Abstract
The purpose of this basic, exploratory study is to examine primary grades (K-2) teachers’ perceptions of the self-efficacy of their students in mathematics, whether or not there is a difference in the self-efficacy between students based on their performance, and to gather information about how teachers are differentiating instruction. Forty teachers completed an online open-ended survey. Data from responses was analyzed through a constant comparative process in order to answer the research questions. Teachers indicated that advanced students generally have a higher mathematical self-efficacy than their peers, therefore possibly influencing advanced students’ potential for higher academic achievement in mathematics. Additionally, many teachers reported using small groups and manipulatives as vehicles to differentiate instruction. However, the convenience sample and data collected warrants further studies to more closely examine the interaction between students’ self-efficacy, teachers’ differentiation, and student achievement.
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References
Bandura, A. (1993). Perceived self-efficacy in cognitive development and functioning. Educational Psychologist, 28, 117–148.
Boaler, J. (2019). Developing Mathematical Mindsets: The need to interact with numbers flexibly and conceptually. American Educator, 42(4), 28–33.
Black, P., Harrison, C., Lee, C., Marshall, B., & Wiliam, D. (2004). Working inside the black box: Assessment for learning in the classroom. Phi Delta Kappan, 86(1), 8–21.
Burnette, J. L., Pollack, J. M., Forsyth, R. B., Hoyt, C. L., Babij, A. D., Thomas, F. N., et al. (2020). A growth mindset intervention: Enhancing students entreprenurial self-efficacy and career development. Entrepreneurship Theory and Practice, Mindset: The New Psychology of Success, 44(5), 878–908.
Christenson, B., & Wager, A. A. (2012). Increasing participation through differentiation. Teaching Children Mathematics, 19(3), 194–200. https://doi.org/10.5951/teacchilmath.19.3.0194
Dweck, C. (2007). Mindset: The new psychology of success. Ballantine Books.
Edins, C. A. (2009). Self-efficacy and self-esteem in gifted and non-gifted students in the elementary school system. [Doctoral Dissertation, Capella University]. ProQuest Dissertations Publishing.
Eysink, T. H. S., Hulsbeek, M., & Gijlers, H. (2017). Supporting primary school teachers in differentiating in the regular classroom. Teaching and Teacher Education, 66, 107–116.
Fast, L. A., Lewis, J. L., Bryant, M. J., Bocian, K. A., Cardullo, R. A., Rettig, M., & Hammond, K. A. (2010). Does math self-efficacy mediate the effect of the perceived classroom environment on standardized math test performance? Journal of Educational Psychology, 102(3), 729–740. https://doi.org/10.1037/a0018863
Galla, B. M., & Wood, J. J. (2012). Emotional self efficacy moderates anxiety-related impairments in math performance in elementary school-age youth. Personality and Individual Differences, 52(2), 118–122. https://doi.org/10.1016/j.paid.2011.09.012
Gavin, M. K., Casa, T. M., Adelson, J. L., Carroll, S. R., Sheffield, L. J., & Spinelli, A. M. (2007). M3: Mentoring mathematical minds—A research-based curriculum for talented elementary students. Journal of Advanced Academics, 18(4), 566–585.
Gutiérrez, R. (2009). Framing equity: Helping students “play the game” and “change the game.” Teaching for Excellence and Equity in Mathematics, 1(1), 4–8.
Kapner, L. (2017). The Myth of the Math Brain. Retrieved October 22, 2018 from http://giftededucationcommunicator.com/gec-spring-2017/the-myth-of-the-math-brain/.
Krutetskii, V. A. (1976). The Psychology of Mathematical Abilities in Schoolchildren, University of Chicago Press, ISBN 0-226-45492-4. Translated from the Russian by Joan Teller; edited by Jeremy Kilpatrick and Izaak Wirszup.
Lewis, W. M., & Colonnese, M. W. (2021). Fostering mathematical creativity through problem posing and three-act tasks. Gifted Child Today, 44(3), 141–150.
Matthews, M. S., & Rhodes, H. A. (2020). Examining identification practices and services for young advanced and gifted learners in selected North Carolina school districts. Journal of Advanced Academics, 1, 1–25.
McMillian, K. (2017). An examination of elementary math anxiety, self-efficacy, and academic achievement. [Doctoral Dissertation, University of North Carolina at Charlotte]. ProQuest LLC.
Merriam, S. B., & Tisdell, E. J. (2016). Qualitative research: A guide to design and implementation (4th ed.). Jossey-Bass.
Mullis, I. V. S., Martin, M. O., & Loveless, T. (2016). 20 Years of TIMSS: International Trends in Mathematics and Science Achievement, Curriculum, and Instruction. Retrieved from: http://timssandpirls.bc.edu/timss2015/international-results/timss2015/wp-content/uploads/2016/T15-20-years-of-TIMSS.pdf.
