Skip to main content

Advertisement

SpringerLink
Log in

Developing Number Sense in Pre-K with Five-Frames

  • Published:
Early Childhood Education Journal Aims and scope Submit manuscript

Abstract

Teachers in early childhood and elementary classrooms (grades K-5) have been using ten-frames as an instructional tool to support students’ mathematics skill development for many years. Use of the similar five-frame has been limited, however, despite its apparent potential as an instructional scaffold in the early elementary grades. Due to scant evidence of teacher use and a lack of systematic research we know little to nothing about both the developmental and pedagogical implications of using five frames and related instructional manipulatives in early childhood mathematics classrooms. In this paper, we provide an overview of five-frames and specifically demonstrate ways that five-frames, if used in conjunction with concrete manipulatives, can support pre-kindergarten (pre-K) children’s development of Gelman and Gallistel’s (1978) three basic counting principles: the stable-order principle, one-to-one correspondence, and cardinality. We conclude by discussing the developmental and instructional implications of using five-frames, as well as offer a set of teaching tips designed to help teachers maximize the potential advantages of integrating five-frames in the pre-K classroom.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  • Alibali, M. W., & DiRusso, A. A. (1999). The function of gesture in learning to count: More than keeping track. Cognitive Development, 14, 37–56.

    Article  Google Scholar 

  • Ashlock, R. B. (2006). Error patterns in computation: Using error patterns to improve instruction. Upper Saddle River, NJ: Pearson.

    Google Scholar 

  • Baroody, A. J. (2009). Fostering early numeracy in preschool and kindergarten. Encyclopedia of language and literacy development (pp. 1–9). London, ON: Canadian Language and Literacy Research Network. Retrieved [March 4, 2010] from http://literacyencyclopedia.ca/pdfs/topic.php?topId=271.

  • Baroody, A. J., & Wilkins, J. L. M. (1999). The development of informal counting, number, and arithmetic skills and concepts. In Mathematics in the Early Years (pp. 48–65). Washington, DC: NAEYC.

  • Berch, D. B. (2005). Making sense of number sense: Implications for children with mathematical disabilities. Journal of Learning Disabilities, 38, 333–339.

    Article  Google Scholar 

  • Bermejo, V., Morales, S., & Garcia deOsuna, J. (2004). Supporting children’s development of cardinality understanding. Learning and Instruction, 14, 381–398.

    Article  Google Scholar 

  • Boulton-Lewis, G. (1992). The processing loads of young children's and teachers’ representations of place value and implications for teaching. Mathematics Education Research Journal, 4(1), 1–23.

    Article  Google Scholar 

  • Boulton-Lewis, G. M. (1998). Children’s strategy use and interpretations of mathematical representations. Journal of Mathematical Behavior, 17(2), 219–237.

    Article  Google Scholar 

  • Bramald, R. (2001). So you think counting is easy! Mathematics Education Review, 13, 10–21.

    Google Scholar 

  • Briars, D., & Siegler, R. S. (1984). A featural analysis of children’s counting. Developmental Psychology, 20, 607–618.

    Article  Google Scholar 

  • Butterworth, B. (2004). The development of arithmetical abilities. Journal of Child Psychology and Psychiatry, 46, 3–18.

    Google Scholar 

  • Clements, D. H. (2001). Mathematics in the preschool. Teaching Children Mathematics, 7(4), 270–275.

    Google Scholar 

  • Clements, D. H. (2004). Part one: Major themes and recommendations. In Engaging young children in mathematics: Standards for early childhood mathematics education. (pp. 7–72). Mahwah, NJ: Lawrence Erlbaum.

  • Clements, D. H. (2009, November). The building blocks of early mathematics. Lecture presented at the University of Virginia, Charlottesville, Virginia.

  • Clements, D. H., & Samara, J. (2007). Early childhood mathematics learning. In F. K. Lester, Jr (Ed.), Second handbook on mathematics teaching and learning (pp. 461–555). Charlotte, NC: Information Age.

  • Copley, J. V. (2000). The young child and mathematics. Washington, DC: NAEYC.

    Google Scholar 

  • Duncan, G., Dowsett, C., Claessens, A., Magnuson, K., Huston, A., Klebanov, P., et al. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428–1446.

    Article  Google Scholar 

  • Fischer, F. E. (1990). A part–part-whole curriculum for teaching number in kindergarten. Journal for Research in Mathematics Education, 21(3), 207–215.

