Teaching Mathematics for Conceptual Understanding: Teachers’ Beliefs and Practices and the Role of Constraints

A major influence on mathematics teachers’ instruction is their beliefs. However, teachers’ instructional practices do not always neatly align with their beliefs because of factors perceived as constraints. The purpose of this article is to introduce a new approach for examining the relationship between teachers’ beliefs and practices, an approach that focuses on specific instructional practices that support the development of students’ conceptual understanding and on mismatches that occur between what teachers believe to be important and what they report actually doing in the classroom. We also examine the relationship between teachers’ self-reported constraints and mismatches between teachers’ beliefs and practices.

Contributor Notes

Bilge Yurekli, Learning Research and Development Center, University of Pittsburgh, 3939 O’Hara Street, Pittsburgh, PA 15260; yureklib@pitt.edu

Mary Kay Stein, Learning Research and Development Center, University of Pittsburgh, 3939 O’Hara Street, Pittsburgh, PA 15260; mkstein@pitt.edu

Richard Correnti, Learning Research and Development Center, University of Pittsburgh, 3939 O’Hara Street, Pittsburgh, PA 15260; rcorrent@pitt.edu

Zahid Kisa, Learning System Institute, Florida State University, 2000 Levy Avenue, Tallahassee, FL 32310; zahidkisa@gmail.com

(Corresponding author is Yurekli yureklib@pitt.edu)(Corresponding author is Stein mkstein@pitt.edu)(Corresponding author is Correnti rcorrent@pitt.edu)(Corresponding author is Kisa zahidkisa@gmail.com)
Journal for Research in Mathematics Education
  • 1.

    AgodiniR. & HarrisB. (2016). How teacher and classroom characteristics moderate the effects of four elementary math curricula. The Elementary School Journal117(2) 216236. doi:10.1086/688927

    • Search Google Scholar
    • Export Citation
  • 2.

    AndersonJ. WhiteP. & SullivanP. (2005). Using a schematic model to represent influences on, and relationships between, teachers’ problem-solving beliefs and practices. Mathematics Education Research Journal17(2) 938. doi:10.1007/BF03217414

    • Search Google Scholar
    • Export Citation
  • 3.

    BostonM. D. & SmithM. S. (2009). Transforming secondary mathematics teaching: Increasing the cognitive demands of instructional tasks used in teachers’ classrooms. Journal for Research in Mathematics Education40(2) 119156.

    • Search Google Scholar
    • Export Citation
  • 4.

    BrayW. S. (2011). A collective case study of the influence of teachers’ beliefs and knowledge on error-handling practices during class discussion of mathematics. Journal for Research in Mathematics Education42(1) 238. doi:10.5951/jresematheduc.42.1.0002

    • Search Google Scholar
    • Export Citation
  • 5.

    BuehlM. M. & BeckJ. S. (2015). The relationship between teachers’ beliefs and teachers’ practices. In H. Fives & M. G. Gill (Eds.) International handbook of research on teachers’ beliefs (pp. 6684). New York, NY: Routledge. doi:10.4324/9780203108437

    • Search Google Scholar
    • Export Citation
  • 6.

    CarneyM. B. BrendefurJ. L. ThiedeK. HughesG. & SuttonJ. (2016). Statewide mathematics professional development: Teacher knowledge, self-efficacy, and beliefs. Educational Policy30(4) 539572. doi:10.1177/0895904814550075

    • Search Google Scholar
    • Export Citation
  • 7.

    ClarkL. M. DePiperJ. N. FrankT. J. NishioM. CampbellP. F. SmithT. M. ChoiY. (2014). Teacher characteristics associated with mathematics teachers’ beliefs and awareness of their students’ mathematical dispositions. Journal for Research in Mathematics Education45(2) 246284. doi:10.5951/jresematheduc.45.2.0246

    • Search Google Scholar
    • Export Citation
  • 8.

    Copur-GencturkY. (2015). The effects of changes in mathematical knowledge on teaching: A longitudinal study of teachers’ knowledge and instruction. Journal for Research in Mathematics Education46(3) 280330. doi:10.5951/jresematheduc.46.3.0280

    • Search Google Scholar
    • Export Citation
  • 9.

    CrossD. I. (2009). Alignment, cohesion, and change: Examining mathematics teachers’ belief structures and their influence on instructional practices. Journal of Mathematics Teacher Education12(5) 325346. doi:10.1007/s10857-009-9120-5

    • Search Google Scholar
    • Export Citation
  • 10.

    Cross FrancisD. I. (2015). Dispelling the notion of inconsistencies in teachers’ mathematics beliefs and practices: A 3-year case study. Journal of Mathematics Teacher Education18(2) 173201. doi:10.1007/s10857-014-9276-5

    • Search Google Scholar
    • Export Citation
  • 11.

    Cross FrancisD. RapackiL. & EkerA. (2015). The individual, the context, and practice: A review of the research on teachers’ beliefs related to mathematics. In H. Fives & M. G. Gill (Eds.) International handbook of research on teachers’ beliefs (pp. 336352). New York, NY: Routledge. doi:10.4324/9780203108437

    • Search Google Scholar
    • Export Citation
  • 12.