National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematics success for all. Reston, VA: National Council of Teachers of Mathematics.
National Center for Educational Statistics (NCES). (2018). 2017 NAEP mathematics and reading assessments: Highlighted results at grades 4 and 8 for the nation, states, and districts. Author.
OECD. (2013). PISA 2012 Results: What Students Know and Can Do (Volume I): Student Performance in Mathematics, Reading and Science. Retrieved from: http://www.oecd.org/pisa/keyfindings/pisa-2012-results-overview.pdf
Patton, M. Q. (2002). Two decades of developments in qualitative inquiry: A personal, experiential perspective. Qualitative Social Work, 1(3), 261–283. https://doi.org/10.1177/1473325002001003636
Polly, D. (2021). Advancing equity-based mathematics teaching in the primary grades: The case of two clinical practice experiences. International Journal of Teacher Education and Professional Development, 4(1), 68–88.
Polly, D., & Holshouser, K. (2021). Supporting elementary education teacher candidates’ knowledge and implementation of equity-based practices. PDS Partners: Bridging Research to Practice, 16(3), 42–53.
Polly, D., Wang, C., Martin, C. S., Lambert, R. G., Pugalee, D. K., & Middleton, C. W. (2017). The influence of an internet-based formative assessment tool on primary grades students’ number sense achievement. School Science and Mathematics, 117(3–4), 127–136. https://doi.org/10.1111/ssm.12214
Preckel, F., Schmidt, I., Stumpf, E., Motschenbacher, M., Vogl, K., Scherrer, V., & Schneider, W. (2019). High-ability grouping: Benefits for gifted students’ achievement development without costs in academic self-concept. Child Development, 90(4), 1185–1201. https://doi.org/10.1111/cdev.12996
Rakoczy, K., Pinger, P., Hochweber, J., Klieme, E., Schütze, B., & Besser, M. (2019). Formative assessment in mathematics: Mediated by feedback’s perceived usefulness and students’ self-efficacy. Learning and Instruction, 60(1), 154–165.
Samuels, C. (2014). Teachers’ perspectives of fifth grade students’ attitudes toward mathematics and mathematics achievement. [Doctoral Dissertation, Walden University]. ProQuest Dissertations and Theses.
Tomlinson, C. A. (2001). How to differentiate in mixed-ability classrooms (2nd ed.). ASCD.
van de walle, J., Karp, K., & Bay-Williams, J. (2018). Elementary and middle school Mathematics: Teaching develpmentally (10th Ed). Pearson.
Wiliam, D., & Thompson, M. (2007). Integrating assessment with instruction: What will it take to make it work? In C. A. Dwyer (Ed.), The future of assessment: Shaping teaching and learning (pp. 53–82). Lawrence Erlbaum Associates.
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Appendix A
Appendix A
Survey Questions
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1.
What grade do you teach?
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2.
How long have you been teaching this grade?
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3.
How long have you been teaching overall? What other grades have you taught?
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4.
Have you received any professional development on gifted education or differentiating in mathematics? If so, how much?
Please respond to the questions below in at least a paragraph or more. They include questions about advanced and non-advanced students in math. We ask that you carefully and accurately identify students who are advanced and non-advanced through a variety of methods (Test scores, observations, etc.). Characteristics of advanced students in math include flexibility, curtailment, logical thought, and formalization (Krutetskii, 1976). Here are Krutetskii’s definitions of these characteristics:
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Flexibility: “Being able to switch strategies in solving a problem easily.”
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Curtailment: “Being able to skip explicit steps when problem solving as though looking at the solution as a whole instead of a series of steps.”
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Logical Thought: “Looking at the world from a logical perspective so they can filter all incoming data through this lens.”
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Formalization: “The ability to see the overall structure of a problem and to make generalizations only from a few examples.”
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How would you define self-efficacy for math?
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6.How would you describe the overall mathematical self-efficacy of the students in your classroom?
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7.Is there a difference in self-efficacy between students who are advanced and non-advanced?
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8.How does self-efficacy correlate with academic performance in your classroom with both groups of students?
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9.What teaching methods do you use to differentiate for both advanced and non-advanced students in mathematics?
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10.What strategies do you use to assist advanced and non-advanced students in mathematics?
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McNeill, H., Polly, D. Exploring Primary Grades Teachers’ Perceptions of Their Students’ Mathematics Self-Efficacy and How They Differentiate Instruction. Early Childhood Educ J 51, 79–88 (2023). https://doi.org/10.1007/s10643-021-01281-3
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DOI: https://doi.org/10.1007/s10643-021-01281-3