Skip to main content
SpringerLink
Log in

(Mis)alignment between noticing and instructional quality: the role of psychological and cognitive constructs

  • Published:
Journal of Mathematics Teacher Education Aims and scope Submit manuscript

Abstract

In this study, we investigated the relationship between teachers’ post-instruction noticing (PIN) and the quality of their mathematics instruction. We analyzed the conversations of elementary teachers around five coached lessons and scored their level of post-instruction noticing and the mathematical quality of the instruction of the lesson. We compared teachers’ PIN levels with their instructional quality, using scores from the Mathematical Quality of Instruction (MQI) rubric, for each coached lesson. There was both alignment and discrepancies between the level of PIN and MQI scores. Explorations of the cognitive and psychological constructs that seemed to influence teacher’s noticing showed that mathematical knowledge for teaching (MKT), efficacy, beliefs, emotions, and identity was influential on teachers’ PIN although they seemed to influence teachers differently. In some cases, the constructs appeared to support attentiveness to students’ thinking and in other cases they did not. We discuss implications for professional development and future research on teachers’ noticing.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

Notes

  1. We acknowledge here that the connection between IMN and teaching quality made by Jacobs et al., (2010) is a theoretical one. However, in this paper, we define teaching quality along specific items and dimensions of the Mathematical Quality of Instruction (MQI) Instrument (Hill et al., 2014), which explicitly captures teachers’ abilities to identify and attending to students’ productions. Thus, for the purposes of this study our alignment between IMN and teacher quality is specifically defined by MQI dimension Working with Students and Mathematics.

References

  • Amador, J. M., Carter, I., & Hudson, R. A. (2016). Analyzing preservice mathematics teachers’ professional noticing. Action in Teacher Education, 38(4), 371–383. https://doi.org/10.1080/01626620.2015.1119764

    Article  Google Scholar 

  • Anantharajan, M. (2020). Teacher noticing of mathematical thinking in young children’s representations of counting. Journal for Research in Mathematics Education, 51(3), 268–300.

    Article  Google Scholar 

  • Askew, M., & Venkat, H. (2017). “I hate maths”: Changing primary school teachers’ relationship with mathematics. In U. X. Eligio (Ed.), Understanding emotions in mathematical thinking and learning (pp. 339–354). Elsevier Inc.

  • Ayalon, A., & Herskovich, R. (2018). Mathematics teachers attention to potential classroom situations of argumentation. The Journal of Mathematical Behavior, 49, 163–173. https://doi.org/10.1016/j.jmathb.2017.11.010

    Article  Google Scholar 

  • Ball, D. L., & Cohen, D. K. (1999). Developing practice, developing practitioners: Toward a practice-based theory of professional education. In G. Sykes & L. Darling-Hammond (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 3–32). Jossey Bass.

  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching. Journal of Teacher Education, 59(5), 389–407. https://doi.org/10.1177/0022487108324554

    Article  Google Scholar 

  • Bartlett, F. C. (1932). Remembering: A study in experimental and social psychology. Cambridge University Press.

    Google Scholar 

  • Biza, I., Nardi, E., & Zachariades, T. (2007). Using tasks to explore teacher knowledge in situation-specific contexts. Journal of Mathematics Teacher Education, 10(4–6), 301–309. https://doi.org/10.1007/s10857-007-9043-y

    Article  Google Scholar 

  • Brookfield, S. (2017). Becoming a critically reflective teacher, 2nd ed. Jossey Bass.

  • Brown, A. B., Westenskow, A., & Moyer-Packenham, P. S. (2011). Elementary pre-service teachers: Can they experience mathematics teaching anxiety without having mathematics anxiety? Issues in the Undergraduate Mathematics Preparation of School Teachers, 5, 1–14.

    Google Scholar 

  • Cai, J., Magone, M. E., Wang, N., & Lane, S. (1996). A cognitive analysis of QUASAR’s mathematics performance assessment tasks and their sensitivity to measuring changes in middle school students’ thinking and reasoning. Research in Middle Level Education Quarterly, 19(3), 63–94. https://doi.org/10.1080/10848959.1996.11670075

    Article  Google Scholar 

  • Coleman, N., & Williams, P. Y. (2015). Looking for my self: Identity-driven attention allocation. Journal of Consumer Psychology, 25, 504–511.

    Article  Google Scholar 

  • Cross, D. (2009). Alignment, cohesion and change: Examining mathematics teachers’ belief structure and its influence on instructional practice. Journal of Mathematics Teacher Education, 12(5), 325–346.