    Article  Google Scholar 

  • Fosnot, C. T., & Dolk, M. (2001). Young mathematicians at work: Constructing number sense, addition, and subtraction. Portsmouth, NH: Heinemann.

    Google Scholar 

  • Frye, D., Braisby, N., Lowe, J., Maroudas, C., & Nicholls, J. (1989). Young children’s understanding of counting and cardinality. Child Development, 60(5), 1158–1171.

    Article  Google Scholar 

  • Fuson, K. (1986). Roles of representation and verbalization in the teaching of multi-digit addition and subtraction. European Journal of Psychology of Education, 1, 35–36.

    Article  Google Scholar 

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

    Book  Google Scholar 

  • Gelman, R., & Gallistel, C. R. (1978). The child’s understanding of number. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Gelman, R., & Meck, E. (1983). Preschoolers’ counting: Principles before skill. Cognition, 13, 343–359.

    Article  Google Scholar 

  • Gelman, R., Meck, E., & Merkin, S. (1986). Young children’s numerical competence. Cognitive Development, 1, 1–29.

    Article  Google Scholar 

  • Ginsburg, H. P., & Allardice, B. S. (1984). Children’s difficulties with school mathematics. In Everyday cognition: Its development in social contexts (pp. 194–219). Cambridge, MA: Harvard University Press.

  • Griffin, S., & Case, R. (1997). Rethinking the primary school math curriculum: An approach based on cognitive science. Issues in Education, 3(1), 1–49.

    Google Scholar 

  • Hunting, R. P. (2003). Part-whole number knowledge in preschool children. Journal of Mathematical Behavior, 22, 217–235.

    Article  Google Scholar 

  • Jordan, N. C. (2007). The need for number sense. Educational Leadership, 65(2), 63–66.

    Google Scholar 

  • Jordan, N. C., Kaplan, D., Locuniak, M. N., & Ramineni, C. (2007). Predicting first-grade math achievement from developmental number sense trajectories. Learning Disabilities Research & Practice, 22(1), 36–46.

    Article  Google Scholar 

  • Jordan, N. C., Kaplan, D., Nabors Ola’h, L., & Locuniak, M. N. (2006). Number sense growth in kindergarten: A longitudinal investigation of children at risk for mathematics difficulties. Child Development, 77(1), 153–175.

    Article  Google Scholar 

  • Kelly, C. A. (2006). Using manipulatives in mathematical problem solving: A performance-based analysis. The Montana Enthusiast, 3(2), 184–193.

    Google Scholar 

  • Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up. Washington, DC: National Academies Press.

    Google Scholar 

  • Levine, S. C., Jordan, N. C., & Huttenlocher, J. (1992). Development of calculation abilities in young children. Journal of Experimental Child Psychology, 53, 72–103.

    Article  Google Scholar 

  • Marmasse, N., Bletsas, A., & Marti, S. (2000). Numerical mechanisms and children’s concept of numbers. M.I.T. media laboratory online publication. Accessed: November 22, 2009 from: http://web.media.mit.edu/~stefanm/society/som_final_natalia_aggelos_stefan.pdf.

  • McGuire, P. & Wiggins, A.K. (2009). Mathematical reasoning and number sense. In Preschool sequence and teacher handbook (pp. 171–218). Charlottesville, VA: Core Knowledge Foundation.

  • McNeil, N. M., & Uttal, D. H. (2009). Rethinking the use of concrete materials in learning: Perspectives from development and education. Child Development Perspectives, 3(3), 137–139.

    Article  Google Scholar 

  • Miura, I. T., Okamoto, Y., Kim, C. C., Steere, M., & Fayol, M. (1993). First graders’ cognitive representation of number and understanding of place value: Cross-national comparisons–France, Korea, Sweden, and the United States. Journal of Educational Psychology, 85(1), 24–30.

    Article  Google Scholar 

  • National Council of Teacher of Mathematics. (2008). Number and operations standard for grades Pre-k–2. Retrieved October 17, 2009 from: http://standards.nctm.org/document/Chapter4/numb.htm.

  • National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA. Retrieved June 7, 2010 from: http://standards.nctm.org/document/chapter4/numb.htm.

  • National Mathematics Advisory Panel. (2008). The final report of the national mathematics advisory panel. Washington, DC: Author.

