How Textbooks Can Promote Inquiry: Using a Narrative Framework to Investigate the Design of Mathematical Content in a Lesson

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Leslie Dietiker Boston University, MA

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Andrew S. Richman Boston University, MA

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We use a narrative framework to investigate how mathematics textbook lessons can promote sustained student inquiry. Our analysis of four high school textbook lessons on the SSA congruence property, three of which contain explorations, reveals how explorations can promote problem-solving perseverance by inspiring readers to raise mathematical questions and by keeping these questions open throughout significant portions of the lesson. Furthermore, student curiosity and anticipation can be enhanced through ambiguity. Stark structural differences exist among lessons with explorations, suggesting that explorations are not necessarily supportive of sustained student inquiry. These insights not only enable educators to learn whether and how a lesson encourages inquiry but also support the design of new curricular materials aligned with the goals of reform.

Footnotes

The authors would like to share our appreciation for the other members of our research team: Shana Frank, Jackie Persuit, Francesca Schiavello, and Ari Schwartz for their work on the analysis, and Ann Lawrence for her help with the manuscript. We also appreciate the numerous recommendations from our reviewers, who identified important ways to improve this article. Finally, we wish to thank Jinfa Cai, whose patience and guidance was invaluable.

This article was accepted under the editorship of Jinfa Cai.

Contributor Notes

Leslie Dietiker, Wheelock College of Education & Human Development, Boston University, Two Silber Way, Boston, MA 02215; dietiker@bu.edu

Andrew S. Richman, Wheelock College of Education & Human Development, Boston University, Two Silber Way, Boston, MA 02215; asrich@bu.edu

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  • 1.

    Bal, M. (1986). Tell-tale theories. Poetics Today, 7(3), 555564. https://doi.org/10.2307/1772511

  • 2.

    Barthes, R. (1974). S/Z: An essay (R. Miller , Trans.). Hill and Wang.

  • 3.

    Boaler, J. (2002). Learning from teaching: Exploring the relationship between reform curriculum and equity. Journal for Research in Mathematics Education, 33(4), 239258. https://doi.org/10.2307/749740

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 4.

    Boaler, J., & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of Railside School. Teachers College Record, 110(3), 608645.

    • Search Google Scholar
    • Export Citation
  • 5.

    Borasi, R. (1992). Learning mathematics through inquiry. Heinemann.

  • 6.

    Borasi, R. (1994). Capitalizing on errors as “springboards for inquiry": A teaching experiment. Journal for Research in Mathematics Education, 25(2), 166208. https://doi.org/10.2307/749507

    • Search Google Scholar
    • Export Citation
  • 7.

    Boston, M. D., & Smith, M. S. (2009). Transforming secondary mathematics teaching: Increasing the cognitive demands of instructional tasks used in teachers’ classrooms. Journal for Research in Mathematics Education, 40(2), 119156.

    • Search Google Scholar
    • Export Citation
  • 8.

    Brown, S. I., & Walter, M. I. (1990). The art of problem posing (2nd ed.). Lawrence Erlbaum Associates.

  • 9.

    Burger, E. B., Chard, D. J., Hall, E. J., Kennedy, P. A., Leinwand, S. J., Renfro, F. L., Seymour, D. G., & Waits, B. K. (2007). Geometry (Teacher ed.). Holt, Rinehart and Winston.

    • Search Google Scholar
    • Export Citation
  • 10.

    CME Project. (2009). Geometry (Teacher ed.). Pearson.

  • 11.

    Dietiker, L. (2013). Mathematical texts as narrative: Rethinking curriculum. For the Learning of Mathematics, 33(3), 1419.

  • 12.

    Dietiker, L. (2015a). Mathematical story: A metaphor for mathematics curriculum. Educational Studies in Mathematics, 90(3), 285302. https://doi.org/10.1007/s10649-015-9627-x

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 13.

    Dietiker, L. (2015b). What mathematics education can learn from art: The assumptions, values, and vision of mathematics education. Journal of Education, 195(1), 110. https://doi.org/10.1177/002205741519500102

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 14.

    Dietiker, L. (2016a). Generating student interest with mathematical stories. The Mathematics Teacher, 110(4), 304308. https://doi.org/10.5951/mathteacher.110.4.0304

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 15.

    Dietiker, L. (2016b). The role of sequence in the experience of mathematical beauty. Journal of Humanistic Mathematics, 6(1), 152173. https://doi.org/10.5642/jhummath.201601.10

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 16.

    Dietiker, L., Males, L. M., Amador, J. M., & Earnest, D. (2018). Curricular noticing: A framework to describe teachers’ interactions with curriculum materials. Journal for Research in Mathematics Education, 49(5), 521532. https://doi.org/10.5951/jresematheduc.49.5.0521

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 17.