  • Cross Francis, D. (2015). Dispelling the notion of inconsistencies in teachers’ mathematics beliefs and practices: A three-year case study. Journal of Mathematics Teacher Education, 18(2), 173–201.

  • Cross Francis, D., Eker, A., Lloyd, K., Lui, J., & Alhaayan, A. (2017). Exploring the relationship between teachers’ noticing, mathematical knowledge for teaching, emotions and efficacy. In E. Galindo & J. Newton (Eds.), Proceedings of the 39th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 122–1225). Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators.

  • Cross Francis, D., Eker, A., Lloyd, K., Lui, J., & Alhaayan, A. (2018). High-quality instruction ≠ High-level noticing: Examining factors that influence teachers’ noticing. 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. 1020–1027). Greenville, SC: University of South Carolina & Clemson University.

  • Cross Francis, D., Hong J,. Liu, J., Eker, A., Lloyd, K., Bharaj, P. K., & Jeon, M. (2020). The dominance of blended emotions: A qualitative study of elementary teachers’ emotions related to mathematics teaching. Frontiers in Psychology, 11, 1865. https://doi.org/10.3389/fpsyg.2020.01865.

  • da Ponte, J. P. (2011). Teachers’ knowledge, practice, and identity: Essential aspects of teachers’ learning. Journal of Mathematics Teacher Education, 14(6), 413–417. https://doi.org/10.1007/s10857-011-9195-7

    Article  Google Scholar 

  • Dick, L. K. (2017). Investigating the relationship between professional noticing and specialized content knowledge. In E. O. Schack, M. H. Fisher, & J. A. Wilhelm (Eds.), Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 339–358). Springer.

    Chapter  Google Scholar 

  • Ding, L., & Domínguez, H. (2016). Opportunities to notice: Chinese prospective teachers noticing students’ ideas in a distance formula lesson. Journal of Mathematics Teacher Education, 19(4), 325–347. https://doi.org/10.1007/s10857-015-9301-3

    Article  Google Scholar 

  • Dreher, A., & Kuntze, S. (2015). Teachers’ professional knowledge and noticing: The case of multiple representations in the mathematics classroom. Educational Studies in Mathematics, 88(1), 89–114. https://doi.org/10.1007/s10649-014-9577-8

    Article  Google Scholar 

  • Emmer, E. T., & Stough, L. M. (2001). Classroom management: A critical part of educational psychology, with implications for teacher education. Educational Psychologist, 36(2), 103–112.

    Article  Google Scholar 

  • Erickson, F. (2011). On noticing teacher noticing. In M. Sherin, R. Phillip, & V. Jacobs (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 17–34). Routledge.

    Google Scholar 

  • Ernest, P. (1989). The knowledge, beliefs and attitudes of the mathematics teacher: A model. Journal of Education for Teaching, 15(1), 13–33. https://doi.org/10.1080/0260747890150102

    Article  Google Scholar 

  • Evans, C. O. (1970). The subject of consciousness. George Allen & Unwin.

    Google Scholar 

  • Fives, H., & Buehl, M. M. (2011). 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. M. Royer, & M. Zeidner (Eds.) APA educational psychology handbook, Vol 2: Individual differences and cultural and contextual factors. (pp. 471–499). American Psychological Association.

  • Fives, H., & Gill, M. G. (Eds.). (2015). International handbook of research on teachers’ beliefs. Routledge.

  • Franke, M. L., Carpenter, T. P., Levi, L., & Fennema, E. (2001). Capturing teachers’ generative change: A follow-up study of professional development in mathematics. American Educational Research Journal, 38(3), 653–689. https://doi.org/10.3102/00028312038003653

    Article  Google Scholar 

  • Frenzel, A. C., Pekrun, R., Goetz, T., Daniels, L. M., Durksen, T. L., Becker-Kurz, B., & Klassen, R. M. (2016). Measuring teachers’ enjoyment, anger, and anxiety: The Teacher Emotions Scales (TES). Contemporary Educational Psychology, 46, 148–163. https://doi.org/10.1016/j.cedpsych.2016.05.003

    Article  Google Scholar 

  • Gresham, G. (2009). An examination of mathematics teacher efficacy and mathematics anxiety in elementary pre-service teachers. The Journal of Classroom Interaction, 44(2), 22–34.

    Google Scholar 

  • Guskey, T. R. (1988). Teacher efficacy, self-concept, and attitudes toward the implementation of instructional innovation. Teaching and Teacher Education, 4(1), 63–69. https://doi.org/10.1016/0742-051X(88)90025-X

    Article  Google Scholar 

  • Hiebert, J., Carpenter, T., Fennema, E., Fuson, K., Wearne, D., Murray, H., Olivier, A., & Human, P. (1997). Making sense: Teaching and learning mathematics with understanding. Heinemann.

