Skip to main content

Advertisement

SpringerLink
Log in

“It was smart when:” Supporting prospective teachers’ noticing of students’ mathematical strengths

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

Abstract

Learning to name and notice students’ mathematical strengths is a challenging process requiring time and multiple iterations of practice for prospective teachers (PTs) to adopt. Mathematics teacher educators (MTEs) can approximate and decompose the complex practice of naming and noticing students’ mathematical strengths so PTs learn to teach mathematics while emphasizing what students know and can do. This study uses two tools MTEs can use to support PTs as they learn to name and notice students’ mathematical strengths: A LessonSketch experience, a digital platform with comic-based storyboards showing children engaged in a mathematics task, and a strengths-based sentence frame. Our study presents the findings from the 111 noticing statements from 18 PTs as they engaged in the LessonSketch digital experience and practiced making noticing statements about what children know about mathematics. The study found that after a sentence-frame intervention, the PTs are more likely to use strengths-based language and more likely to identify mathematical evidence in their noticing statements. Uncommitted language (statements that do not align with a strength- or deficit-based coding scheme), suggests a fruitful, yet complex space for supporting more PTs as they learn to name and notice students’ mathematical strengths. The paper concludes with implications for future research in teacher education.

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
Fig. 2
Fig. 3

Similar content being viewed by others

Notes

  1. With that said, we chose to keep the blue skin tones of the comic-based representations of children for the original version of the Making Bags of Apples LessonSketch. We acknowledge how NNSMS does not reflect the racial diversity in American classrooms and leave open future opportunities for PTs as they learn to interpret the comic-based representations of students as racialized forms of experiences in mathematics (Martin 2012). The storyboards presented in this study (and as described in Bannister et al. 2018) are only the first in many steps MTEs might take with their PTs as they think about the role of power, identity, and race in mathematics classrooms.

References

  • Aguirre, J., Mayfield-Ingram, K., & Martin, D. (2013). The impact of identity in K-8 mathematics: Rethinking equity-based practices. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Aguirre, J., Herbel-Eisenmann, B., Celedón-Pattichis, S., Civil, M., Wilkerson, T., Stephan, M., et al. (2017). Equity within mathematics education research as a political act: Moving from choice to intentional collective professional responsibility. Journal for Research in Mathematics Education, 48(2), 124–147. https://doi.org/10.5951/jresematheduc.48.2.0124.

    Article  Google Scholar 

  • Banks, C. A. M., & Banks, J. A. (1995). Equity pedagogy: An essential component of multicultural education. Theory into Practice, 34(3), 152–158. https://doi.org/10.1080/00405849509543674.

    Article  Google Scholar 

  • Bannister, N., Kalinec-Craig, C., Bowen, D., & Crespo, S. (2018). Learning to notice and name students’ mathematical strengths: A digital experience. Journal of Technology and Teacher Education, 26(1), 13–31.

    Google Scholar 

  • Brasel, J., Garner, B., & Horn, I. S. (2016). Scaffolding into ambitious teaching: Representations of practice in teacher workgroups. In C. K. Looi, J. L. Polman, U. Cress, & P. Reimann (Eds.), Transforming learning, empowering learners: The international conference of the learning sciences (ICLS) 2016 (Vol. 2, pp. 671–678). Singapore: International Society of the Learning Sciences.

    Google Scholar 

  • Celedón-Pattichis, S., & Ramirez, N. G. (2012). Beyond good teaching: Advancing mathematics education for ELLs. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Chao, T., Murray, E., & Gutiérrez, R. (2016). Classroom practices that support equity-based mathematics teaching. Retrieved September 14, 2017, from https://www.nctm.org/Research-and-Advocacy/Research-Brief-and-Clips/Classroom-practices-that-support-equity-based-mathematics-teaching/.

  • Chapin, S. H., O'Connor, C., O'Connor, M. C., & Anderson, N. C. (2009). Classroom discussions: Using math talk to help students learn, Grades K-6. Sausalito, CA: Math Solutions.

