Skip to main content

Advertisement

Log in

Using Lesson Study to Support the Teaching of Early Number Concepts: Examining the Development of Prospective Teachers’ Specialized Content Knowledge

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

Abstract

Growing awareness of the importance of education in the early years has led professional organizations and policy makers to consider the effectiveness of mathematics education for young children. Factors such as educational environments, early years curricula and teacher education are some of the many aspects that have been examined. This paper describes the types of mathematical content knowledge that 25 prospective primary teachers developed as they designed, taught and reflected upon early number lessons. This Lesson Study approach involved two mathematics educators and 25 prospective primary teachers designing, teaching and re-teaching five early number lessons in two elementary classrooms with 4–5 year old children. The results suggest that effective teaching of early number concepts draws on mathematical knowledge that is specialized and unique to teachers; in other words Specialized Content Knowledge (SCK). The study found that engaging in Lesson Study promoted mathematics SCK development in two primary ways, notable by: (1) raising awareness of the complex relationships between early number concepts that contribute to developing robust early number understandings and (2) developing expertise in identifying the nature and source of children’s mathematical errors. The development of participants’ early number SCK is described and recommendations are made for the design of experiences in Initial Teacher Education (ITE) to support teachers in the provision of high quality mathematics experiences to young learners.

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
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Author, 2010, 2013, 2015, 2015a, 2015b, 2015c, 2015d, 2016.

  • 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.

    Google Scholar 

  • Cajkler, W., Wood, P., Norton, J., & Pedder, D. (2013). Lesson study: Towards a collaborative approach to learning in Initial Teacher Education? Cambridge. Journal of Education, 43(4), 537–554.

    Google Scholar 

  • Central Applications Office (CAO), (2015). CAO Handbook, [Accessed on-line], http://www2.cao.ie/handbook/handbook/hb.pdf. Accessed 19 Feb 2015.

  • Clements, D. H., & Sarama, J. (2009). Early childhood mathematics learning. In F. K. Lester(Ed.), Second handbook of research on mathematics teaching and learning (pp. 461–555). Charlotte: Information Age.

    Google Scholar 

  • Delaney, S., Ball, D. L., Hill, H. C., Schilling, S. G., & Zopf, D. (2008). Mathematical knowledge for teaching: Adapting U.S. measures for use in Ireland. Journal of Mathematics Teacher Education, 11(3), 171–197.

    Article  Google Scholar 

  • Ding, L., He, J., & Koon Shing Leung, F. (2014). Relations between subject matter knowledge and pedagogical content knowledge: A study of Chinese pre-service teachers on the topic of three-term ratio. The Mathematics Educator, 15(2), 50–76.

    Google Scholar 

  • Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., Pagani, L. S., Feinstein, L., Engel, M., Brooks-Gunn, J., Sexton, H., Duckworth, K., & Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428–1446. 10.1037/0012-1649.43.6.1428.

    Article  Google Scholar 

  • Ertle, B., Chokshi, S., & Fernandez, C. (2001). Lesson planning tool. www.tc.columbia.edu/centers/lessonstudy/doc/Lesson_Planning_Tool.pdf. Accessed 28 Nov 2016.

  • Fauskanger, J. (2015). Challenges in measuring teachers’ knowledge. Educational Studies in Mathematics, 90(1), 57–73.

    Article  Google Scholar 

  • Flores, E., Escudero, D. I., & Carrillo, J. (2013). A theoretical review of specialised content knowledge. In Proceedings of the Eighth Congress of European Research in Mathematics Education (CERME 8), 6–10 February 2013, Antalya, Turkey.

  • Hill, H., Ball, D. L., & Schilling, S. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research of Mathematics Education, 39(4), 372–400.

    Google Scholar 

  • Hill, H. C., Sleep, L., Lewis, J. M., & Ball, D. L. (2007). Assessing teachers’ mathematical knowledge: What knowledge matters and what evidence counts? In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 111–155). Charlotte: Information Age Publishing.

    Google Scholar 

  • Hourigan, M., & Leavy, A. (2015a). Geometric patterns: What’s the rule? Australian Primary Mathematics Classroom, 20(4), 31–39.

    Google Scholar 

  • Hourigan, M., & Leavy, A. (2015b). What’s a real shape? Designing appropriate geometric instruction. Australian Primary Mathematics Classroom, 20(1), 24–29.

    Google Scholar 

  • Hourigan, M., & Leavy, A. M. (2016). Practical problems: Introducing statistics to kindergarteners. Teaching Children Mathematics, 22(5), 283–291.

    Google Scholar 

  • Hourigan, M., Leavy, A. M. & Carroll, C. (2016). ‘Come in with an open mind’: Changing attitudes towards mathematics in primary teacher education. Educational Research. doi:10.1080/00131881.2016.1200340.

    Google Scholar 

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

    Google Scholar 

  • Jordan, N. C., Glutting, J., Ramineni, C., & Watkins, M. W. (2010). Validating a number sense screening tool for use in kindergarten and first grade: Prediction of mathematics efficiency in third grade. School Psychology Review, 39, 181–195.

    Google Scholar 

  • Kilday, C. R., & Kinzie, M. B. (2009). An analysis of instruments that measure the quality of mathematics teaching in early childhood. Early Childhood Education Journal, 36(4), 365–372. doi:10.1007/s10643-008-0286-8.