    Google Scholar 

  • Hill, H. C., Blunk, M. L., Charalambous, C. Y., Lewis, J. M., Phelps, G. C., Sleep, L., & Ball, D. L. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26(4), 430–511. https://doi.org/10.1080/07370000802177235

    Article  Google Scholar 

  • Holland, D., Lachicotte, W., Skinner, D., & Cain, C. (1998). Agency and identity in cultural worlds. Harvard University Press.

    Google Scholar 

  • Hong, J. Y. (2010). Pre-service and beginning teachers’ professional identity and its relation to dropping out of the profession. Teaching and Teacher Education, 26(8), 1530–1543. https://doi.org/10.1016/j.tate.2010.06.003

    Article  Google Scholar 

  • Izadinia, M. (2013). A review of research on student teachers’ professional identity. British Educational Research Journal, 39(4), 694–713. https://doi.org/10.1080/01411926.2012.679614

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Kilic, H., Cross, D., Ersoz, A., Mewborn, D., May, D., & Kim, J. (2010). Teacher facilitation techniques for small group discourse. Teaching Children Mathematics, 16(6), 350–360.

  • LaRochelle, R. & Mammo, B. (2019). Correlations between professional noticing of students’ mathematical thinking and specialized content knowledge. In Otten, S., Candela, A. G., de Araujo, Z., Haines, C., & Munter, C. (2019). Proceedings of the forty-first annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. St Louis, MO: University of Missouri. (pp. 725–729)

  • Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge University Press.

    Book  Google Scholar 

  • Leatham, K. R., Peterson, B. E., Stockero, S. L., & Van Zoest, L. R. (2015). Conceptualizing mathematically significant pedagogical opportunities to build on student thinking. Journal for Research in Mathematics Education, 46(1), 88–124. https://doi.org/10.5951/jresematheduc.46.1.0088

    Article  Google Scholar 

  • Lesseig, K., Elliott, R., Kazemi, E., Kelley-Petersen, M., Campbell, M., Mumme, J., & Carroll, C. (2017). Leader noticing of facilitation in videocases of mathematics professional development. Journal of Mathematics Teacher Education, 20(6), 591–619. https://doi.org/10.1007/s10857-016-9346-y

    Article  Google Scholar 

  • Lowery, N. (2003). The fourth “R”: Reflection. The Mathematics Educator, 13(2), 23–33.

    Google Scholar 

  • Lutovac, S., & Kaasila, R. (2014). Pre-service teachers’ future-oriented mathematical identity work. Educational Studies in Mathematics, 85(1), 129–142. https://doi.org/10.1007/s10649-013-9500-8

    Article  Google Scholar 

  • MacLeod, C. (1999). Anxiety and anxiety disorders. In T. Dalgleish & M. J. Power (Eds.), Handbook of cognition and emotion (pp. 447–477). Wiley.

  • Makhwathana, R. M., Mudzielwana, N. P., Mulovhedzi, S. A., & Mudau, T. J. (2017). Effects of teachers’ emotions in teaching and learning in the foundation phase. Journal of Psychology, 8(1), 28–35. https://doi.org/10.1080/09764224.2017.1335677

    Article  Google Scholar 

  • Mason, J. (2002). Researching your own practice: The discipline of noticing. Routledge.

    Book  Google Scholar 

  • Mathews, A., & Macleod, C. (1985). Selective processing of threat cues in anxiety states. Behaviour Research and Therapy, 23(5), 563–569.

    Article  Google Scholar 

  • Meschede, N., Fiebranz, A., Möller, K., & Steffensky, M. (2017). Teachers’ professional vision, pedagogical content knowledge and beliefs: On its relation and differences between pre-service and in-service teachers. Teaching and Teacher Education, 66, 158–170. https://doi.org/10.1016/j.tate.2017.04.010

    Article  Google Scholar 

  • Myler, R. (1962). How big is a foot? Atheneum.

    Google Scholar 

  • National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Re ston, VA: NCTM.

  • Oyserman, D. (2009). Identity-based motivation: Implications for action-readiness, procedural-readiness, and consumer behavior. Journal of Consumer Psychology, 19(3), 250–260.

    Article  Google Scholar 

  • Pintrich, P. R., & Schunk, D. H. (2002). Motivation in education: Theory, research, and applications. Prentice Hall.