    Google Scholar 

  • Cohen, E. G., Lotan, R. A., Scarloss, B. A., & Arellano, A. R. (1999). Complex instruction: Equity in cooperative learning classrooms. Theory into Practice, 38(2), 80–86. https://doi.org/10.1080/00405849909543836.

    Article  Google Scholar 

  • Cohen, E. G., & Lotan, R. A. (2014). Designing groupwork: Strategies for the heterogeneous classroom (3rd ed.). New York: Teachers College Press.

    Google Scholar 

  • Corbin, J. M., & Strauss, A. L. (2008). Basics of qualitative research: Techniques and procedures for developing grounded theory (3rd ed.). Los Angeles, CA: Sage Publishers.

    Book  Google Scholar 

  • Crespo, S. (2000). Seeing more than right and wrong answers: Prospective teachers' interpretations of students' mathematical work. Journal of Mathematics Teacher Education, 3(2), 155–181.

    Article  Google Scholar 

  • Crespo, S. (2002). Praising and correcting: Prospective teachers investigate their teacherly talk. Teaching and Teacher Education, 18(6), 739–758.

    Article  Google Scholar 

  • Crespo, S., & Featherstone, H. (2012). Counteracting the language of math ability: Prospective teachers explore the role of status in elementary classrooms (pp. 159–179). Equity and social justice: Mathematics teacher education in the public interest.

    Google Scholar 

  • Crespo, S. (2015). A collection of problem-posing experiences for prospective mathematics teachers that make a difference. In Mathematical problem posing (pp. 493–511). Springer, New York, NY.

  • Creswell, J., & Plano Clark, V. (2007). Designing and conducting mixed methods research. Thousand Oaks, CA: Sage Publishers.

    Google Scholar 

  • Featherstone, H., Crespo, S., Jilk, L. M., Oslund, J. A., Parks, A. N., & Wood, M. B. (2011). Smarter together! Collaboration and equity in the elementary math classroom. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Felton-Koestler, M. D., & Koestler, C. (2017). Should mathematics teacher education be politically neutral? Mathematics Teacher Educator, 6(1), 67–72. https://doi.org/10.5951/mathteaceduc.6.1.0067.

    Article  Google Scholar 

  • García, O., & Kleifgen, J. A. (2010). Educating emergent bilinguals: Policies, programs, and practices for English language learners. New York: Teachers College Press.

    Google Scholar 

  • Grossman, P., Compton, C., Igra, D., Ronfeldt, M., Shahan, E., & Williamson, P. (2009). Teaching practice: A cross-professional perspective. Teachers College Record, 111(9), 2055–2100.

    Google Scholar 

  • Grossman, P., & McDonald, M. (2008). Back to the future: Directions for research in teaching and teacher education. American Educational Research Journal, 45(1), 184–205.

    Article  Google Scholar 

  • Gutiérrez, R. (2018). Political conocimiento for teaching mathematics: Why teachers need it and how to develop it. In S. E. Kastberg, A. M. Tyminski, A. E. Lischka, & W. B. Sanchez (Eds.), Building support for scholarly practices in mathematics methods (pp. 11–38). Charlotte, NC: Information Age Publishing.

    Google Scholar 

  • Gutiérrez, R., & Goffney, I. (2018). Annual perspectives in mathematics education 2018: Rehumanizing mathematics for students who are Black, Indigenous, and/or Latinx. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Herbst, P., Chazan, D., Chen, C. L., Chieu, V. M., & Weiss, M. (2011). Using comics-based representations of teaching, and technology, to bring practice to teacher education courses. ZDM Mathematics Education, 43(1), 91–103. https://doi.org/10.1007/s11858-010-0290-5.

    Article  Google Scholar 

  • Herbst, P., Chazan, D., Chieu, V. M., Milewski, A., Kosko, K., & Aaron, W. (2016). Technology-mediated mathematics teacher development: Research on digital pedagogies of practice. In M. Niess, K. Hollebrands, & S. Driskell (Eds.), Handbook of research on transforming mathematics teacher education in the digital age (pp. 78–106). Hershey, PA: IGI Global.

