Skip to main content
SpringerLink
Log in

Rethinking Early Mathematics: What Is Research-Based Curriculum for Young Children?

  • Chapter
Reconceptualizing Early Mathematics Learning

Part of the book series: Advances in Mathematics Education ((AME))

Abstract

Descriptions of curricula as “research-based” have been overused and underdeveloped. Two major conceptual tools support efforts of researchers and practitioners to collaborate on producing, evaluating, and implementing truly research-based curricula for early mathematics. The first is a set of learning trajectories that describe how children learn major topics in mathematics and how teachers can support that learning. These learning trajectories constitute the core of the second conceptual tool, a framework for developing curricula and teaching strategies. The chapter describes a framework comprising criteria and procedures for creating scientifically-based curricula using learning trajectories.

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

Access this chapter

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
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
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

Institutional subscriptions

Notes

  1. 1.

    These are not limited to recent work on learning trajectories, of course. They have been raised by other projects, such as cognitively-guided instruction (Siegler and Jenkins 1989) on which our notion of learning trajectories are based (for a discussion of these roots, see Clements and Sarama 2007a).

References

  • 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).

    Google Scholar 

  • Antell, S. E., & Keating, D. P. (1983). Perception of numerical invariance in neonates. Child Development, 54, 695–701.

    Article  Google Scholar 

  • Baroody, A. J. (2004). The developmental bases for early childhood number and operations standards. In D. H. Clements, J. Sarama, & A.-M. DiBiase (Eds.), Engaging young children in mathematics: standards for early childhood mathematics education (pp. 173–219). Mahwah: Erlbaum.

    Google Scholar 

  • Battista, M. T., & Clements, D. H. (2000). Mathematics curriculum development as a scientific endeavor. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 737–760). Mahwah: Erlbaum.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Carpenter, T. P., & Franke, M. L. (2004). Cognitively guided instruction: challenging the core of educational practice. In J. Glennan, K. Thomas, S. J. Bodilly, J. R. Galegher, & K. A. Kerr (Eds.), Expanding the reach of education reforms: perspectives from leaders in the scale-up of educational interventions (pp. 41–80). Santa Monica: RAND Corporation.

    Google Scholar 

  • Carpenter, T. P., & Moser, J. M. (1984). The acquisition of addition and subtraction concepts in grades one through three. Journal for Research in Mathematics Education, 15, 179–202.

    Article  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. (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 & Francis.

    Google Scholar 

  • Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 420–464). New York: Macmillan.

    Google Scholar 

  • Clements, D. H., & Burns, B. A. (2000). Students’ development of strategies for turn and angle measure. Educational Studies in Mathematics, 41, 31–45.

    Article  Google Scholar 

  • Clements, D. H., & Conference Working Group (2004). Part one: major themes and recommendations. In D. H. Clements, J. Sarama, & A.-M. DiBiase (Eds.), Engaging young children in mathematics: standards for early childhood mathematics education (pp. 1–72). Mahwah: Erlbaum.

    Google Scholar 

  • Clements, D. H., & Sarama, J. (2002). Teaching with computers in early childhood education: strategies and professional development. Journal of Early Childhood Teacher Education, 23, 215–226.

    Article  Google Scholar 

  • Clements, D. H., & Sarama, J. (2003). DLM early childhood express math resource guide. Columbus: SRA/McGraw-Hill.

    Google Scholar 

  • Clements, D. H., & Sarama, J. (2004a). Building Blocks for early childhood mathematics. Early Childhood Research Quarterly, 19, 181–189.

    Article  Google Scholar 

  • Clements, D. H., & Sarama, J. (2004b). 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. (2007a). Building blocks [computer software], Columbus: SRA/McGraw-Hill.

    Google Scholar 

  • Clements, D. H., & Sarama, J. (2007b). Building blocks curriculum, grade PreK. Columbus: SRA/McGraw-Hill.

    Google Scholar 

  • Clements, D. H., & Sarama, J. (2007c). Building blocks—SRA real math teacher’s edition, grade PreK. Columbus: SRA/McGraw-Hill.

    Google Scholar 

  • Clements, D. H., & Sarama, J. (2007d). 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. (2008). Experimental evaluation of the effects of a research-based preschool mathematics curriculum. American Educational Research Journal, 45, 443–494.

    Article  Google Scholar 

  • Clements, D. H., & Sarama, J. (2009). Learning and teaching early math: the learning trajectories approach. New York: Routledge.

    Google Scholar 

  • Clements, D. H., & Sarama, J. (2012). Mathematics learning, assessment, and curriculum. In R. C. Pianta, L. Justice, S. W. Barnett, & S. Sheridan (Eds.), Handbook of early education (pp. 217–239). New York: Guilford.

