional content and student knowledge in kindergarten. Educational Evaluation and Policy Analysis.

    Google Scholar 

  • Fish, R. (2003). Effects of attending prekindergarten on academic achievement. Unpublished Masters’ Thesis, University of Buffalo, State University of New York, Buffalo, NY.

    Google Scholar 

  • Fryer, J., & Levitt, S.D. (2004). Understanding the black-white test score gap in the first two years of school. The Review of Economics and Statistics, 86, 447–464.

    Article  Google Scholar 

  • Hall, G. E., & Hord, S. M. (2001). Implementing change: Patterns, principles, and potholes. Boston: Allyn and Bacon.

    Google Scholar 

  • Huberman, M. (1992). Critical introduction. In M. G. Fullan (Ed.), Successful school improvement (pp. 1–20). Philadelphia: Open University Press.

    Google Scholar 

  • Jackson, K. (2011). Exploring relationships between mathematics teachers’ views of students’ mathematical capabilities, visions of instruction, and instructional practices. Paper presented at the American Educational Research Association, New Orleans, LA, April 2008.

    Google Scholar 

  • 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.

    Google Scholar 

  • Kaser, J. S., Bourexis, P. S., Loucks-Horsley, S., & Raizen, S. A. (1999). Enhancing program quality in science and mathematics. Thousand Oaks: Corwin.

    Google Scholar 

  • 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: University of California, Irvine Department of Education.

    Google Scholar 

  • MacDonald, A., Davies, N., Dockett, S., & Perry, B. (2012). Early childhood mathematics education. In B. Perry, T. Lowrie, T. Logan, A. MacDonald, & J. Greenlees (Eds.), Research in mathematics education in Australasia: 2008–2011 (pp. 169–192). Rotterdam: Sense.

    Google Scholar 

  • Mullis, I. V. S., Martin, M. O., Foy, P., & Arora, A. (2012). TIMSS 2011 international results in Mathematics. Chestnut Hill: TIMSS & PIRLS International Study Center, Boston College.

    Google Scholar 

  • 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.

    Google Scholar 

  • National Research Council. (2009). Mathematics in early childhood: Learning paths toward excellence and equity. Washington, DC: National Academy Press.

    Google Scholar 

  • Natriello, G., McDill, E. L., & Pallas, A. M. (1990). Schooling disadvantaged children: Racing against catastrophe. New York: Teachers College Press.

    Google Scholar 

  • Perry, B. (2010). Mathematical thinking of preschool children in rural and regional Australia: An overview. Journal of Australian Research in Early Childhood Education, 16(2), 1–12.

    Google Scholar 

  • Perry, B., Young-Loveridge, J. M., Dockett, S., & Doig, B. (2008). The development of young children’s mathematical understanding. In H. Forgasz, A. Barkatsas, A. Bishop, B. A. Clarke, S. Keast, W. T. Seah, et al. (Eds.), Research in mathematics education in Australasia 2004–2007 (pp. 17–40). Rotterdam: Sense.

    Google Scholar 

  • Perry, B., Dockett, S., & Harley, E. (2012a). The early years learning framework for Australia and the Australian curriculum—Mathematics: Linking educators’ practice through pedagogical inquiry questions. In B. Atweh, M. Goos, R. Jorgensen, & D. Siemon (Eds.), Engaging the Australian curriculum Mathematics: Perspectives from the field (pp. 153–174). Adelaide: Mathematics Education Research Group of Australasia.

    Google Scholar 

  • Perry, B., Lowrie, T., Logan, T., MacDonald, A., & Greenlees, J. (2012b). Research in mathematics education in Australasia: 2008–2011. Rotterdam: Sense.

    Google Scholar 

  • Pianta, R. C., Howes, C., Burchinal, M. R., Bryant, D., Clifford, R. M., Early, D. M., & et al. (2005). Features of pre-kindergarten programs, classrooms, and teachers: Do they predict observed classroom quality and child–teacher interactions? Applied Developmental Science, 9, 144–159.

    Article  Google Scholar 

  • Preschool Curriculum Evaluation Research Consortium. (2008). Effects of preschool curriculum programs on school readiness (NCER 2008–2009). Washington, DC: Government Printing Office.

    Google Scholar 

  • Ramey, C. T., & Ramey, S. L. (1998). Early intervention and early experience. American Psychologist, 53, 109–120.