    Google Scholar 

  • Reed, A., II., Forehand, M. R., Puntoni, S., & Warlop, L. (2012). Identity-based consumer behavior. International Journal of Research in Marketing, 29, 310–321.

    Article  Google Scholar 

  • Roberts, K. J., & Henson, R. K. (2000). Self-Efficacy Teaching and Knowledge Instrument for Science Teachers (SETAKIST): A Proposal for a new efficacy instrument. [Paper Presentation]. The 28th Annual Meeting of the Mid-South Educational Research Association, Bowling Green, KY, United States.

  • Roose, I., Vantieghem, W., Vanderlinde, R., & Van Avermaet, P. (2019). Beliefs as filters for comparing inclusive classroom situations: Connecting teachers’ beliefs about teaching diverse learners to their noticing of inclusive classroom characteristics in videoclips. Contemporary Educational Psychology, 56, 140–151.

    Article  Google Scholar 

  • Rowland, T., & Zazkis, R. (2013). Contingency in the mathematics classroom: Opportunities taken and opportunities missed. Canadian Journal of Science, Mathematics and Technology Education, 13(2), 137–153.

    Article  Google Scholar 

  • Santagata, R., Zannoni, C., & Stigler, J. W. (2007). The role of lesson analysis in pre-service teacher education: An empirical investigation of teacher learning from a virtual video-based field experience. Journal of Mathematics Teacher Education, 10(2), 123–140. https://doi.org/10.1007/s10857-007-9029-9

    Article  Google Scholar 

  • Schoenfeld, A. H. (2010). How we think? Routledge.

    Book  Google Scholar 

  • Schoenfeld, A. H. (2011). Toward professional development for teachers grounded in a theory of decision making. ZDM - International Journal on Mathematics Education, 43(4), 457–469. https://doi.org/10.1007/s11858-011-0307-8

    Article  Google Scholar 

  • Schutz, P. A., Hong, J. Y., Cross, D. I., & Osbon, J. N. (2006). Reflections on investigating emotion in educational activity settings. Educational Psychology Review, 18(4), 343–360.

  • Schutz, P., Hong, J., & Cross Francis, D. (2020). Teachers’ goals, beliefs, emotions, and identity development: Investigating complexities in the profession. Taylor and Francis.

  • Sherin, M. G., Jacobs, V. R., & Philipp, R. A. (2011). Mathematics teacher noticing: Seeing through teachers’ eyes. Routledge.

    Book  Google Scholar 

  • Sherin, M. G., & van Es, E. A. (2009). Effects of video club participation on teachers’ professional vision. Journal of Teacher Education, 60(1), 20–37. https://doi.org/10.1177/0022487108328155

    Article  Google Scholar 

  • Simon, H. A. (1994). The bottleneck of attention: Connecting thought with motivation. In W. D. Spaulding (Ed.), Nebraska symposium in motivation: Vol. 41. Integrative views of motivation, cognition, and emotion (pp. 1-21). University of Nebraska Press.

  • Skultety, L. (2018). Factors influencing preservice teachers’ noticing of students’ mathematical thinking. Unpublished Dissertation. University of Illinois-Champaign

  • Star, J. R., & Strickland, S. K. (2008). Learning to observe: Using video to improve preservice mathematics teachers’ ability to notice. Journal of Mathematics Teacher Education, 11(2), 107–125. https://doi.org/10.1007/s10857-007-9063-7

    Article  Google Scholar 

  • Stein, M. K., & Wang, M. C. (1988). Teacher development and school improvement: The process of teacher change. Teaching and Teacher Education, 4(2), 171–187. https://doi.org/10.1016/0742-051X(88)90016-9

    Article  Google Scholar 

  • Tamir, M., & Robinson, M. D. (2007). The happy spotlight: Positive mood and selective attention to rewarding information. Personality and Social Psychology Bulletin, 33(8), 1124–1136.

    Article  Google Scholar 

  • Taylor, J. G., & Fragopanagos, N. F. (2005). The interaction of attention and emotion. Neural Networks, 18(4), 353–369.

    Article  Google Scholar 

  • Teuscher, D., Moore, K. C., & Carlson, M. P. (2016). Decentering: A construct to analyze and explain teacher actions as they relate to student thinking. Journal of Mathematics Teacher Education, 19(5), 433–456. https://doi.org/10.1007/s10857-015-9304-0

    Article  Google Scholar 

  • Thomas, J., Fisher, M. H., Jong, C., Schack, E. O., Krause, L., & Kasten, S. (2015). Professional noticing: Learning to teach responsively. Mathematics Teaching in the Middle School, 21(4), 238–243.