    Google Scholar 

  • National Research Council. (2009). In C. T. Cross, T. A. Woods, & H. Schweingruber (Eds.), Mathematics learning in early childhood: Paths toward excellence and equity. Committee on Early Childhood Mathematics, Center for Education. Division of Behavioral and Social Sciences in Education. Washington, DC: The National Academies Press.

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

    Google Scholar 

  • Novakowski, J. (2007). Developing “five-ness” in kindergarten. Teaching Children Mathematics, 14(4), 226–231.

    Google Scholar 

  • Resnick, L. (1983). A developmental theory of number understanding. In The development of mathematical understanding (pp. 109–151). New York, NY: Academic Press.

  • Sarama, J. S., & Clements, D. H. (2007). How children problem solve. Scholastic Early Childhood Today, 21(7), 18–19.

    Google Scholar 

  • Siegler, R. S. (1991). In young children’s counting, procedures precede principles. Educational Psychology Review, 3, 127–135.

    Article  Google Scholar 

  • Siegler, R. S., DeLoache, J., & Eisenberg, N. (2006). How children develop (2nd ed.). New York, NY: Worth.

    Google Scholar 

  • Sophian, C. (2007). The origins of mathematical knowledge in children. Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Sowell, E. J. (1989). Effects of manipulative materials in mathematics instruction. Journal for Research in Mathematics Education, 20(5), 498–505.

    Article  Google Scholar 

  • Stock, P., Desoete, A., & Roeyers, H. (2009). Mastery of the counting principles in toddlers: A crucial step in the development of budding arithmetic abilities? Learning and Individual Differences, 19, 419–422.

    Article  Google Scholar 

  • Sweller, J. (1994). Cognitive load theory, learning difficulty, and instructional design. Learning and Instruction, 4, 295–312.

    Article  Google Scholar 

  • Tzuriel, D., Kaniel, S., Kanner, E., & Haywood, H. C. (1999). Effects of the “Bright Start” program in kindergarten on transfer and academic achievement. Early Childhood Research Quarterly, 14, 111–141.

    Article  Google Scholar 

  • Uttal, D. H., Scudder, K. V., & Deloache, J. S. (1997). Manipulatives as symbols: A new perspective on the use of concrete objects to teach mathematics. Journal of Applied Developmental Psychology, 18(1), 37–54.

    Article  Google Scholar 

  • Van de Walle, J. A. (2003). Developing early number concepts and number sense. In Elementary and middle school mathematics: Teaching developmentally (pp. 115–134). Boston, MA: Allyn & Bacon.

  • Van de Walle, J. A. (2007). Elementary and middle school mathematics: Teaching developmentally (6th ed.). Boston, MA: Pearson Education.

    Google Scholar 

  • Wright, R. J., Stanger, C., Cowper, M., & Dyson, R. (1996). First graders’ progress in an experimental mathematics recovery program. In Children’s number learning: A research monograph of MERGA/AAMT (pp. 55–72). Adelaide, Australia: Australian Association of Mathematics Teachers.

  • Wynn, K. (1990). Children’s understanding of counting. Cognition, 36, 155–193.

    Article  Google Scholar 

  • Wynn, K. (1992). Children’s acquisition of the number words and the counting system. Cognitive Psychology, 24, 220–251.

    Article  Google Scholar 

  • Zur, O., & Gelman, R. (2004). Young children can add and subtract by predicting and checking. Early Childhood Research Quarterly, 19, 121–137.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Education, University of Colorado at Colorado Springs, 1420 Austin Bluffs Parkway, Columbine Hall 3039, Colorado Springs, CO, 80907, USA

    Patrick McGuire

  2. Curry School of Education, University of Virginia, Ruffner Hall 238, 405 Emmet Street, Charlottesville, VA, 22904-4261, USA

    Mable B. Kinzie

  3. Curry School of Education, University of Virginia, Ruffner Hall 194, 405 Emmet Street, Charlottesville, VA, 22904-4261, USA

    Daniel B. Berch

Authors
  1. Patrick McGuire
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mable B. Kinzie
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Daniel B. Berch
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Patrick McGuire.

Rights and permissions

Reprints and permissions

About this article

Cite this article

McGuire, P., Kinzie, M.B. & Berch, D.B. Developing Number Sense in Pre-K with Five-Frames. Early Childhood Educ J 40, 213–222 (2012). https://doi.org/10.1007/s10643-011-0479-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10643-011-0479-4

Keywords

Search

Navigation