Professional Development to Support Elementary Mathematics and Co-teaching Practices: Collaborations Between General and Special Education
Keywords:
Mathematics teacher education research, Elementary school , Co-teaching, Professional development, Special educationAbstract
Professional development is necessary to support and empower teachers in meeting the high stakes demands of mathematics teaching and to ensure equitable, accessible, and high-quality instruction for all students. Using the Interconnected Model of Professional, we designed and implemented a longitudinal, multi-faceted professional development project for teams of elementary general education and special education educators to enhance instruction in their inclusive elementary mathematics classrooms. Focused on high-quality mathematics tasks and co-teaching models, we explored changes in both instructional and collaborative practices. Findings indicated statistically significant increases in educators’ mathematics content knowledge and pedagogical content knowledge. Additionally, statistically significant improvements in observed teacher facilitation, student engagement, and co-teaching practices were found. Implications for practice and research are discussed.
References
Assessment and Learning in Knowledge Space. (n.d.). McGraw-Hill Education. https://www.aleks.com
Atteberry, A., Loeb, S., & Wyckoff, J. (2017). Teacher churning: Reassignment rates and implications for student achievement. Educational Evaluation and Policy Analysis, 39(1), 3–30. https://doi.org/10.3102/0162373716659929
Bell, C. A., Wilson, S. M., Higgins, T., & McCoach, D. B. (2010). Measuring the effects of professional development on teacher knowledge: The case of developing mathematical ideas. Journal for Research in Mathematics Education, 41(5), 479–512. http://www.jstor.org/stable/41110411
Borko, H. (2004). Professional development and teacher learning: Mapping the terrain. Educational Researcher, 33(8), 3–15. https://doi.org/10.3102/0013189X033008003
Borko, H., Jacobs, J., Koellner, K., & Swackhamer, L. E. (2015). Mathematics professional development: Improving teaching using the problem-solving cycle and leadership preparation models. Teachers College Press.
Boston, M. D., & Smith, M. S. (2011). A ‘task-centric approach’ to professional development: Enhancing and sustaining mathematics teachers’ ability to implement cognitively challenging mathematical tasks. ZDM Mathematics Education, 43(6–7), 965–977. https://doi.org/10.1007/s11858-011-0353-2
Brendefur, J., Champion, J., Strother, S., Thiede, K. W., & Osguthorpe, R. D. (2021). The effects of mathematics professional development on elementary student achievement. International Journal of Science and Mathematics Education, 20(6), 1079–1097. https://doi.org/10.1007/s10763-021-10184-z
Caddle, M. C., Bautista, A., Brizuela, B. M., & Sharpe, S. T. (2016). Evaluating mathematics teachers' professional development motivations and needs. Journal of Research in Mathematics Education, 5(2), 112–134. http://dx.doi.org/10.17583/redimat.2016.2093
Clarke, D. J. (1988). Realistic assessment. In D. Firth (Ed.), Maths counts—who cares? (pp. 187–192). Mathematical Association of Victoria.
Clarke, D., & Hollingsworth, H. (2002). Elaborating a model of teacher professional growth. Teaching and Teacher Education, 18(8), 947–967. https://doi.org/10.1016/S0742-051X(02)00053-7
Cohen, J. (1969). Statistical power analysis for behavior sciences. Academic Press.
Darling-Hammond, L., Hyler, M. E., & Gardner, M. (2017). Effective teacher professional development. Learning Policy Institute.
Desimone, L. M. (2009). Improving impact studies of teachers’ professional development: Toward better conceptualizations and measures. Educational Researcher, 38(3), 181–199. https://doi.org/10.3102/0013189X08331140
Every Student Succeeds Act, Pub. L. No. 114–95. (2015).
Faulkner, V. N., & Cain, C. R. (2013). Improving the mathematical content knowledge of general and special educators: Evaluating a professional development module that focuses on number sense. Teacher Education and Special Education, 36(2), 115–131. https://doi.org/10.1177/0888406413479613
Flores, A. (2007). Examining disparities in mathematics education: Achievement gap or opportunity gap? The High School Journal, 91(1), 29–42.
Friend, M. & Cook, L. (2017). Interactions: Collaboration skills for school professionals (8th ed.). Pearson Education.
Fullan, M. (1992). Successful school improvement: The implementation perspective and beyond. McGraw-Hill Education (UK).
Gee, D., & Whaley, J. (2016). Learning together: Practice-centred professional development to enhance mathematics instruction. Mathematics Teacher Education and Development, 18(1), 87–99.
Gleason, J., Livers, S.D., & Zelkowski, J. (2015). Mathematics classroom observation protocol for practices: Descriptors manual. http://jgleason.people.ua.edu/mcop2.html
Gleason, J., Livers, S. D., & Zelkowski, J. (2017). Mathematics classroom observation protocol for practices (MCOP2): A validation study. Investigations in Mathematics Learning, 9(3), 111–129. https://doi.org/10.1080/19477503.2017.1308697
González, G., & Vargas, G. E. (2020). Teacher noticing and reasoning about student thinking in classrooms as a result of participating in a combined professional development intervention. Mathematics Teacher Education and Development, 22(1), 5–32. https://mted.merga.net.au/index.php/mted/article/view/449
Goos, M., Doles, S., & Makar, K. (2007). Designing professional development to support teachers' learning in complex environments. Mathematics Teacher Education and Development, 8, 23–47.