    Article  Google Scholar 

  • Raudenbush, S. W. (2008). Advancing educational policy by advancing research on instruction. American Educational Research Journal, 45, 206–230.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Rogers, E. M. (2003). Diffusion of innovations (5th ed.). New York: The Free Press.

    Google Scholar 

  • Sanders, W. L., & Horn, S. P. (1998). Research findings from the Tennessee Value-Added Assessment System (TVAAS) database: Implications for educational evaluation and research. Journal of Personnel Evaluation in Education, 12(3), 247–256.

    Article  Google Scholar 

  • Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. New York: Routledge.

    Google Scholar 

  • Sarama, J., & Clements, D. H. (2013). Lessons learned in the implementation of the TRIAD scale-up model: Teaching early mathematics with trajectories and technologies. In T. G. Halle, A. J. Metz, & I. Martinez-Beck (Eds.), Applying implementation science in early childhood programs and systems (pp. 173–191). Baltimore: Brookes.

    Google Scholar 

  • Sarama, J., Clements, D. H., & Vukelic, E. B. (1996). The role of a computer manipulative in fostering specific psychological/mathematical processes. In E. Jakubowski, D. Watkins, & H. Biske (Eds.), Proceedings of the 18th annual meeting of the North America chapter of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 567–572). Columbus: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Sarama, J., Clements, D. H., Wolfe, C. B., & Spitler, M. E. (2012a). Longitudinal evaluation of a scale-up model for teaching mathematics with trajectories and technologies. Journal of Research on Educational Effectiveness, 5(2), 105–135.

    Article  Google Scholar 

  • Sarama, J., Lange, A., Clements, D. H., & Wolfe, C. B. (2012b). The impacts of an early mathematics curriculum on emerging literacy and language. Early Childhood Research Quarterly, 27, 489–502. doi:10.1016/j.ecresq.2011.12.002.

    Article  Google Scholar 

  • Thomson, S., Rowe, K., Underwood, C., & Peck, R. (2005). Numeracy in the early years: Project good start. Camberwell: Australian Council for Educational Research.

    Google Scholar 

  • Trinick, T., & Stevenson, B. (2009). Longitudinal patterns of performance: Te Poutama Tau. In Ministry of Education (Ed.), Findings from the New Zealand numeracy development projects 2008 (pp. 27–38). Wellington: Learning Media.

    Google Scholar 

  • Turner, R. C., & Ritter, G. W. (2004). Does the impact of preschool childcare on cognition and behavior persist throughout the elementary years? Paper presented to the American Educational Research Association annual meeting, San Diego, CA.

    Google Scholar 

  • van den Heuvel-Panhuizen, M. (1996). Assessment and realistic mathematics education. Utrecht: Freudenthal Institute, Utrecht University.

    Google Scholar 

  • Wright, B. (1991). What number knowledge is possessed by children beginning the kindergarten year of school? Mathematics Education Research Journal, 3(1), 1–16.

    Article  Google Scholar 

  • Wright, S. P., Horn, S. P., & Sanders, W. L. (1997). Teacher and classroom context effects on student achievement: Implications for teacher evaluation. Journal of Personnel Evaluation in Education, 11, 57–67.

    Article  Google Scholar 

  • Wylie, C., Hodgen, E., Hipkins, R., & Vaughan, K. (2009). Competent learners on the edge of adulthood. A summary of key findings from the competent learners @16 project. Wellington: Ministry of Education.

    Google Scholar 

Download references

Acknowledgements

This research was supported by the Institute of Education Sciences, U.S. 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 students 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.

Author information

Authors and Affiliations

  1. University of Denver, Denver, USA

    Julie Sarama & Douglas H. Clements

Authors
  1. Julie Sarama
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Douglas H. Clements
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Julie Sarama .

Editor information

Editors and Affiliations

  1. School of Education, Charles Sturt University, Albury, New South Wales, Australia

    Bob Perry

  2. School of Education, Charles Sturt University, Albury, New South Wales, Australia

    Amy MacDonald

  3. Faculty of Education, Monash University, Melbourne, Victoria, Australia

    Ann Gervasoni

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer Science+Business Media Singapore

About this chapter

Cite this chapter

Sarama, J., Clements, D. (2015). Scaling Up Early Mathematics Interventions: Transitioning with Trajectories and Technologies. In: Perry, B., MacDonald, A., Gervasoni, A. (eds) Mathematics and Transition to School. Early Mathematics Learning and Development. Springer, Singapore. https://doi.org/10.1007/978-981-287-215-9_10

Download citation

Publish with us

Policies and ethics

Search

Navigation