    Article  Google Scholar 

  • Leavy, A. M. (2010). The challenge of preparing preservice teachers to teach informal inferential reasoning. Statistics Education Research Journal, 9(1), 46–67.

    Google Scholar 

  • Leavy, A. M. (2015). Looking at practice: Revealing the knowledge demands of teaching data handling in the primary classroom. Mathematics Education Research Journal, 27(3), 283–309. DOI:10.1007/s13394-014-0138-3.

    Article  Google Scholar 

  • Leavy, A., & Hourigan, M. (2015a). Motivating inquiry in statistics and probability in the primary classroom. Teaching Statistics, 37(2), 41–47. doi:10.1111/test.12062.

    Google Scholar 

  • Leavy, A., & Hourigan, M. (2015b). Budding architects: Exploring the designs of pyramids and prisms. Australian Primary Mathematics Classroom, 20(3), 17–23.

    Google Scholar 

  • Leavy, A., & Hourigan, M. (2016). Using lesson study to support knowledge development in initial teacher education: Insights from early number classrooms. Teaching and Teacher Education, 57, 161–175. doi:10.1016/j.tate.2016.04.002.

    Article  Google Scholar 

  • Leavy, A., McMahon, A., & Hourigan, M. (2013). Early algebra: Developing understanding of the equals sign. Teaching Children Mathematics, 20(4), 246–252.

    Article  Google Scholar 

  • Leavy, A. M., Hourigan, M., & Carroll, C. (2015). Exploring the impact of reform mathematics on entry-level pre-service primary teachers attitudes towards mathematics. International Journal of Science and Mathematics Education. doi:10.1007/s10763-015-9699-1.

    Google Scholar 

  • Lee, J., & Md-Yunus, S. (2016). Investigating children’s abilities to count and make quantitative comparisons. Early Childhood Education Journal, 44, 255–262.

    Article  Google Scholar 

  • Leinhardt, G., & Smith, D. A. (1985). Expertise in mathematics instruction: Subject matter knowledge. Journal of Educational Psychology, 77(3), 247–271.

    Article  Google Scholar 

  • Lewis, C., & Tsuchida, I. (1998). A lesson is like a swiftly flowing river: How research lessons improve Japanese education. American Educator, 22(4), 12–17, 50–52.

    Google Scholar 

  • Lewis Presser, A., Clements, M., Ginsburg, H., & Ertle, B. (2015). Big math for little kids: The effectiveness of a preschool and kindergarten mathematics curriculum. Early Education and Development, 26(3), 399–426.

    Article  Google Scholar 

  • Magargee, S. D., & Beauford, J. E. (2016). Do explicit number names accelerate pre-kindergarteners’ numeracy and place value acquisition? Educational Studies in Mathematics, 92(2), 179–192.

    Article  Google Scholar 

  • Morris, A. K., Hiebert, J., & Spitzer, S. M. (2009). Mathematical knowledge for teaching in planning and evaluating instruction: What can pre-service teachers learn? Journal for Research in Mathematics Education, 40(5), 491–529.

    Google Scholar 

  • Murata, A., & Pothen, E. B. (2011). Lesson study in preservice elementary mathematics courses: Connecting emerging practice and understanding. In L. Hart, A. Alston & A. Murata (Eds.), Lesson study research and practice in mathematics education: Learning together (pp. 103–116). New York: Springer.

    Chapter  Google Scholar 

  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.

    Article  Google Scholar 

  • Simpson, A., & Linder, S. M. (2014). An examination of mathematics professional development opportunities in early childhood settings. Early Childhood Education Journal, 42(5), 335–342.

    Article  Google Scholar 

  • Sims, L., & Walsh, D. (2009). Lesson study with preservice teachers: Lessons from lessons. Teaching and Teacher Education, 25(5), 724–733.

    Article  Google Scholar 

  • Speer, N. M., & Wagner, J. F. (2009). Knowledge needed by a teacher to provide analytic scaffolding during undergraduate mathematics classroom discussions. Journal for Research in Mathematics Education, 40(5), 530–562.

    Google Scholar 

  • Stigler, J. W., & Hiebert, J. (1999). The teaching gap. [Chapter 7]. New York: Free Press.

    Google Scholar 

  • van Es, E. A., & Sherin, M. G. (2002). Learning to notice: Scaffolding new teachers’ interpretations of classroom interactions. Journal of Technology and Teacher Education, 10, 571–576.

    Google Scholar 

  • Wang, A. H. (2010). Optimizing early mathematics experiences for children from low-income families: A study on opportunity to learn mathematics. Early Childhood Education Journal, 37(4), 295–302. doi:10.1007/s10643-009-0353-9.

    Article  Google Scholar 

Download references

Acknowledgements

We acknowledge the support of Mary Immaculate College faculty seed funding that supported this research.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Aisling Leavy.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Leavy, A., Hourigan, M. Using Lesson Study to Support the Teaching of Early Number Concepts: Examining the Development of Prospective Teachers’ Specialized Content Knowledge. Early Childhood Educ J 46, 47–60 (2018). https://doi.org/10.1007/s10643-016-0834-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10643-016-0834-6

Keywords

Navigation