Elementary teachers’ experience of engaging with Teaching Through Problem Solving using Lesson Study

Mathematics Education Research Journal - Tập 35 - Trang 901-927 - 2022
Mairéad Hourigan1, Aisling M. Leavy1
1Department of STEM Education, Mary Immaculate College, University of Limerick, Limerick, Ireland

Tóm tắt

For many decades, problem solving has been a focus of elementary mathematics education reforms. Despite this, in many education systems, the prevalent approach to mathematics problem solving treats it as an isolated activity instead of an integral part of teaching and learning. In this study, two mathematics teacher educators introduced 19 Irish elementary teachers to an alternative problem solving approach, namely Teaching Through Problem Solving (TTP), using Lesson Study (LS) as the professional development model. The findings suggest that the opportunity to experience TTP first-hand within their schools supported teachers in appreciating the affordances of various TTP practices. In particular, teachers reported changes in their beliefs regarding problem solving practice alongside developing problem posing knowledge. Of particular note was teachers’ contention that engaging with TTP practices through LS facilitated them to appreciate their students’ problem solving potential to the fullest extent. However, the planning implications of the TTP approach presented as a persistent barrier.

Tài liệu tham khảo

Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education., 59(5), 389–408. Cai, J. (2003). What research tells us about teaching mathematics through problem solving. In F. Lester (Ed.), Research and issues in teaching mathematics through problem solving (pp. 241–255). National Council for Curriculum and Assessment. Cai, J., & Lester, F. (2010). Why is teaching through problem solving important to children learning? National Council of Teachers of Mathematics. Cajkler, W., Wood, P., Norton, J., Pedder, D., & Xu, H. (2015). Teacher perspectives about lesson study in secondary school departments: A collaborative vehicle for professional learning and practice development. Research Papers in Education, 30(2), 192–213. Chapman, O. (2015). Mathematics teachers’ knowledge for teaching problem solving. LUMAT International Journal on Math Science and Technology Education, 3(1), 19–36. Charalambous, C. Y. (2008). Mathematical knowledge for teaching and the unfolding of tasks in mathematics lessons: Integrating two lines of research. In O. Figueras, J. Cortina, S. Alatorre, T. Rojano, & A. Sepúlveda (Eds.), Proceedings of the 32nd conference of the International Group for the Psychology of Mathematics Education (pp. 281–288). PME. Cheeseman, J. (2018). Teachers’ perceptions of obstacles to incorporating a problem solving style of mathematics into their teaching, In J. Hunter, P. Perger, & L. Darragh (Eds.), Making waves, opening spaces (Proceedings of the 41st annual conference of the Mathematics Education Research Group of Australasia) (pp. 210–217). MERGA. Clarke, D., Cheeseman, J., Roche, A., & Van Der Schans, S. (2014). Teaching strategies for building student persistence on challenging tasks: Insights emerging from two approaches to teacher professional learning. Mathematics Teacher Education and Development, 16(2), 46–70. Creswell, J. W. (2009). Research design- Qualitative, quantitative and mixed methods approaches (3rd ed). Sage. Crespo, S., & Featherstone, H. (2006). Teacher learning in mathematics teacher groups: One math problem at a time. In K. Lynch-Davis & R. L. Rider (Eds.), The work of mathematics teacher educators: Continuing the conversation (pp. 97–115). Association of Mathematics Teacher Educators. Department of Education and Science (DES). (1999). Primary school mathematics curriculum. The Stationery Office. Department of Education and Skills (DES). (2011). Literacy and numeracy for learning and life: The national strategy to improve literacy and numeracy among children and young people 2011–2020. The Stationary Office. Dooley, T., Dunphy, E., & Shiel, G. (2014). Mathematics in early childhood and primary education. Research report 18. National Council for Curriculum and Assessment. Dudley, P., Xu, H., Vermunt, J. D., & Lang, J. (2019). Empirical evidence of the impact of lesson study on students’ achievement, teachers’ professional learning and on institutional and system evolution. European Journal of Education, 54, 202–217. https://doi.org/10.1111/ejed.12337 Dunphy, E., Dooley, T., Shiel, G. (2014). Mathematics