Skip to main content
SpringerLink
Log in

Adapting Japanese Lesson Study to enhance the teaching and learning of geometry and spatial reasoning in early years classrooms: a case study

  • Original Article
  • Published:
ZDM Aims and scope Submit manuscript

Abstract

Increased efforts are needed to meet the demand for high quality mathematics in early years classrooms. Despite the foundational role of geometry and spatial reasoning for later mathematics success, the strand receives inadequate instructional time and is limited to concepts of static geometry. Moreover, early years teachers typically lack both content knowledge and confidence in teaching geometry and spatial reasoning. We describe our attempt to deal with these issues through a research initiative known as the Math for Young Children project. The project integrates effective features of both design research and Japanese Lesson Study and is designed to support teachers in developing content knowledge and new approaches for teaching geometry and spatial reasoning. Central to our Professional Development model is the integration of four adaptations to the Japanese Lesson Study model: (1) teachers engaging in the mathematics, (2) teachers designing and conducting task-based clinical interviews, (3) teachers and researchers co-designing and carrying out exploratory lessons and activities, and (4) the creation of resources for other educators. We present our methods and the results of our adaptations through a case study of one Professional Learning Team. Our results suggest that the adaptations were effective in: (1) supporting teachers’ content knowledge of and comfort level with geometry and spatial reasoning, (2) increasing teachers’ perceptions of young children’s mathematical competencies, (3) increasing teachers’ awareness and commitment for the inclusion of high quality geometry and spatial reasoning as a critical component of early years mathematics, and (4) the creation of innovative resources for other educators. We conclude with theoretical considerations and implications of our results.

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

Similar content being viewed by others

Notes

  1. Throughout this paper we will be referring to geometry and spatial reasoning as both separate and unified subject areas. This decision is based on differences in the way spatial reasoning and geometry are conceived, studied, and discussed in the psychological versus mathematics education literature. The term spatial reasoning or spatial thinking will be used when referring to work conducted by psychologists or cognitive psychologists. Geometry and spatial reasoning will be used to reflect the work of mathematics educators and researchers. Whereas psychologists and cognitive scientists generally study spatial reasoning or spatial thinking as a collection of cognitive skills and processes, mathematics educators generally consider geometry and spatial reasoning as a unified strand of mathematics having to do more with geometrical concepts than spatial skills per se. Within our own work in mathematics education, we consider geometry and spatial thinking as closely linked, i.e., geometry as the study of spatial relationships. We also recognize that various spatial cognitive skills (e.g., visualization) are necessarily part of understanding certain geometric concepts (e.g., composing/decomposing 2D shapes). In this way, we see the importance of simultaneously developing children’s geometric and spatial skills alongside conceptual understandings in order to support a deeper and more useful understanding of geometry and spatial reasoning.

  2. Henceforth, the term PLT will signify reference to the entire team, including the principal, numeracy facilitator and student achievement officer. We will use the term ‘teacher team’ to exclusively refer to the classroom teachers.

  3. http://www.oise.utoronto.ca/robertson/Inquiry-based_Mathematics/Math_For_Young_Children/St._Andrew_Catholic_School.html.

References

  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: what makes it special? Journal of Teacher Education, 59(5), 389–407.

    Article  Google Scholar 

  • Bruce, C. D., & Ladky, M. S. (2011). What’s going on backstage? Revealing the work of Lesson Study with Mathematics Teachers. In Lesson Study Research and Practice in Mathematics Education (pp. 243–249). Netherlands: Springer.

  • Bruce, C., Moss, J., & Ross, J. (2012). Survey of JK to Grade 2 teachers in Ontario, Canada: Report to the Literacy and Numeracy Secretariat of the Ministry of Education. Toronto: Ontario Ministry of Education.

    Google Scholar 

  • Casey, B. M., Andrews, N., Schincler, H., Kersh, J. E., Samper, A., & Copley, J. (2008). The development of spatial skills through interventions involving block building activities. Cognition and Instruction, 26(3), 269–309.

    Article  Google Scholar 

  • Clarke, D., Clarke, B., & Roche, A. (2011). Building teachers’ expertise in understanding, assessing and developing children’s mathematical thinking: the power of task-based, one-to-one assessment interviews. ZDM–The International Journal on Mathematics Education, 43(6–7), 901–913.

    Article  Google Scholar 

  • Clements, D. H. (2004). Geometric and spatial thinking in early childhood education. In D. Clements, J. Sarama, & M. A. DiBaise (Eds.), Engaging young children in mathematics: results of the conference on standards for pre-school and kindergarten mathematics education (pp. 83–90). New Jersey: Erlbaum.