    Article  Google Scholar 

  • Thomas, J., Jong, C., Fisher, M. H., & Schack, E. O. (2017). Noticing and knowledge: Exploring theoretical connections between professional noticing and mathematical knowledge for teaching. The Mathematics Educator, 26(2), 3–25.

    Google Scholar 

  • Thompson, A. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 127–146). Macmillan Publishing Co, Inc.

  • Trigwell, K. (2012). Relations between teachers’ emotions in teaching and their approaches to teaching in higher education. Instructional Science, 40(3), 607–621.

    Article  Google Scholar 

  • Tschannen-Moran, M., Hoy, A. W., & Hoy, W. K. (1998). Teacher efficacy: Its meaning and measure. Review of Educational Research, 68(2), 202–248. https://doi.org/10.3102/00346543068002202

    Article  Google Scholar 

  • Van der Heijden, A. H. C. (1992). Selective attention in vision. Routledge.

    Google Scholar 

  • Van Es, E. A. (2011). A framework for learning to notice student thinking. In M. G. Sherin, V. Jacobs, & R. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 134–151). Routledge.

    Google Scholar 

  • Walkoe, J. (2014). Exploring teacher noticing of student algebraic thinking in a video club. Journal of Mathematics Teacher Education, 18(6), 523–550. https://doi.org/10.1007/s10857-014-9289-0

    Article  Google Scholar 

  • Walkoe, J., & Levin, D. M. (2018). Using technology in representing practice to support preservice teachers’ quality questioning: The roles of noticing in improving practice. Journal of Technology and Teacher Education, 26(1), 127–147.

    Google Scholar 

  • Walshaw, M., & Anthony, G. (2008). Creating productive learning communities in the mathematics classroom: An international literature review. Pedagogies: An International Journal, 3(3), 133–149.

    Article  Google Scholar 

  • Walshaw, M., & Anthony, G. (2008b). The teacher’s role in classroom discourse: A review of recent research into mathematics classrooms. Review of Educational Research, 78(3), 516–551. https://doi.org/10.3102/0034654308320292

    Article  Google Scholar 

  • Williams, R., Watts, F., MacLeod, C., & Matthews, A. (1997). Cognitive psychology and emotional disorders. Wiley.

    Google Scholar 

  • Wilson, S. M., Shulman, L. S., & Richert, A. E. (1987). “150 different ways” of knowing: Representations of knowledge in teaching. In J. Calderhead (Ed.), Exploring teachers’ thinking (pp. 104–124). Caswell.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Education, University of North Carolina at Chapel Hill, 201B Peabody Hall, CB #3500, Chapel Hill, NC, 27599, USA

    Dionne Cross Francis

  2. Giresun University, Giresun, Turkey

    Ayfer Eker

  3. Indiana University, Bloomington, USA

    Jinqing Liu, Kemol Lloyd & Pavneet Bharaj

Authors
  1. Dionne Cross Francis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ayfer Eker
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jinqing Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Kemol Lloyd
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Pavneet Bharaj
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dionne Cross Francis.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix

Appendix

MKT Dimensions_Scoring

Wilma’s KCT

Construct

Sub-construct

Overall description

Content-specific description

(indicators)

Score

Score Description

MKT (Length Measurement for 2nd graders)

KCT

KCT (knowledge of content and teaching) combines knowing about teaching and knowing about mathematics. It involves task selection and sequencing requiring a coordination between specific mathematical understanding and pedagogical knowledge about what issues affect student learning

Teacher demonstrates 5–6 of the indicators below

Development or selection of task that support students in developing knowledge of length measurement that includes the following:

Measurement units must be placed end to end

No gaps between measurement units

Measuring starts from one end of the object and the measurement unit is iterated to the other end of the object

Use measurement unit that are smaller than the object being measured

Use measurement unit that will require multiple to determine the length of the object

Select appropriate number of objects to measure for allotted time (2–3 objects for 20-min activity)

Select appropriate number of measurement units to measure object (2 maximum)

Make appropriate decisions about which student contributions to take up and pursue

Low

Teacher demonstrates 1–2 of the indicators

Medium

Teacher demonstrates 3–4 of the indicators

High

Teacher demonstrates 5–6 of the indicators below

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cross Francis, D., Eker, A., Liu, J. et al. (Mis)alignment between noticing and instructional quality: the role of psychological and cognitive constructs. J Math Teacher Educ 25, 599–632 (2022). https://doi.org/10.1007/s10857-021-09509-0

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10857-021-09509-0

Keywords

Search

Navigation