Greenstein, S., & Baglieri, S. (2018). Imagining mathematical thinking for inclusive curriculum: A conversation. Investigations in Mathematics Learning, 10(3), 133–144. https://doi.org/10.1080/19477503.2018.1467091
Gregory, G. & Chapman, C. (2002). Differentiated instructional strategies: One size doesn’t fit all. Corwin Press.
Griffin, C. C., Dana, N. F., Pape, S. J., Algina, J., Bae, J., Prosser, S. K., & League, M. B. (2018). Prime online: Exploring teacher professional development for creating inclusive elementary mathematics classrooms. Teacher Education and Special Education, 41(2), 121–139. https://doi.org/10.1177/0888406417740702
Grossman, P., Hammerness, K., & McDonald, M. (2009). Redefining teaching, re‐imagining teacher education. Teachers and Teaching: Theory and Practice, 15(2), 273–289. https://doi.org/10.1080/13540600902875340
Guskey, T. R. (2000). Evaluating professional development. Corwin Press.
Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406. https://doi.org/10.3102/00028312042002371
Hill, H. C., Schilling, S. G., & Ball, D. L. (2004) Developing measures of teachers’ mathematics knowledge for teaching. The Elementary School Journal, 105(1), 11–30. https://doi.org/10.1086/428763
Hilton, A., Hilton, G., Dole, S., & Goos, M. (2015). School leaders as participants in teachers’ professional development: The impact on teachers’ and school leaders’ professional growth. Australian Journal of Teacher Education, 40(12), 104–125. http://dx.doi.org/10.14221/ajte.2015v40n12.8
Harbour, K. E. & Livers, S. D. (2018). Using coaching cycles to transfer and sustain effective instructional practices. In T. E. Hodges, G. J. Roy, & A. M. Tyminski, (Eds.), Proceedings of the 40th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 374–377). Greenville, SC.
Individuals with Disabilities Education Act, 20 United States Code (U.S.C.) § 1400 (2004).
Ingvarson, L., Meiers, M. & Beavis, A. (2005). Factors affecting the impact of professional development programs on teachers’ knowledge, practice, student outcomes & efficacy. Education Policy Analysis Archives, 13(10), 1–28. https://doi.org/10.14507/epaa.v13n10.2005
Jones, K., & Pepin, B. (2016). Research on mathematics teachers as partners in task design. Journal of Mathematics Teacher Education, 19(2–3), 105–121. https://doi.org/10.1007/s10857-016-9345-z
Joyce, B., & Showers, B. (2002). Student achievement through professional development. Designing training and peer coaching: Our need for learning. Association for Supervision and Curriculum Development.
Korthagen, F. A., & Kessels, J. P. (1999). Linking theory and practice: Changing the pedagogy of teacher education. Educational Researcher, 28(4), 4–17. https://doi.org/10.3102/0013189X028004004
Lambert, R., & Tan, P. (2017). Conceptualizations of students with and without disabilities as mathematical problem solvers in educational research: A critical review. Education Sciences, 7(2), 51. https://doi.org/10.3390/educsci7020051
Learning Mathematics for Teaching Project. (2011). Measuring the mathematical quality of instruction. Journal of Mathematics Teacher Education, 14(1), 25–47. https://doi.org/10.1007/s10857-010-9140-1
Lester, F. K. (2003). Teaching mathematics through problem solving: Prekindergarten-Grade 6. National Council of Teachers of Mathematics.
Livers, S. D. (2022). A whole school agreement: Professional learning with a focus on environmental STEM. Investigations in Mathematics Learning, 14(1), 49–62. https://doi.org/10.1080/19477503.2021.2023843
Maccini, P. & Gagnon, J. C. (2002). Perceptions and applications of NCTM standards by special and general teachers. Exceptional Children, 68(3), 325–344. https://doi.org/10.1177/001440290206800303
Maccini, P. & Gagnon, J. C. (2006). Mathematics instructional practices and assessment accommodations by secondary special and general educators. Exceptional Children, 72(2), 217–234. https://doi.org/10.1177/001440290607200206
McKenna, J. W., Shin, M., & Ciullo, S. (2015). Evaluating reading and mathematics instruction for students with learning disabilities: A synthesis of observation research. Learning Disability Quarterly, 38(4), 195–207. https://doi.org/10.1177/0731948714564576
Murawski, W. W., & Lochner, W. W. (2011). Observing co-teaching: What to ask for, look for, and listen for. Intervention in School and Clinic, 46(3), 174–183. https://doi.org/10.1177/1053451210378165
National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. National Council of Teachers of Mathematics.
No Child Left Behind Act of 2001, Pub. L. No. 107–110, 20 U.S.C. 6301 (2002).