    Google Scholar 

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

    Google Scholar 

  • Clements, D. H., & Swaminathan, S. (1995). Technology and school change: new lamps for old? Childhood Education, 71, 275–281.

    Article  Google Scholar 

  • Clements, D. H., Nastasi, B. K., & Swaminathan, S. (1993). Young children and computers: crossroads and directions from research. Young Children, 48(2), 56–64.

    Google Scholar 

  • Clements, D. H., Wilson, D. C., & Sarama, J. (2004). Young children’s composition of geometric figures: a learning trajectory. Mathematical Thinking and Learning, 6, 163–184. doi:10.1207/s15327833mtl0602_1.

    Article  Google Scholar 

  • Cook, T. D. (2002). Randomized experiments in educational policy research: a critical examination of the reasons the educational evaluation community has offered for not doing them. Educational Evaluation and Policy Analysis, 24, 175–199.

    Article  Google Scholar 

  • El’konin, D. B., & Davydov, V. V. (1975). Children’s capacity for learning mathematics. In L. P. Steffe (Ed.), Soviet studies in the psychology of learning and teaching mathematics (Vol. 7, pp. 1–11). Chicago: University of Chicago Press.

    Google Scholar 

  • Fuson, K. C. (1988). Children’s counting and concepts of number. New York: Springer.

    Book  Google Scholar 

  • Fuson, K. C. (1992). Research on whole number addition and subtraction. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 243–275). New York: Macmillan.

    Google Scholar 

  • Fuson, K. C. (1997). Research-based mathematics curricula: new educational goals require programs of four interacting levels of research. Issues in Education, 3(1), 67–79.

    Google Scholar 

  • Fuson, K. C. (2004). Pre-K to grade 2 goals and standards: achieving 21st century mastery for all. In D. H. Clements, J. Sarama, & A.-M. DiBiase (Eds.), Engaging young children in mathematics: standards for early childhood mathematics education (pp. 105–148). Mahwah: Erlbaum.

    Google Scholar 

  • Fuson, K. C., Carroll, W. M., & Drueck, J. V. (2000). Achievement results for second and third graders using the Standards-based curriculum Everyday Mathematics. Journal for Research in Mathematics Education, 31, 277–295.

    Article  Google Scholar 

  • Hiebert, J. C. (1999). Relationships between research and the NCTM Standards. Journal for Research in Mathematics Education, 30, 3–19.

    Article  Google Scholar 

  • Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: helping children learn mathematics. Washington: National Academy Press.

    Google Scholar 

  • Klein, A., Starkey, P., & Ramirez, A. B. (2002). Pre-K mathematics curriculum. Glenview: Scott Foresman.

    Google Scholar 

  • Kobayashi, T., Hiraki, K., Mugitani, R., & Hasegawa, T. (2004). Baby arithmetic: one object plus one tone. Cognition, 91, B23–B34.

    Article  Google Scholar 

  • Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. Chicago: University of Chicago Press.

    Google Scholar 

  • Maloney, A. P., Confrey, J., & Nguyen, K. (Eds.) (in press). Learning over time: learning trajectories in mathematics education. New York: Information Age.

    Google Scholar 

  • Mansfield, H. M., & Scott, J. (1990). Young children solving spatial problems. In G. Booker, P. Cobb, & T. N. deMendicuti (Eds.), Proceedings of the 14th annual conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 275–282). Oaxlepec: International Group for the Psychology of Mathematics Education.

    Google Scholar 

  • Murata, A. (2004). Paths to learning ten-structured understanding of teen sums: addition solution methods of Japanese Grade 1 students. Cognition and Instruction, 22, 185–218.

    Article  Google Scholar 

  • National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston: National Council of Teachers of Mathematics.

    Google Scholar 

  • National Council of Teachers of Mathematics (2006). Curriculum focal points for prekindergarten through grade 8 mathematics: a quest for coherence. Reston: National Council of Teachers of Mathematics.

    Google Scholar 

  • National Research Council (2001). Eager to learn: educating our preschoolers. Washington: National Academy Press.

    Google Scholar 

  • National Research Council (2002). Scientific research in education. Washington: National Research Council, National Academy Press.

    Google Scholar 

  • National Research Council (2004). On evaluating curricular effectiveness: judging the quality of K-12 mathematics evaluations. Washington: Mathematical Sciences Education Board, Center for Education, Division of Behavioral and Social Sciences and Education, The National Academies Press.

    Google Scholar 

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

    Google Scholar 

  • Perlmutter, J., Bloom, L., Rose, T., & Rogers, A. (1997). Who uses math? Primary children’s perceptions of the uses of mathematics. Journal of Research in Childhood Education, 12(1), 58–70.

    Article  Google Scholar 

  • Preschool Curriculum Evaluation Research Consortium (2008). Effects of preschool curriculum programs on school readiness (NCER 2008–2009). Washington: Government Printing Office. Retrieved from http://ncer.ed.gov.