    Chapter  Google Scholar 

  • Herbst, P., Chieu, V. M., & Rouge, A. (2014). Approximating the practice of mathematics teaching: What learning can web based, multimedia storyboarding software enable? Contemporary Issues in Technology and Teacher Education, 14(4), 356–383.

    Google Scholar 

  • Herbst, P., Owen, S., & Umland, K. (2012). Making bags of apples task. Retrieved February 04, 2018, from https://www.slideshare.net/pgherbst/making-bags-of-apples.

  • Horn, I. S. (2017). Motivated: Designing math classrooms where students want to join in. Portsmouth, NH: Heinemann.

    Google Scholar 

  • Horn, I. S. (2012). Strength in numbers: Collaborative learning in secondary mathematics. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Horn, I. S., Garner, B., Kane, B. D., & Brasel, J. (2017). A taxonomy of instructional learning opportunities in teachers’ workgroup conversations. Journal of Teacher Education, 68(1), 41–54. https://doi.org/10.1177/0022487116676315.

    Article  Google Scholar 

  • Horn, I. S., & Kane, B. D. (2015). Opportunities for professional learning in mathematics teacher workgroup conversations: Relationships to instructional expertise. Journal of the Learning Sciences, 24(3), 373–418. https://doi.org/10.1080/10508406.2015.1034865.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Jansen, A., Cooper, B., Vascellaro, S., & Wandless, P. (2016). Rough draft talk in mathematics classrooms. Mathematics Teaching in the Middle School, 22(5), 304–307. https://doi.org/10.5951/mathteacmiddscho.22.5.0304.

    Article  Google Scholar 

  • Jilk, L. M. (2016). Supporting teacher noticing of students' mathematical strengths. Mathematics Teacher Educator, 4(2), 188–199. https://doi.org/10.5951/mathteaceduc.4.2.0188.

    Article  Google Scholar 

  • Joseph, N. M., Hailu, M., & Boston, D. (2017). Black women’s and girls’ persistence in the P–20 mathematics pipeline: Two decades of children, youth, and adult education research. Review of Research in Education, 41(1), 203–227.

    Article  Google Scholar 

  • Kalinec-Craig, C. A. (2017). The rights of the learner: A framework for promoting equity through formative assessment in mathematics education. Democracy and Education, 25(2), 5.

    Google Scholar 

  • Lampert, M., Franke, M. L., Kazemi, E., Ghousseini, H., Turrou, A. C., Beasley, H., et al. (2013). Keeping it complex: Using rehearsals to support novice teacher learning of ambitious teaching. Journal of Teacher Education, 64(3), 226–243. https://doi.org/10.1177/0022487112473837.

    Article  Google Scholar 

  • Louie, N. L. (2017). The culture of exclusion and its persistence in equity-oriented teaching. Journal for Research in Mathematics Education, 28(5), 488–519. https://doi.org/10.5951/jresematheduc.48.5.0488.

    Article  Google Scholar 

  • Martin, D. (2012). Teaching other people’s children to teach other people’s children: Reflections on integrating equity issues into a mathematics content course for elementary teachers. In L. J. Jacobsen, J. Mistele, & B. Sriraman (Eds.), Mathematics teacher education in the public interest (pp. 3–23). Charlotte, NC: Information Age Publishing.

    Google Scholar 

  • Nasir, N. S., Cabana, C., Shreve, B., Woodbury, E., & Louie, N. (2014). Mathematics for equity: A framework for successful practice. New York: Teachers College Press.

    Google Scholar 

  • Nieto, S. (2013). Finding joy in teaching students of diverse backgrounds: Culturally responsive and socially just practices in U.S. classrooms. Portsmouth: Heinemann.

    Google Scholar 

  • Oakes, J. (2005). Keeping track: How schools structure inequality (2nd ed.). New Haven, CT: Yale University Press.

    Google Scholar 

  • Roth McDuffie, A., Foote, M. Q., Bolson, C., Turner, E. E., Aguirre, J. M., Bartell, T. G., et al. (2014). Using video analysis to support prospective K-8 teachers’ noticing of students’ multiple mathematical knowledge bases. Journal of Mathematics Teacher Education, 17(3), 245–270. https://doi.org/10.1007/s10857-013-9257-0.