    FivesH. & BuehlM. M. (2012). Spring cleaning for the “messy” construct of teachers’ beliefs: What are they? Which have been examined? What can they tell us? In K. R. Harris S. Graham T. Urdan S. Graham J. R. Royer & M. Zeidner (Eds.) APA Educational Psychology Handbook: Vol 2. Individual differences and cultural and contextual factors (pp. 471499). Washington, DC: American Psychological Association. doi:10.1037/13274-019

    • Search Google Scholar
    • Export Citation
  • 13.

    HauckK. & StreetA. (2006). Performance assessment in the context of multiple objectives: A multivariate multilevel analysis. Journal of Health Economics25(6) 10291048. doi:10.1016/j.jhealeco.2005.07.009

    • Search Google Scholar
    • Export Citation
  • 14.

    HiebertJ. S. & GrouwsD. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. K. Lester Jr. (Ed.) Second handbook of research on mathematics teaching and learning (pp. 371404). Charlotte, NC: Information Age.

    • Search Google Scholar
    • Export Citation
  • 15.

    HoffmanL. & RovineM. J. (2007). Multilevel models for the experimental psychologist: Foundations and illustrative examples. Behavior Research Methods39(1) 101117. doi:10.3758/BF03192848

    • Search Google Scholar
    • Export Citation
  • 16.

    LobatoJ. ClarkeD. & EllisA. B. (2005). Initiating and eliciting in teaching: A reformulation of telling. Journal for Research in Mathematics Education36(2) 101136.

    • Search Google Scholar
    • Export Citation
  • 17.

    LuiA. M. & BonnerS. M. (2016). Preservice and inservice teachers’ knowledge, beliefs, and instructional planning in primary school mathematics. Teaching and Teacher Education56113. doi:10.1016/j.tate.2016.01.015

    • Search Google Scholar
    • Export Citation
  • 18.

    National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: Author.

  • 19.

    PajaresM. F. (1992). Teachers’ beliefs and educational research: Cleaning up a messy construct. Review of Educational Research62(3) 307332. doi:10.3102/00346543062003307

    • Search Google Scholar
    • Export Citation
  • 20.

    PhilippR. A. (2007). Mathematics teachers’ beliefs and affect. In F. K. Lester Jr. (Ed.) Second handbook of research on mathematics teaching and learning (pp. 257315). Charlotte, NC: Information Age.

    • Search Google Scholar
    • Export Citation
  • 21.

    RaudenbushS. W. & BrykA. S. (2002). Hierarchical linear models: Applications and data analysis methods. Thousand Oaks, CA: Sage.

  • 22.

    RaymondA. M. (1997). Inconsistency between a beginning elementary school teacher’s mathematics beliefs and teaching practice. Journal for Research in Mathematics Education28(5) 550576. doi:10.2307/749691

    • Search Google Scholar
    • Export Citation
  • 23.

    SkottJ. (2015). The promises, problems, and prospects of research on teachers’ beliefs. In H. Fives & M. G. Gill (Eds.) International handbook of research on teachers’ beliefs (pp. 1330). New York, NY: Routledge. doi:10.4324/9780203108437

    • Search Google Scholar
    • Export Citation
  • 24.

    SonJ.-W. & KimO.-K. (2016). Curriculum enactment patterns and associated factors from teachers’ perspectives. Mathematics Education Research Journal28(4) 585614. doi:10.1007/s13394-016-0181-3

    • Search Google Scholar
    • Export Citation
  • 25.

    SteinM. K. CorrentiR. MooreD. RussellJ. L. & KellyK. (2017). Using theory and measurement to sharpen conceptualizations of mathematics teaching in the Common Core era. AERA Open3(1) 120. doi:10.1177/2332858416680566

    • Search Google Scholar
    • Export Citation
  • 26.

    SteinM. K. GroverB. W. & HenningsenM. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal33(2) 455488. doi:10.3102/00028312033002455

    • Search Google Scholar
    • Export Citation
  • 27.

    SztajnP. (2003). Adapting reform ideas in different mathematics classrooms: Beliefs beyond mathematics. Journal of Mathematics Teacher Education6(1) 5375. doi:10.1023/A:1022171531285

    • Search Google Scholar
    • Export Citation
  • 28.

    ThompsonA. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. A. Grouws & NCTM (Eds.) Handbook of research on mathematics teaching and learning (pp. 127146). Reston, VA: NCTM.

    • Search Google Scholar
    • Export Citation
  • 29.

    WarshauerH. K. (2015). Productive struggle in middle school mathematics classrooms. Journal of Mathematics Teacher Education18(4) 375400. doi:10.1007/s10857-014-9286-3

    • Search Google Scholar
    • Export Citation
  • 30.

    WilhelmA. G. (2014). Mathematics teachers’ enactment of cognitively demanding tasks: Investigating links to teachers’ knowledge and conceptions. Journal for Research in Mathematics Education45(5) 636674. doi:10.5951/jresematheduc.45.5.0636

    • Search Google Scholar
    • Export Citation

Metrics

All Time Past Year Past 30 Days
Abstract Views 285 285 54
Full Text Views 240 240 25
PDF Downloads 176 176 15
EPUB Downloads 0 0 0