in early childhood and primary education. Research report 17. National Council for Curriculum and Assessment. Ertle, B., Chokshi, S., & Fernandez, C. (2001). Lesson planning tool. Available online: https://sarahbsd.files.wordpress.com/2014/09/lesson_planning_tool.pdf Fernandez, C. (2005). Lesson Study: A means for elementary teachers to develop the knowledge of mathematics needed for reform-minded teaching? Mathematical Thinking and Learning, 7(4), 265–289. Fernandez, C., Cannon, J., & Chokshi, S. (2003). A US–Japan lesson study collaboration reveals critical lenses for examining practice. Teaching and Teacher Education, 19, 171–185. Flanagan, B. (2021). Teachers’ understandings of lesson study as a professional development tool, Unpublished thesis, University of Limerick. Glaser, B. G. (1978). Theoretical sensitivity: Advances in the methodology of grounded theory. Sociology Press. Goldenberg, E. P., Shteingold, N., & Feurzig, N. (2001). Mathematical habits of mind for young children. In F. Lester (Ed.), Research and issues in teaching mathematics through problem solving (pp. 15–30). National Council for Curriculum and Assessment. Gutierez, S. B. (2016). Building a classroom-based professional learning community through lesson study: Insights from elementary school science teachers. Professional Development in Education, 42(5), 801–817. Hiebert, J. (2003). Signposts for teaching mathematics through problem solving. In F. Lester (Ed.), Research and issues in teaching mathematics through problem solving (pp. 53–62). National Council for Curriculum and Assessment. Hourigan, M., & Leavy, A. (2015). Geometric growing patterns: What’s the rule? Australian Primary Mathematics Classroom, 20(4), 31–40. Hourigan, M., & Leavy, A. M. (2021). The complexities of assuming the ‘teacher of teachers’ role during Lesson Study. Professional Development in Education. Online first. https://doi.org/10.1080/19415257.2021.1895287 Ingram, N., Holmes, M., Linsell, C., Livy, S., McCormick, M., & Sullivan, P. (2020). Exploring an innovative approach to teaching mathematics through the use of challenging tasks: A New Zealand perspective. Mathematics Education Research Journal, 32(3), 497–522. Kapur, M. (2010). Productive failure in mathematical problem solving. Instructional Science, 38, 523–550. Klein, S., & Leikin, R. (2020). Opening mathematical problems for posing open mathematical tasks: What do teachers do and feel? Educational Studies in Mathematics, 105, 349–365. Koichu, B., Harel, G., & Manaster, A. (2013). Ways of thinking associated with mathematics teachers’ problem posing in the context of division of fractions. Instructional Science, 41(4), 681–698. Lambdin, D. V. (2003). Benefits of teaching through problem solving. In F. Lester (Ed.), Research and issues in teaching mathematics through problem solving (pp. 2–15). National Council for Curriculum and Assessment. Leavy, A., & Hourigan, M. (2018). The role of perceptual similarity, data context and task context when selecting attributes: Examination of considerations made by 5-6 year olds in data modelling environments. Educational Studies in Mathematics. 97(2), 163–183. https://doi.org/10.1007/s10649-017-9791-2 Lesh, R., & Zawojewski, J. (2007). Problem solving and modeling. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 763–804). Charlotte, NC: Information Age. Lester, F. K., Jr. (2013). Thoughts about research on mathematical problem-solving instruction. The Mathematics Enthusiast, 10(1–2), 245–278. 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. Murata, A., Bofferding, L., Pothen, B. E., Taylor, M. W., & Wischnia, S. (2012). Making connections among student learning, content, and teaching: Teacher talk paths in elementary mathematics lesson study. Journal for Research in Mathematics Education, 43(5), 616–650. National Council for Curriculum and Assessment (NCCA). (2016). Background paper and brief for the development of a new primary mathematics curriculum. NCCA. National Council for Curriculum and Assessment (NCCA). (2017). Primary mathematics curriculum. Draft specifications. Junior infant to second class. For Consultation. NCCA. National Council for Curriculum and Assessment (NCCA). (2020). Draft primary curriculum framework. For consultation. Primary curriculum review and development. NCCA. O’Shea, J., & Leavy, A. M. (2013). Teaching mathematical problem-solving from an emergent constructivist perspective: the experiences of Irish primary teachers. Journal of Mathematics