    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(2), 136–163.

    Google Scholar 

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

    Google Scholar 

  • Clements, D. H., & Sarama, J. (2011). Early childhood teacher education: the case of geometry. Journal of Mathematics Teacher Education, 14(2), 133–148.

    Article  Google Scholar 

  • Cobb, P., Jackson, K., & Munoz, C. (2015). Design research: a critical analysis. In L. English & D. Kirshner (Eds.), Handbook of International Research in Mathematics Education (3rd Ed.). Manuscript submitted for publication. New York: Taylor & Francis (in press).

  • Copley, J. V. (2004). The early childhood collaborative: a professional development model to communicate and implement the standards. In D. H. Clements & J. Sarama (Eds.), Engaging young children in mathematics: standards for early childhood (pp. 404–414). New Jersey: Erlbaum.

    Google Scholar 

  • Cross, C. T., Woods, T. A., & Schweingruber, H. (Eds). (2009). Mathematics learning in early childhood: paths toward excellence and equity. Committee on Early Childhood Mathematics. National Research Council and National Academy of Sciences.

  • Darling-Hammond, L., Chung Wei, R., Andree, A., & Richardson, N. (2009). Status Report on Teacher Development in the United States and Abroad features of good professional development. United States of America: National Staff Development Council and The School Redesign Network at Stanford University.

  • Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., & Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428–1446. doi:10.1037/0012-1649.43.6.1428.

  • Freudenthal, H. (1981). Major problems of mathematics education. Educational Studies in Mathematics Education., 12(2), 133–150.

    Article  Google Scholar 

  • Garet, M. S., Porter, A. C., Desimone, L., Birman, B. F., & Yoon, K. S. (2001). What makes professional development effective? Results from a national sample of teachers. American Educational Research Journal, 38(4), 915–945.

    Article  Google Scholar 

  • Ginsburg, H. P. (1997). Entering the child’s mind: the clinical interview in psychological research and practice. New York: Cambridge University Press.

    Book  Google Scholar 

  • Ginsburg, H. P., Cannon, J., Eisenband, J., & Pappas, S. (2006). Mathematical thinking and learning. In K. McCartney & D. Phillips (Eds.), Blackwell handbook of early childhood development (pp. 208–229). Massachusetts: Blackwell Publishing.

    Chapter  Google Scholar 

  • Ginsburg, H. P., Lee, J. S., & Boyd, J. S. (2008). Mathematics education for young children: what it is and how to promote it. Social Policy Report of the Society for Research in Child Development, 22(1), 1–23.

    Google Scholar 

  • Hachey, A. C. (2013). The early childhood mathematics education revolution. Early Education and Development, 24(4), 419–430.

    Article  Google Scholar 

  • Hill, H. C., Rowan, B., & Ball, D. L. (2005). The effects of teacher’s mathematical knowledge for teaching on student achievement. American Educational Research, 42(2), 371–406.

    Article  Google Scholar 

  • Huang, R., Li, Y., Zhang, J., & Li, X. (2011). Improving teachers’ expertise in mathematics instruction through exemplary lesson development. ZDM–The International Journal on Mathematics Education, 43, 805–817.

    Article  Google Scholar 

  • Jacobs, V. R., Lamb, L. C., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal of Research in Mathematics Education, 41(2), 169–202.

    Google Scholar 

  • Jones, K. (2000). Critical issues in the design of the geometry curriculum. In Bill Barton (Ed.), Readings in Mathematics Education (pp. 75–90). Auckland: University of Auckland.

    Google Scholar 

  • Lee, J. (2010). Exploring kindergarten teachers’ pedagogical content knowledge of mathematics. International Journal of Early Childhood, 42(1), 27–41.

    Article  Google Scholar 

  • Lee, J. S., & Ginsburg, H. P. (2009). Early childhood teachers’ misconceptions about mathematics education for young children in the United States. Australian Journal of Early Childhood, 33(4), 37–45.

    Google Scholar 

  • Levenson, E., Tirosh, D., & Tsamir, P. (2011). Preschool Geometry: Theory, Research and Practical Perspectives. Boston: Sense Publishers.

    Book  Google Scholar 

  • Lewis, C., Perry, R., & Murata, A. (2006). How should research contribute to instructional improvement? The case of Lesson Study. Educational Researcher, 35(3), 3–14.

