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Didactical Disciplinary Literacy in Mathematics: Making Meaning From Textbooks

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Abstract

In this study, we investigated the literacy practices of undergraduate calculus students and non-mathematics STEM faculty members as they read excerpts from a calculus textbook. We found several differences in their practices that appeared to be tied to the didactical nature of the excerpts and the participants’ identities and power relationships with the textbook. We use these differences to explore the concept of didactical disciplinary literacy to examine the ways readers approach the process of learning from a mathematics textbook and how their practices are related to their positionality with respect to the text. We also explore the development of the readers’ thinking about the mathematical concepts and suggest connections between this development and their literacy practices. The study results have implications for the ways that mathematics textbooks can be used as resources for learning the content and literacy practices of the field.

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Notes

  1. Disciplinary literacy contrasts with content area literacy in that the latter focuses on cross-content, generalizable reading and study skills, whereas disciplinary literacy points out that communication traditions differ dramatically across fields. For more on these connections and differences, see Shanahan and Shanahan (2012).

  2. While there is a body of research on identity specifically in mathematics (e.g., Darragh, 2016), we are adopting the perspective of positionality and identity that is commonly used when working through the lens of disciplinary literacy.

  3. The original study (reported in Wiesner et al., 2020) was designed with general literacy practices, rather than (specifically) didactical disciplinary literacy, in mind, so the interview protocol did not specify the ways in which the interviewer should use pronouns. However, most of the interview prompts avoided the use of pronouns, and an analysis of pronoun usage found that the interviewer’s pronoun usage did not appear to influence the participants’ choice of pronoun.

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Authors and Affiliations

  1. Department of Mathematics, Ithaca College, Ithaca, NY, USA

    Aaron Weinberg & Emilie Wiesner

  2. Department of Education, Ithaca College, Ithaca, NY, USA

    Ellie Fitts Fulmer

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  1. Aaron Weinberg
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  2. Emilie Wiesner
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Correspondence to Aaron Weinberg.

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Appendices

Appendix: Materials Used in Interviews

Interview Questions

  1. 1.

    Background knowledge, experience, and positionality questions:

    1. a.

      Please tell me a little bit about your Calculus background.

    2. b.

      In what ways – if any – do you use Calculus in your own [for faculty] teaching or research [for students] your life outside of calculus?

    3. c.

      How would you describe what a derivative is?

    4. d.

      How would you describe what a Riemann sum is?

    5. e.

      How would you describe what an integral is?

  2. 2.

    Background Content Questions (Using electric charge question below):

    [Before reading the scenario]

    1. a.

      Are you familiar with circuits, currents, amps and volts?

    2. b.

      [If so] are those concepts you work with regularly, or just seen in the past?

      [After reading the scenario]

    3. c.

      What is this graph telling us about this scenario?

    4. d.

      What would a Riemann sum tell you about this scenario?

    5. e.

      What would an integral tell you about this scenario?

    6. f.

      How are Riemann sums and integrals related to each other?

    7. g.

      When would we use a Riemann sum, and when would we use an integral?

  3. 3.

    Background Textbook Questions

    1. a.

      How do you usually read the textbook [for faculty, in their discipline; for students, their calculus textbook] for the purpose of learning new material?

    2. b.

      What aspects/features of the textbook do you think are helpful or useful for learning new material?

    3. c.

      What aspects/features of the textbook do you think are not so helpful or useful for learning new material?

  4. 4.

    Questions about the content in the excerpts

    1. a.

      Is arc length something you are familiar with?

    2. b.

      [If so] What is arc length, and how would you find it?

  5. 5.

    Read Chapter 8.2 intro paragraph (p. 398) and Arc Length, through example 5 (p. 403)

    Use a message q/ing protocol: Ask the student to read the text and stop at places where they either have a question or have to think through what they’re reading a bit. At each stopping point, engage in an analysis of their question.

  6. 6.

    Ask general follow-up questions:

    1. a.

      What were the main ideas of the section?

    2. b.

      If the above response was short or lacked detail, ask the next two questions

      1. i.

        What aspects of the text do you think were most useful or important?

      2. ii.

        What aspects of the text do you think were least useful or important?

  7. 7.

    Ask the student to set up and, if there’s time, solve the following problems, thinking through them out loud as much as possible

    82 #43; add on problem #12 if there’s time (p. 404–5).

  8. 8.

    Ask directed follow-up questions:

    1. a.

      How would you summarize what the introductory paragraph is saying?

    2. b.

      How would you describe what arc length is?

    3. c.

      How would you summarize the book’s method for finding arc length? Why does it make sense?

    4. d.

      Why does the book use a Riemann sum first when finding the length?

    5. e.

      How is the Riemann sum related to the integral?

  9. 9.

    Read Chapter 8.4 Density and Center of Mass through example 2 (p. 415–416)

  10. 10.

    Ask general follow-up questions:

    1. a.

      What were the main ideas of the section?

    2. b.

      What aspects of the text do you think were most useful or important?

    3. c.

      What aspects of the text do you think were least useful or important?

  11. 11.

    Ask the student to set up and, if there’s time, solve the following problems, thinking through them out loud as much as possible

    1. a.

      8.4 #20 (just total mass, not center of mass); add on problem #11 if there’s time (pp. 422–423)

  12. 12.

    Ask directed follow-up questions:

    1. a.

      How would you summarize what the introductory paragraph is saying?

    2. b.

      How would you describe what’s happening in Example 1? Why does the book’s method make sense?

    3. c.

      How would you describe what’s happening in Example 2? Why does the book’s method make sense?

    4. d.

      Why does the book use a Riemann sum first in the examples?

    5. e.

      How is the Riemann sum related to the integral?

Background Content Questions

An ampere is a measure of electric current. At a point in an electric circuit, a measurement of one ampere means that roughly 6 × 1018 electrons are passing by that point each second.

NASA engineers designed a battery for an electric circuit, and then measured the current at the end of the circuit over a 90-min period. The graph below shows their measurements.

figure a
  1. 1.

    What would a Riemann sum tell you about this scenario?

  2. 2.

    What would an integral tell you about this scenario?

  3. 3.

    How are Riemann sums and integrals related to each other?

  4. 4.

    When would we use a Riemann sum, and when would we use an integral?

Introduction to the Section “Applications to Geometry”

figure b

Section on Arc Length

figure c

Section on Density

figure e
figure f

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Weinberg, A., Wiesner, E. & Fulmer, E.F. Didactical Disciplinary Literacy in Mathematics: Making Meaning From Textbooks. Int. J. Res. Undergrad. Math. Ed. 9, 491–523 (2023). https://doi.org/10.1007/s40753-022-00164-1

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