    Dietiker, L., Richman, A. S., Brakoniecki, A., & Miller, E. R. (2016). Woo! Aesthetic variations of the “same" lesson. In M. B. Wood, E. E. Turner, M. Civil, & J. A. Eli (Eds.), Proceedings of the thirty-eighth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 6673). University of Arizona.

    • Search Google Scholar
    • Export Citation
  • 18.

    Dietiker, L., Riling, M., & Gates, M. (2019). The impact of mathematically captivating learning experiences. In S. Otten, A. G. Candela, Z. de Araujo, C. Haines, & C. Munter (Eds.), Proceedings of the forty-first annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 96100). University of Missouri.

    • Search Google Scholar
    • Export Citation
  • 19.

    Fiori, N., & Selling, S. K. (2016). Truth isn’t everything: Promoting aesthetically guided choice in mathematical work. The Journal of Mathematical Behavior, 41, 219234. https://doi.org/10.1016/j.jmathb.2015.10.002

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 20.

    Goos, M. (2004). Learning mathematics in a classroom community of inquiry. Journal for Research in Mathematics Education, 35(4), 258291. https://doi.org/10.2307/30034810

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 21.

    Harel, G. (2013). Intellectual need. In K. R. Leatham (Ed.), Vital directions for mathematics education research (pp. 119151). Springer. https://doi.org/10.1007/978-1-4614-6977-3_6

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 22.

    Hayes, M. L. (2019). 2018 NSSME+: Status of high school mathematics. Horizon Research.

  • 23.

    Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28(5), 524549. https://doi.org/10.2307/749690

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 24.

    Hiebert, J., & Wearne, D. (1993). Instructional tasks, classroom discourse, and students’ learning in second-grade arithmetic. American Educational Research Journal, 30(2), 393425. https://doi.org/10.3102/00028312030002393

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 25.

    Iasevoli, B. (2014, April 14). Textbooks and math standards have little in common. Education Writers Association. https://www.ewa.org/blog-educated-reporter/textbooks-and-math-standards-have-little-common

    • Search Google Scholar
    • Export Citation
  • 26.

    Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27(1), 2963. https://doi.org/10.3102/00028312027001029

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 27.

    Lehrer, R., Kobiela, M., & Weinberg, P. J. (2013). Cultivating inquiry about space in a middle school mathematics classroom. ZDM, 45(3), 365376. https://doi.org/10.1007/s11858-012-0479-x

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 28.

    Lehrer, R., Schauble, L., & Lucas, D. (2008). Supporting development of the epistemology of inquiry. Cognitive Development, 23(4), 512529. https://doi.org/10.1016/j.cogdev.2008.09.001

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 29.

    Lloyd, G. M., Cai, J., & Tarr, J. E. (2017). Issues in curriculum studies: Evidence-based insights and future directions. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 824852). National Council of Teachers of Mathematics.

    • Search Google Scholar
    • Export Citation
  • 30.

    Males, L. M., Earnest, D., Dietiker, L., & Amador, J. M. (2015). Examining K–12 prospective teachers’ curricular noticing. In T. G. Bartell, K. N. Bieda, R. T. Putnam, K. Bradfield, & H. Dominguez (Eds.), Proceedings of the thirty-seventh annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 8895). Michigan State University.

    • Search Google Scholar
    • Export Citation
  • 31.

    Miller, E. R., Dietiker, L., Ryan, L., Brakoniecki, A., & Richman, A. S. (2016). Mathematics lessons as stories: A reason to do the math. In M. B. Wood, E. E. Turner, M. Civil, & J. A. Eli (Eds.), Proceedings of the thirty-eighth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (p. 435). University of Arizona.

    • Search Google Scholar
    • Export Citation
  • 32.

    National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics.

  • 33.

    National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. https://www.nctm.org/Standards-and-Positions/Principles-and-Standards/

    • Search Google Scholar
    • Export Citation
  • 34.

    National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core state standards for mathematics. http://www.corestandards.org/

    • Search Google Scholar
    • Export Citation
  • 35.

    Netz, R. (2005). The aesthetics of mathematics: A study. In P. Mancosu, K. F. J⊘rgensen, & S. A. Pedersen (Eds.), Visualization, explanation and reasoning styles in mathematics (pp. 251293). Springer. https://doi.org/10.1007/1-4020-3335-4_10

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 36.

    Nodelman, P., & Reimer, M. (2003). The pleasures of children’s literature (3rd ed.). Allyn and Bacon.

  • 37.

    Remillard, J. T. (2005). Examining key concepts in research on teachers’ use of mathematics curricula. Review of Educational Research, 75(2), 211246. https://doi.org/10.3102/00346543075002211

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 38.

    Remillard, J. T., & Bryans, M. B. (2004). Teachers’ orientations toward mathematics curriculum materials: Implications for teacher learning. Journal for Research in Mathematics Education, 35(5), 352388. https://doi.org/10.2307/30034820

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 39.

    Richman, A. S., Dietiker, L., & Riling, M. (2019). The plot thickens: The aesthetic dimensions of a captivating mathematics lesson. The Journal of Mathematical Behavior, 54, Article 100671. https://doi.org/10.1016/j.jmathb.2018.08.005

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 40.

    Richman, A., Miller, E., Brakoniecki, A., & Dietiker, L. (2016). Opportunities created by misdirection in mathematics lessons. In M. B. Wood, E. E. Turner, M. Civil, & J. A. Eli (Eds.), Proceedings of the thirty-eighth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 109112). University of Arizona.

    • Search Google Scholar
    • Export Citation
  • 41.

    Rosenblatt, L. M. (1988). Writing and reading: The transactional theory (Technical Report No. 416). University of Illinois at Urbana-Campaign. https://files.eric.ed.gov/fulltext/ED292062.pdf

    • Search Google Scholar
    • Export Citation
  • 42.

    Ryan, L., & Dietiker, L. (2017, April 5–8). Mathematics lessons as stories: Engaging learners with plot twists [Paper presentation]. Annual meeting of the National Council of Teachers of Mathematics, San Antonio, TX, United States.

    • Search Google Scholar
    • Export Citation
  • 43.

    Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334370). Macmillan.

    • Search Google Scholar
    • Export Citation
  • 44.

    Schoenfeld, A. H. (2002). Making mathematics work for all children: Issues of standards, testing, and equity. Educational Researcher, 31(1), 1325. https://doi.org/10.3102/0013189X031001013

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 45.

    Serra, M. (2013). Discovering geometry: An investigative approach (4th ed., Teacher ed.). Kendall Hunt.

  • 46.

    Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 1928.

  • 47.

    Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. Zentralblatt Für Didaktik Der Mathematik, 29(3), 7580. https://doi.org/10.1007/s11858-997-0003-x

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 48.

    Silver, E. A., & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education, 27(5), 521539. https://doi.org/10.2307/749846

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 49.

    Sinclair, N. (2004, June). Chorus, colour and contrariness in school mathematics [Paper presentation]. Symposium on Online Mathematical Investigation as Narrative Experience, London, Ontario, Canada. https://www.edu.uwo.ca/mathstory/Sinclair.pdf

    • Search Google Scholar
    • Export Citation
  • 50.

    Smith, J. P., III , Males, L. M., Dietiker, L. C., Lee, K., & Mosier, A. (2013). Curricular treatments of length measurement in the United States: Do they address known learning challenges? Cognition and Instruction, 31(4), 388433. https://doi.org/10.1080/07370008.2013.828728

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 51.

    Smith, M. S., & Stein, M. K. (1998). Selecting and creating mathematical tasks: From research to practice. Mathematics Teaching in the Middle School, 3(5), 344350.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 52.

    Staples, M. (2007). Supporting whole-class collaborative inquiry in a secondary mathematics classroom. Cognition and Instruction, 25(2-3), 161217.  https://doi.org/10.1080/07370000701301125

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 53.

    Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455488. https://doi.org/10.3102/00028312033002455

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 54.

    Stein, M. K., Remillard, J., & Smith, M. S. (2007). How curriculum influences student learning. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 319369). Information Age.

    • Search Google Scholar
    • Export Citation
  • 55.

    Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2000). Implementing standards-based mathematics instruction: A casebook for professional development. Teachers College Press.

    • Search Google Scholar
    • Export Citation
  • 56.

    Tarr, J. E., Reys, R. E., Reys, B. J., Chávez, Ó., Shih, J., & Osterlind, S. J. (2008). The impact of middle-grades mathematics curricula and the classroom learning environment on student achievement. Journal for Research in Mathematics Education, 39(3), 247280.

    • Search Google Scholar
    • Export Citation
  • 57.

    Uhrmacher, P. B. (2009). Toward a theory of aesthetic learning experiences. Curriculum Inquiry, 39(5), 613636. https://doi.org/10.1111/j.1467-873X.2009.00462.x

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 58.

    University of Chicago School Mathematics Project. (2009). Geometry (3rd ed., Teacher ed.). Wright Group/McGraw-Hill.

  • 59.

    Usiskin, Z. (2014). We need another revolution: Five decades of mathematics curriculum papers (B. J. Reys & R. E. Reys, Eds.). National Council of Teachers of Mathematics.

    • Search Google Scholar
    • Export Citation
  • 60.

    Wong, D. (2007). Beyond control and rationality: Dewey, aesthetics, motivation, and educative experiences. Teachers College Record, 109(1), 192220.

    • Search Google Scholar
    • Export Citation
  • 61.

    Zwaan, R. A. (1994). Effect of genre expectations on text comprehension. Journal of Experimental Psychology: Learning, Memory, and Cognition, 20(4), 920933. https://doi.org/10.1037/0278-7393.20.4.920

    • Search Google Scholar
    • Export Citation
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