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A new generation of mathematics textbook research and development

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Abstract

This paper adopts a multimodal approach to the latest generation of digital mathematics textbooks (print and online) to investigate how the design, content, and features facilitate the construction of mathematical knowledge for teaching and learning purposes. The sequential organization of the print version is compared to the interactive format of the online version which foregrounds explanations and important mathematical content while simultaneously ensuring a high level of connectivity and coherence across hierarchical layers of mathematical knowledge. For example, mathematical content in the online version is linked to definitions, theorems, examples and exercises that can be viewed in the original context in which the material was presented, and the content can also be linked to mathematics software. Significantly, the development process for the new generation of mathematics textbooks involves using a ‘design neutral’ markup language so that the books are simultaneously published as both print books and online books. In this development process, the structure of the chapters, sections, and subsections with their various elements are explicitly marked-up in the master document and preserved in the output format, giving rise to new methodologies for large-scale analysis of mathematics textbooks and student use of these books. For example, tracking methodologies and interactive visualizations of student viewings of online mathematical textbooks are identified as new research directions for investigating how students engage with mathematics textbooks within and across different educational contexts.

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Notes

  1. https://hal-emse.ccsd.cnrs.fr/CREAD/hal-01207678v1.

  2. FCLA PDF: http://linear.ups.edu/download/fcla-3.50-print.pdf.

  3. FCLA Online: http://linear.ups.edu/fcla/index.html.

  4. http://www.gnu.org/licenses/licenses.html#FDL.

  5. http://linear.ups.edu/fcla/preface-2.html.

  6. https://pretextbook.org.

  7. http://linear.ups.edu/fcla/section-LT.html.

  8. http://multimodal-analysis.com/products/multimodal-analysis-image/software/index.html.

  9. http://www.sagemath.org/.

  10. This work is part of a study being undertaken by Vilma Mesa, Angeliki Mali, Robert Beezer, and David Farmer at the University of Michigan. For further information, see: http://utmost.aimath.org/.

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Acknowledgements

Robert Beezer wrote the First Course in Linear Algebra. He started work on the textbook in 2004 and continues to work on it today. David Farmer developed the interactive visualizations of the student viewing data. Vilma Mesa and Angeliki Mali, in collaboration with Tom Judson, Robert Beezer and David Farmer, are investigating how instructors and students use FCLA and an Abstract Algebra textbook authored by Tom Judson. Kay O’Halloran and Robert Beezer met at the II International Conference on Mathematics Textbook Research and Development (ICMT-2) in Rio de Janeiro, Brazil on 7–11 May 2017 where they attended each other’s talks. This paper is the result of those meetings and the correspondence between the three authors that subsequently took place. The authors thank Vilma Mesa and Angeliki Mali for their comments on earlier drafts of this paper. Partial support for the work undertaken by Robert Beezer and David Farmer was provided by the United States National Science Foundation’s Improving Undergraduate STEM Education (IUSE) program under Award No. 1626455. Vilma Mesa and Angeliki Mali are both personnel on the NSF grant. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the United States National Science Foundation.

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Authors and Affiliations

  1. Curtin University, Perth, Australia

    Kay L. O’Halloran

  2. University of Puget Sound, Tacoma, Washington, USA

    Robert A. Beezer

  3. American Institute of Mathematics, San Jose, California, USA

    David W. Farmer

Authors
  1. Kay L. O’Halloran
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  2. Robert A. Beezer
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  3. David W. Farmer
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Correspondence to Kay L. O’Halloran.

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O’Halloran, K.L., Beezer, R.A. & Farmer, D.W. A new generation of mathematics textbook research and development. ZDM Mathematics Education 50, 863–879 (2018). https://doi.org/10.1007/s11858-018-0959-8

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