Teacher Education, 16(4), 293–318. https://doi.org/10.1007/s10857-013-9235-6 Polya, G. (1957). How to solve it (2nd edition). Doubleday. Russo, J., & Hopkins, S. (2019). Teachers’ perceptions of students when observing lessons involving challenging tasks. International Journal of Science and Mathematics Education, 17(4), 759–779. Russo, J., & Minas, M. (2020). Student attitudes towards learning mathematics through challenging problem solving tasks: “It’s so hard-in a good way.” International Electronic Journal of Elementary Education, 13(2), 215–225. Sakshaug, L. E., & Wohlhuter, K. A. (2010). Journey toward teaching mathematics through problem solving. School Science and Mathematics, 110(8), 397–409. Shiel, G., Kavanagh, L., & Millar, D. (2014). The national assessments of english reading and mathematics: Volume 1 performance report. Educational Research Centre. Singer, F. M., & Voica, C. (2013). A problem-solving conceptual framework and its implications in designing problem-posing tasks. Educational Studies in Mathematics, 83(1), 9–26. Stacey, K. (2018). Teaching Mathematics through Problem Solving. Numeros, 98, 7–18. Stake, R. E. (1995). The art of case study research. Thousand Oaks, CA: Sage Publications. Stipek, D. J., Givvin, K. B., Salmon, J. M., & MacGyvers, V. L. (2001). Teachers’ beliefs and practices related to mathematics instruction. Teaching and Teacher Education, 17(2), 213–226. Strauss, A., & Corbin, J. (1998). Basics of qualitative research: Techniques and procedures for developing grounded theory (2nd ed). Sage. Sullivan, P., Askew, M., Cheeseman, J., Clarke, D., Mornane, A., & Roche, A. (2015). Supporting teachers in structuring mathematics lessons involving challenging tasks. Journal of Mathematics Teacher Education, 18(2), 123–140. Sullivan, P., Bobis, J., Downton, A., Feng, M., Hughes, S., Livy, S., McCormick, M., & Russo, J. (2021). An instructional model to support planning and teaching student centred structured inquiry lessons. Australian Primary Mathematics Classroom, 26(1), 9–13. Sullivan, P., Clarke, D., Cheeseman, J., Mornane, A., Roche, A., Sawatzki, C., & Walker, N. (2014). Students’ willingness to engage with mathematical challenges: Implications for classroom pedagogies. In J. Anderson, M. Cavanagh, & A. Prescott (Eds.), Curriculum in focus: Research guided practice. (Proceedings of the 37th annual conference of the Mathematics Education Research Group of Australasia) (pp. 597–604). MERGA. Sullivan, P., Clarke, D. M., Clarke, B., & O’Shea, H. (2010). Exploring the relationship between task, teacher actions, and student learning. PNA, 4(4), 133–142. Suter, W. N. (2012). Introduction to educational research: A critical thinking approach (2nd ed). Sage. Swan, M. (2006). Designing and using research instruments to describe the beliefs and practices of mathematics teachers. Research in Education, 75(1), 58–70. Takahashi, A. (2006). Characteristics of Japanese mathematics lessons. Paper presented at the APEC International Conference on Innovative Teaching Mathematics through Lesson Study, Tokyo, Japan, January 14–20. https://www.criced.tsukuba.ac.jp/math/sympo_2006/takahashi.pdf Takahashi, A. (2008). Beyond show and tell: neriage for teaching through problem-solving—ideas from Japanese problem-solving approaches for teaching mathematics. Paper presented at the 11th International Congress on Mathematics Education in Mexico (Section TSG 19: Research and Development in Problem Solving in Mathematics Education), Monteree, Mexico. Takahashi, A. (2016). Recent trends in Japanese mathematics textbooks for elementary grades: Supporting teachers to teach mathematics through problem solving. Universal Journal of Educational Research, 4(2), 313–319. Takahashi, A., Lewis, C., & Perry, R. (2013). US lesson study network to spread teaching through problem solving. International Journal for Lesson and Learning Studies, 2(3), 237–255. Takahashi, A., & McDougal, T. (2016). Collaborative lesson research: Maximizing the impact of lesson study. ZDM: Mathematics Education, 48, 513–526. Thompson, A. G. (1985). Teachers’ conceptions of mathematics and the teaching of problem solving. In E. A. Silver (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives (pp. 281–294). Erlbaum. Watanabe, T. (2001). Anticipating children’s thinking: A Japanese approach to instruction. National Council for Curriculum and Assessment. Watson, A., & Ohtani, M. (2015). Task design in mathematics education: An ICMI study 22. Springer International.