Skip to main content

Integrating Computational Thinking in Discrete Structures

  • Chapter
  • First Online:

Abstract

Computational thinking (CT) is broadly defined as the thought processes involved in formulating problems and their solutions so that the solutions can be automated. In this twenty-first century, computation is fundamental, and often unavoidable, in most endeavors, thus computing educators have the responsibility to instill in future generations of scientists, mathematicians, and engineers key computational thinking skills. There is a compelling case to be made for the infusion of CT skills into the K-16 education of everyone, given the pervasiveness of computers in all aspects of our lives. This poses the following critical educational challenge: how and when should students learn CT and how and when should it be taught? While discussions, deliberations, and debates will likely continue, the tightly knitted relationship between computational thinking and mathematical thinking suggests that one avenue to acquire CT skills is to integrate CT in the K-16 mathematics curriculum. This chapter describes a study that uses a problem-driven learning pedagogical strategy and the APOS theoretical framework to integrate computational thinking in CSCE 2100, a sophomore level discrete structures course which is a required course for all Information Technology majors. Results demonstrate that integrating computational thinking in a discrete structures course can effectively and significantly influence students’ understanding of a range of CT concepts.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Asiala, M., Brown, A., DeVries, D. J., Dubinsky, E., Mathews, D., & Thomas, K. (1996). A framework for research and curriculum development in undergraduate mathematics education. Research in Collegiate Mathematics Education, 2, 1–32.

    Article  Google Scholar 

  • Baldwin, D., Walker, H., & Henderson, P. (2013). The roles of mathematics in computer science. ACM Inroads, 4(4), 74–80.

    Article  Google Scholar 

  • Barr, V., & Stephenson, C. (2011). Bringing computational thinking to K-12: What is involved and what is the role of the computer science education community? ACM Inroads, 2(1), 48–54.

    Article  Google Scholar 

  • Cormen, T., Leiserson, C., Rivest, R., & Stein, C. (2001). Introduction to algorithms. Cambridge, MA: MIT.

    Google Scholar 

  • Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. Tall (Ed.), Advanced mathematical thinking (pp. 231–250). Dordrecht: Kluwer.

    Google Scholar 

  • Gorman, J., Gsell, S. & Mayfield, C. (2014). Learning relational algebra by snapping blocks. In Proceedings of the 45th SIGCSE technical symposium on computer science education (pp. 73–78).

    Google Scholar 

  • Henderson, P. B. (2003). Mathematical reasoning in software engineering education. Communications of the ACM, 46(9), 45–50.

    Article  Google Scholar 

  • Henderson, P. B., Baldwin, D., et al. (2001). Striving for mathematical thinking, ITiCSE 2000 working group report. SIGCSE Bulletin–Inroads, 33(4), 114–124.

    Article  Google Scholar 

  • Jenkins, J. T., Jerkins, J. A., & Stenger, C. L. (2012). A plan for immediate immersion of computational thinking into the high school math classroom through a partnership with AMSTI. In Proceedings of the 50th annual ACM southeast regional conference (pp. 148–152).

    Google Scholar 

  • Johnson, S. M. (1963). Generation of permutations by adjacent transposition. Mathematics of Computation, 17, 282–285.

    Article  Google Scholar 

  • Kmoch, J. (2013). Computational thinking dispositions and the common core math standards. CSTA Voice, 9(4), 3–5.

    Google Scholar 

  • Knuth, D. (1985). Algorithmic thinking and mathematical thinking. The American Mathematical Monthly, 92(3), 170–181.

    Article  Google Scholar 

  • Kynigos, C. (2007). Using half-baked microworlds to challenge teacher educators knowing. Journal of Computers for Math Learning, 12(2), 87–111.

    Article  Google Scholar 

  • Larson, P., Fitzgerald, J., & Brooks, T. (1996). Applying formal specification in industry. IEEE Software, 13(3), 48–56.

    Article  Google Scholar 

  • Lu, J. & Fletcher, G. (2009). Thinking about computational thinking. In Proceedings of the 40th SIGCSE technical symposium on computer science education (pp. 260–264).

    Google Scholar 

  • McMaster, K. (2008). Two gestalts for mathematics: Logical vs. computational. Information Systems Education Journal, 6(20), 1–13.

    Google Scholar 

  • Piaget, J. (1970). Genetic epistemology. New York, NY: Columbia University Press.

    Google Scholar 

  • Rich, P., Leatham, K., & Wright, G. (2013). Convergent cognition. Instructional Science, 41(2), 431–453.

    Article  Google Scholar 

  • Roberts, E. (Ed.). (2002). Computing curricula 2001: Computer science final report. New York, NY: IEEE Computer Society.

    Google Scholar 

  • Sherin, B. (2001). A comparison of programming languages and algebraic notation as expressive languages for physics. International Journal of Computers for Mathematics Learning, 6(1), 1–61.

    Article  Google Scholar 

  • Sobel, A. (2000). Empirical results of a software engineering curriculum incorporating forma methods. SIGCSE Bulletin, 32(1), 157–161.

    Article  Google Scholar 

  • Trotter, H. F. (1962). Algorithm 115: Perm. Communications of the ACM, 5(8), 434–435.

    Article  Google Scholar 

  • Wing, J. M. (2006). Computational thinking. Communications of the ACM, 49(3), 33–35.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Gerard Rambally .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Rambally, G. (2017). Integrating Computational Thinking in Discrete Structures. In: Rich, P., Hodges, C. (eds) Emerging Research, Practice, and Policy on Computational Thinking. Educational Communications and Technology: Issues and Innovations. Springer, Cham. https://doi.org/10.1007/978-3-319-52691-1_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-52691-1_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-52690-4

  • Online ISBN: 978-3-319-52691-1

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics