Skip to main content
Log in

Analysis of Place Value Instruction and Development in Pre-Kindergarten Mathematics

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

Abstract

Development of two-digit place value understanding in the elementary grades has been the subject of some study; however, research at the pre-kindergarten (Pre-K) level is limited. This two-part paper begins by providing an overview of two-digit place value instruction in Pre-K and describes the component parts of a research-based math curriculum, MyTeachingPartner Math (MTP Math). Part two presents the results of a video analysis of classroom interactions across four MTP Math place value activities facilitated by two high quality teachers. Particular attention is given to the primary conceptual hurdles faced by students, as well as the scaffolding strategies employed by teachers. Results indicate that students possess a conceptual understanding of the ones place prior to the tens place and initially struggle the concept of unitizing groups of ten. Considerations are discussed for improving the quality of teacher-child interactions in pre-kindergarten that can best support children’s thinking and learning.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  • Access Center. (2004). Concrete-representational-abstract instructional approach. The access center (pp. 1–6). Retrieved September 24, 2012 from http://www.k8accesscenter.org/training_resources/documents/CRAApplicationFinal_000.pdf.

  • Ainsworth, S. (1999). The functions of multiple representations. Computers & Education, 33, 131–152.

    Article  Google Scholar 

  • 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 

  • Ball, D. L. (1992). Magical hopes: Manipulatives and the reform of math education. American Educator, 16(2), 14–18, 46–47.

    Google Scholar 

  • Baroody, A. J. (1990). How and when should place value concepts and skills be taught? Journal for Research in Mathematics Education, 21(4), 281–286.

    Article  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 June 24, 2012 from http://literacyencyclopedia.ca/pdfs/topic.php?topId=271.

  • Biemiller, A. (2001). Teaching vocabulary: Early, direct, and sequential. The American Educator, 25(1), 24–28.

    Google Scholar 

  • Carpenter, T., & Lehrer, R. (1999). Teaching and learning mathematics with understanding. In E. Fennema & T. Romberg (Eds.), Mathematics classrooms that promote understanding (pp. 19–32). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Carpenter, T. P., Hiebert, J., & Moser, J. M. (1981). Problem structure and first-grade children’s initial solution processes for simple addition and subtraction problems. Journal for Research in Mathematics Education, 12(1), 27–39.

    Article  Google Scholar 

  • Clement, L. L. (2004). A model for understanding, using, and connecting representations. Teaching Children Mathematics, 11(2), 97–102.

    Google Scholar 

  • Cobb, P., & Wheatley, G. (1988). Children’s initial understandings of ten. Focus on Learning Problems in Mathematics, 10(3), 1–28.

    Google Scholar 

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

    Google Scholar 

  • Dienes, Z. P. (1960). Building up mathematics. London, England: Hutchinson Education.

    Google Scholar 

  • diSessa, A., Hammer, D., Sherin, B., & Kolpakowski, T. (1991). Inventing graphing: Children’s meta-representational expertise. Journal of Mathematical Behavior, 10(2), 117–160.

    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 

  • Flores, M. M. (2010). Using the concrete-representational-abstract sequence to teach subtraction with regrouping to students at risk for failure. Remedial and Special Education, 31(3), 195–207.

    Article  Google Scholar 

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

    Google Scholar 

  • Franke, M. L., Webb, N. M., Chan, A. G., Ing, M., Freund, D., & Battey, D. (2009). Teacher questioning to elicit students’ mathematical thinking in elementary classroom. Journal of Teacher Education, 60(4), 380–392.

    Article  Google Scholar 

  • Fuson, K. (1990). Conceptual structures for multiunit numbers: Implications for learning and teaching multidigit addition, subtraction, and place-value. Cognition and Instruction, 7(4), 343–403.

    Article  Google Scholar 

  • Fuson, K., & Briars, D. (1990). Using a base-ten blocks learning/teaching approach for first- and second-grade place value and multidigit addition and subtraction. Journal for Research in Mathematics Education, 21(3), 180–206.

    Article  Google Scholar 

  • Ginsburg, H. P., Greenes, C., & Balfanz, R. (2003). Big math for little kids: Classroom set. Parsippany, NJ: Dale Seymour Publications.

    Google Scholar 

  • Hiebert, J., & Wearne, D. (1992). Links between teaching and learning place value with understanding in first grade. Journal for Research in Mathematics Education, 23(2), 98–122.

    Article  Google Scholar 

  • Ho, C. S., & Cheng, F. S. (1997). Training in place value concepts improves children’s addition skills. Contemporary Educational Psychology, 22(4), 495–506.

    Article  Google Scholar 

  • Hoff, E. (2003). The specificity of environmental influence: Socioeconomic status affects early vocabulary development via maternal speech. Child Development, 74, 1368–1378.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Kamii, C. (1986). Place value: An explanation of its difficulty and educational implications for the primary grades. Journal of Research in Childhood Education, 1, 75–85.

    Article  Google Scholar 

  • Klibanoff, R. S., Levine, S. C., Huttenlocher, J., Vasilyeva, M., & Hedges, L. V. (2006). Preschool children’s mathematical knowledge: The effect of teacher “Math Talk”. Developmental Psychology, 42(1), 59–69.

    Article  Google Scholar 

  • McClain, K. (2003). Supporting preservice teachers’ understanding of place value and multidigit arithmetic. Mathematical Thinking and Learning, 5(4), 281–306.

    Article  Google Scholar 

  • Murata, A. (2004). Paths to learning ten-structured understandings of teen sums: Addition solution methods of Japanese grade 1 students. Cognition and Instruction, 22(2), 185–218.

    Article  Google Scholar 

  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA. Retrieved April 7, 2012 from http://standards.nctm.org/document/chapter4/numb.htm.

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

  • Peterson, S. K., Mercer, C. D., & O’Shea, L. (1988). Teaching learning disabled students place value using the concrete to abstract sequence. Learning Disabilities Research, 4, 52–56.

    Google Scholar 

  • Pianta, R. C., La Paro, K. M., & Hamre, B. K. (2008). The classroom assessment scoring system (CLASS). Baltimore, MD: Paul H. Brookes Publishing Co.

    Google Scholar 

  • Powell, A. B., Francisco, J. M., & Maher, C. A. (2003). An analytical model for studying the development of learners’ mathematical ideas and reasoning using videotape data. Journal of Mathematical Behavior, 22, 405–435.

    Article  Google Scholar 

  • Ross, S. H. (1986). The development of children’s place-value numeration concepts in grades two through five. San Diego, CA: Paper presented at the Annual Meeting of the American Educational Research Association.

    Google Scholar 

  • Sarama, J., & Clements, D. H. (2007). Manual for classroom observation (COEMET)-version 3. Unpublished version.

  • Skemp, R. (1978). Relational understanding and instrumental understanding. Arithmetic Teacher, 26, 9–15.

    Google Scholar 

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

  • Wood, T. (1998). Funneling or focusing? Alternative patterns of communication in mathematics class. In H. Steinbring, M. G. Bartolini-Bussi, & A. Sierpinski (Eds.), Language and communication in the mathematics classroom (pp. 167–178). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Patrick McGuire.

Appendix

Appendix

See Table 1.

Table 1 MTP math activities description and place value teaching tips

Rights and permissions

Reprints and permissions

About this article

Cite this article

McGuire, P., Kinzie, M.B. Analysis of Place Value Instruction and Development in Pre-Kindergarten Mathematics. Early Childhood Educ J 41, 355–364 (2013). https://doi.org/10.1007/s10643-013-0580-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10643-013-0580-y

Keywords

Navigation