    Article  Google Scholar 

  • Sherin, M. G., Linsenmeier, K. A., & van Es, E. A. (2009). Selecting video clips to promote mathematics teachers' discussion of student thinking. Journal of Teacher Education, 60(3), 213–230. https://doi.org/10.1177/0022487109336967.

    Article  Google Scholar 

  • Smith, M., & Stein, M. (1998). Selecting and creating mathematical tasks: From research to practice. Mathematics Teaching in the Middle School, 3(5), 344–350.

    Article  Google Scholar 

  • Son, J.-W., & Crespo, S. (2009). Prospective teachers’ reasoning and response to a student’s non-traditional strategy when dividing fractions. Journal of Mathematics Teacher Education, 12(4), 235–261. https://doi.org/10.1007/s10857-009-9112-5.

    Article  Google Scholar 

  • Tran, T. L., & Wright, R. J. (2017). Teachers’ professional noticing from a perspective of key elements of intensive, one-to-one intervention. In Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 481–504). Springer. https://doi.org/10.1007/978-3-319-46753-5.

  • Walker, E. N. (2012). Cultivating mathematics identities in and out of school and in between. Journal of Urban Mathematics Education, 5(1), 66–83.

    Google Scholar 

  • White, D. Y., Crespo, S., & Civil, M. (Eds.). (2016). Cases for mathematics teacher educators: Facilitating conversations about inequities in mathematics classrooms. Charlotte, NC: Information Age Press.

    Google Scholar 

  • Yeh, C., Ellis, M. W., & Hurtado, C. K. (2017). Reimagining the mathematics classroom: Creating and sustaining productive learning environments, K-6. Reston, VA: The National Council of Teachers of Mathematics.

    Google Scholar 

Download references

Acknowledgements

This publication was supported in part by funds to the fifth author (Sandra Crespo) as a LessonSketch Research and Development fellow and to her inquiry group members (the co-authors in this publication) on NSF Grant DRL-1316241. The graphics used in these images are © 2017 The Regents of the University of Michigan, all rights reserved. All graphics are used with permission, in compliance with terms of use.

Author information

Authors and Affiliations

  1. Department of Interdisciplinary Learning and Teaching, The University of Texas At San Antonio, One UTSA Circle, San Antonio, TX, 78249, USA

    Crystal A. Kalinec-Craig

  2. Department of Teaching and Learning and School of Mathematical and Statistical Sciences, Clemson University, 101 Gantt Circle Office 403, Clemson, SC, 29634, USA

    Nicole Bannister

  3. Department of Mathematical Sciences, University of the Virgin Islands, Charlotte Amalie West, St Thomas, 00802, US Virgin Islands

    Diana Bowen

  4. Department of Curriculum Instruction and Leadership, Louisiana Tech University, WOOH 200E 3163, Ruston, LA, 71272, USA

    Lorraine A. Jacques

  5. Department of Teacher Education, Michigan State University, 362 Erickson Hall, East Lansing, MI, 48824, USA

    Sandra Crespo

Authors
  1. Crystal A. Kalinec-Craig
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nicole Bannister
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Diana Bowen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Lorraine A. Jacques
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Sandra Crespo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Crystal A. Kalinec-Craig.

Additional information

Publisher's Note

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

Appendices

Appendix 1

See Table 7.

Table 7 Examples of coded data
Full size table

Appendix 2

See Table 8.

Table 8 Distribution of language use counts across pre- and post-NNSMS noticing statements
Full size table

Appendix 3

See Table 9.

Table 9 Distribution of mathematical evidence count across pre- and post-NNSMS responses
Full size table

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kalinec-Craig, C.A., Bannister, N., Bowen, D. et al. “It was smart when:” Supporting prospective teachers’ noticing of students’ mathematical strengths. J Math Teacher Educ 24, 375–398 (2021). https://doi.org/10.1007/s10857-020-09464-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10857-020-09464-2

Keywords

Search

Navigation