    Article  Google Scholar 

  • MacDonald, A., Davies, N., Dockett, S., & Perry, B. (2012). Early childhood mathematics education. In B. Perry (Ed.), Research in mathematics education in Australasia 2008–2011 (pp. 169–192). Boston: Sense Publishers.

    Google Scholar 

  • Mix, K. S., & Cheng, Y. L. (2012). Space and math: The developmental and educational implications. In J. B. Benson (Ed.), Advances in child development and behavior (pp. 179–243). New York: Elsevier.

    Google Scholar 

  • Moss, J., Messina, R., Morley, E., & Tepylo, D. (2012). Sustaining professional collaborations over 6 years: Using Japanese Lesson Study to improve the teaching and learning of mathematics. In J. Bay-Williams & W. R. Speer (Eds.), Professional collaborations in mathematics teaching and learning: Seeking success for all (pp. 297–309). Reston: The National Council of Teachers of Mathematics Inc.

    Google Scholar 

  • National Association for the Education of Young Children. (2010). Early childhood mathematics: Promoting good beginnings. Washington, DC: NAEYC. Retrieved 3 March 2014. http://www.naeyc.org/files/naeyc/file/positions/psmath.pdf.

  • National Council of Teachers of Mathematics. (2000). Chapter 4: Standards for pre-K-2. In Principles and Standard for School Mathematics. Reston: NCTM.

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

    Google Scholar 

  • National Research Council. (2006). Learning to think spatially: GIS as a support system in the K-12 curriculum. Washington, DC: National Academic Press.

    Google Scholar 

  • Newcombe, N., Uttal, D., & Sauter, M. (2013). Spatial development. Oxford handbook of developmental psychology, 1, 564–590.

    Google Scholar 

  • Sinclair, N. (2008). The history of the geometry curriculum in the United States. IAP—Information Age Publishing Inc.

  • Uttal, D. H., Meadow, N. G., Tipton, E., Hand, L. L., Alden, A. R., Warren, C., & Newcombe, N. S. (2013). The malleability of spatial skills: a meta-analysis of training studies. Psychological Bulletin, 139(2), 352–402. doi:10.1037/a002844.

    Article  Google Scholar 

  • Van den Heuvel-Panhuizen, M. (2008). Children learn mathematics: a learning-teaching trajectory with intermediate attainment targets for calculation with whole numbers in primary school. Utrecht: Freudenthal Institute.

    Google Scholar 

  • Van den Heuvel-Panhuizen, M., & Buijs, K. (2005). Young children learn measurement and geometry: a learning-teaching trajectory with intermediate attainment targets for the lower grades in primary school. Utrecht: Freudenthal Institute.

    Google Scholar 

  • Verdine, B. N., Golinkoff, R., Hirsh-Pasek, K., Newcombe, N., Filipowocz, A. T., & Chang, A. (2013). Deconstructing builidng blocks: Preschoolers’ spatial assembly performance relates to early mathematics skills. Child Development. doi:10.1111/cdev.12165 (Advance online publication).

  • Verdine, B. N., Golinkoff, R. M., Hirsh-Pasek, K., & Newcombe, N. S. (2014). Finding the missing piece: Blocks, puzzles, and shapes fuel school readiness. Trends in Neuroscience and Education. doi:10.1016/j.tine.2014.02.005 (Advance online publication).

  • Wai, J., Lubinski, D., & Benbow, C. P. (2009). Spatial ability for STEM domains: aligning over fifty years of cumulative psychological knowledge solidifies its importance. Journal of Educational Psychology, 101, 817–835.

    Article  Google Scholar 

  • White, A. L., & Lim, C. S. (2008). Lesson study in Asia Pacific classrooms: Local responses to a global movement. ZDM–The International Journal on Mathematics Education, 40(6), 915–925.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Psychology and Human Development, Ontario Institute for Studies in Education, University of Toronto, Toronto, ON, M5R 2X2, Canada

    Joan Moss, Zachary Hawes, Sarah Naqvi & Beverly Caswell

Authors
  1. Joan Moss
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zachary Hawes
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sarah Naqvi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Beverly Caswell
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Joan Moss.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Moss, J., Hawes, Z., Naqvi, S. et al. Adapting Japanese Lesson Study to enhance the teaching and learning of geometry and spatial reasoning in early years classrooms: a case study. ZDM Mathematics Education 47, 377–390 (2015). https://doi.org/10.1007/s11858-015-0679-2

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11858-015-0679-2

Keywords

Search

Navigation