Novak, D., & Knowles, J. G. (1992, April). Life histories and the transition to teaching as a second career. Paper presented at the annual meeting of the American Educational Research Association, Chicago, IL.
Office of Special Education and Rehabilitative Services. (2018). 40th Annual Report to Congress on the Implementation of the Individuals with Disabilities Education Act, 2018. Office of Special Education Programs, US Department of Education.
Opfer, V. D., Pedder, D. G., & Lavicza, Z. (2011). The role of teachers’ orientation to learning in professional development and change: A national study of teachers in England. Teaching and Teacher Education, 27(2),
–453. https://doi.org/10.1016/j.tate.2010.09.014
Pancsofar, N., & Petroff, J. G. (2013). Professional development experiences in co-teaching: Associations with teacher confidence, interests, and attitudes. Teacher Education and Special Education, 36(2), 83–96. https://doi.org/10.1177/0888406412474996
Pancsofar, N., & Petroff, J. G. (2016). Teachers’ experiences with co-teaching as a model for inclusive education. International Journal of Inclusive Education, 20(10), 1043–1053. https://doi.org/10.1080/13603116.2016.1145264
Pearl, C. E., & Miller, K. J. (2007). Co-taught middle school mathematics classrooms: Accommodations and enhancements for students with specific learning disabilities. Focus on Learning Problems in Mathematics, 29(2),1–20.
Perry, E., & Boylan, M. (2018). Developing the developers: Supporting and researching the learning of professional development facilitators. Professional Development in Education, 44, 254–271. https://doi.org/10.1080/19415257.2017.1287767
Polly, D., Neale, H., & Pugalee, D. K. (2014). How does ongoing task-focused mathematics professional development influence elementary school teachers’ knowledge, beliefs and enacted pedagogies? Early Childhood Education Journal, 42(1), 1–10. https://doi.org/10.1007/s10643-013-0585-6
Richardson, J. T. E. (2011). Eta squared and partial eta squared as measures of effect size in educational research. Educational Research Review, 6(2), 135–147. https://doi.org/10.1016/j.edurev.2010.12.001
Scruggs, T. E., Mastropieri, M. A., & McDuffie, K. A. (2007). Co-teaching in inclusive classrooms: A metasynthesis of qualitative research. Exceptional Children, 73(4), 392–416. https://doi.org/10.1177/001440290707300401
Solis, M., Vaughn, S., Swanson, E., & McCulley, L. (2012). Collaborative models of instruction: The empirical foundations of inclusion and co-teaching. Psychology in the Schools, 49, 498–510. https://doi.org/10.1002/pits.21606
Spangler, D. A. & Wanko, J. J. (2017). Enhancing classroom practice with research behind Principles to Actions. National Council of Teachers of Mathematics.
Stein, M. K., Smith, M., Henningsen, M., & Silver, E. (2009). Implementing standards-based mathematics instruction: A casebook for professional development (2nd ed.). Teachers College Press.
Swackhamer, L. E., Koellner, K., Basile, C., & Kimbrough, D. (2009). Increasing the self-efficacy of inservice teachers through content knowledge. Teacher Education Quarterly, 36(2), 63–78. http://www.jstor.org/stable/23479252
Swan, M. (2006). Designing and using research instruments to describe the beliefs and practices of mathematics teachers. Research in Education, 75(1), 58–70. https://doi.org/10.7227/RIE.75.5
Swars, S. L., & Chestnutt, C. (2016). Transitioning to the Common Core State Standards for Mathematics: A mixed methods study of elementary teachers’ experiences and perspectives. School Science and Mathematics, 116(4), 212–224. https://doi.org/10.1111/ssm.12171
Tan, P. (2016). Developing mathematical understanding and students with emotional and behavioral disorders: A review of the literature. Emotional and Behavioral Difficulties, 21(4), 361–376. https://doi.org/10.1080/13632752.2016.1201639
Tomlinson, C. A. (2017). How to differentiate instruction in academically diverse classrooms (3rd ed.). Association for Supervision and Curriculum Development.
Villa, R. A., Thousand, J. S., & Nevin, A. I. (2013). A guide to co-teaching: New lessons and strategies. Corwin.
Watson, S. (2014). The impact of professional development on mathematics teachers' beliefs and practices [Doctoral dissertation, The University of Nottingham].
Weiss, I. R., & Pasley, J. D. (2006). Scaling up instructional improvement through teacher professional development: Insights from the local systemic change initiative. CPRE Policy Briefs. RB-44. Consortium for Policy Research in Education.
Widjaja, W., Vale, C., Groves, S., & Doig, B. (2017). Teachers’ professional growth through engagement with lesson study. Journal of Mathematics Teacher Education, 20, 357–383. https://doi.org/10.1007/s10857-015-9341-8
Zwart, R. C., Wubbels, T., Bergen, T. C. M. & Bolhuis, S. (2007). Experienced teacher learning within the context of reciprocal peer coaching. Teachers and Teaching, 13, 165–187. https://doi.org/10.1080/13540600601152520