    Google Scholar 

  • Sales, C. (1994). A constructivist instructional project on developing geometric problem solving abilities using pattern blocks and tangrams with young children. Masters, University of Northern Iowa, Cedar Falls, Iowa.

    Google Scholar 

  • Sarama, J. (2004). Technology in early childhood mathematics: Building Blocks™ as an innovative technology-based curriculum. In D. H. Clements, J. Sarama, & A.-M. DiBiase (Eds.), Engaging young children in mathematics: standards for early childhood mathematics education (pp. 361–375). Mahwah: Erlbaum.

    Google Scholar 

  • Sarama, J., & Clements, D. H. (2002). Learning and teaching with computers in early childhood education. In O. N. Saracho & B. Spodek (Eds.), Contemporary perspectives on science and technology in early childhood education (pp. 171–219). Greenwich: Information Age.

    Google Scholar 

  • Sarama, J., & Clements, D. H. (2009a). “Concrete” computer manipulatives in mathematics education. Child Development Perspectives, 3(3), 145–150.

    Article  Google Scholar 

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

    Google Scholar 

  • Sarama, J., & Clements, D. H. (in press). Learning trajectories: foundations for effective, research-based education. In A. P. Maloney, J. Confrey, & K. Nguyen (Eds.), Learning over time: learning trajectories in mathematics education. New York: Information Age.

    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 

  • Senk, S. L., & Thompson, D. R. (2003). Standards-based school mathematics curricula. What are they? What do students learn? Mahwah: Erlbaum.

    Google Scholar 

  • Siegler, R. S., & Jenkins, E. (1989). How children discover new strategies. Mahwah: Erlbaum.

    Google Scholar 

  • Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114–145. doi:10.2307/749205.

    Article  Google Scholar 

  • Sophian, C. (2004). A prospective developmental perspective on early mathematics instruction. In D. H. Clements, J. Sarama, & A.-M. DiBiase (Eds.), Engaging young children in mathematics: standards for early childhood mathematics education (pp. 253–266). Mahwah: Erlbaum.

    Google Scholar 

  • Steffe, L. P. (2004). PSSM from a constructivist perspective. In D. H. Clements, J. Sarama, & A.-M. DiBiase (Eds.), Engaging young children in mathematics: standards for early childhood mathematics education (pp. 221–251). Mahwah: Erlbaum.

    Google Scholar 

  • Steffe, L. P., & Wiegel, H. G. (1994). Cognitive play and mathematical learning in computer microworlds. Journal of Research in Childhood Education, 8(2), 117–131.

    Article  Google Scholar 

  • Vurpillot, E. (1976). The visual world of the child. New York: International Universities Press.

    Google Scholar 

  • Wager, A. A., & Carpenter, T. P. (2012). Learning trajectories through a socio-cultural lens. In J. S. Carlson & J. R. Levine (Eds.), Psychological perspectives on contemporary educational issues: Vol. 3. Instructional strategies for improving student learning: focus on early mathematics and reading (pp. 197–204). Charlotte: Information Age.

    Google Scholar 

  • Wright, R. J. (1994). A study of the numerical development of 5-year-olds and 6-year-olds. Educational Studies in Mathematics, 26, 25–44.

    Article  Google Scholar 

  • Wynn, K. (1992). Addition and subtraction by human infants. Nature, 358, 749–750.

    Article  Google Scholar 

  • Zvonkin, A. (2010). Math from three to seven: the story of a mathematical circle for preschoolers. Berkeley: Mathematical Sciences Research Institute. A. Yarkho & P. Zeitz, Trans.

    Google Scholar 

Download references

Acknowledgements

This chapter was based upon work supported in part by the Institute of Education Sciences (U.S. Dept. of Education) under Grant No. R305K05157. Work on the research was also supported in part by the National Science Foundation under Grants No. DRL-1019925 and DRL-1020118. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the funding agencies.

Author information

Authors and Affiliations

  1. University of Denver, Denver, CO, USA

    Douglas H. Clements & Julie Sarama

Authors
  1. Douglas H. Clements
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Julie Sarama
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Douglas H. Clements .

Editor information

Editors and Affiliations

  1. School of STM Education, Queensland University of Technology, Victoria Park Rd, Kelvin Grove, Brisbane, 4059, Queensland, Australia

    Lyn D. English

  2. Macquarie University, University Avenue, Sydney, 2113, New South Wales, Australia

    Joanne T. Mulligan

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Clements, D.H., Sarama, J. (2013). Rethinking Early Mathematics: What Is Research-Based Curriculum for Young Children?. In: English, L., Mulligan, J. (eds) Reconceptualizing Early Mathematics Learning. Advances in Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6440-8_7

Download citation

Publish with us

Policies and ethics

Search

Navigation