Secondary Student Mentorship and Research in Complex Networks: Process and Effects

  • Catherine B. Cramer
  • Lori Sheetz


There is increasing interest in rethinking approaches to K-12 education that better prepare students to face an adult world and work life of data-driven and interdisciplinary science, technology, engineering, and mathematics (STEM). The science of complex networks, also known as network science, is the application of advanced graph theory to characterize, visualize, and analyze complex connected social, biological, technological, and physical systems. It is an important approach to study many problems in data-driven STEM and provides an intuitive pathway for students of any age to understand complex systems. This paper describes the development of a successful mentorship model that combines deep engagement with team research, enabling high school students and teachers to perform successful research projects in the science of complex networks.


NetSci High NGSS High school Educators Teacher professional development Network science 



The authors would like to acknowledge the National Science Foundation (BCS Award #1027752 and DRL Award #1139478) for supporting this important work. Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the National Science Foundation.


  1. 1.
    Euler, Leonhard (1736). Solutio problematis ad geometriam situs pertinentis. Commentarii Academiae Scientiarum Imperialis Petropolitanae 8. 128.Google Scholar
  2. 2.
    Moreno, J. (1934). Who Shall Survive? A new Approach to the Problem of Human Interrelations. Beacon House.Google Scholar
  3. 3.
    Barnes, J. (1954). Class and Committees in a Norwegian Island Parish. Human Relations 7. Thousand Oaks, CA: Sage Publications. 39.CrossRefGoogle Scholar
  4. 4.
    Barabási A.-L., Albert R. (1999) Emergence of scaling in random networks, Science, Vol. 286, No. 5439. Washington, DC: American Association for the Advancement of Science. 509.Google Scholar
  5. 5.
    Barabási, A.-L. (2002). Linked: How everything is connected to everything else and what it means. New York: Plume.Google Scholar
  6. 6.
    Pastor-Satorras, R. and Vespignani, A. (2001) Epidemic spreading in scale-free networks, Physical Review Letters 86. Ridge NY: American Physical Society. 3200.Google Scholar
  7. 7.
    Lazer, D., Pentland, A., Adamic, L., Aral, S., Barabàsi, A-L., Brewer, D., Christakis, N., Contractor, N., Fowler, J., Gutmann, M., Jebara, T., King, G., Macy, M., Roy, D., and Van Alstyne, M. (2009). Computational social science. Science, 323. Washington, DC: American Association for the Advancement of Science. 721.Google Scholar
  8. 8.
    Forrester, Jay W (1976) Moving into the 21st Century: Dilemmas and Strategies for American Higher Education. Liberal Education, Vol. 62, No. 2. Washington, DC: Association of American Colleges & Universities. 158.Google Scholar
  9. 9.
    Hart, E., Maltas, J. and Rich, B. (1990) Teaching Discrete Mathematics in Grades 7–12. Mathematics Teacher Vol. 83, No. 5. Reston, VA: National Council of Teachers of Mathematics. 362.Google Scholar
  10. 10.
    Bollobas, B. (1998) Modern Graph Theory. Graduate Texts in Mathematics, Vol. 184. New York: Springer.Google Scholar
  11. 11.
    Wilson, S. and Rivera-Marrero, O. (2004) Graph Theory: A Topic for Helping Secondary Teachers. Paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education.Google Scholar
  12. 12.
    Fuhrmann, S. , MacEachren, A. , Deberry, M. , Bosley, J., LaPorte Taylor, R. , Gahegan, M. & Downs, R. (2005) MapStats for Kids: Making Geographic and Statistical Facts Available to Children, Journal of Geography, 104:6, 233–241, DOI: Scholar
  13. 13.
    Smithers, D. (2005) Graph Theory for the Secondary School Classroom. Electronic Theses and Dissertations. Paper 1015. Accessed 1/1/18.
  14. 14.
    Lessner, D. (2011), Graph Theory at Czech Grammar Schools, in WDS’11 Proceedings of Contributed Papers: Part I - Mathematics and Computer Sciences (eds. J. Safrankova and J. Pavlu), Prague, Matfyzpress. 78.Google Scholar
  15. 15.
    Casey, N., Fellows, M., and Hawylycz, M. (1993) This Is MEGA Mathematics: Stories And Activities For Mathematical Problem Solving And Communication, The Los Alamos Workbook. Los Alamos, NM: Los Alamos National Laboratory.Google Scholar
  16. 16.
    Siegel, E., and Uzzo, S. (2010) Connections: The Nature of Networks, Communicating Complex and Emerging Science. In Science Exhibitions, Communication and Evaluation. Edited by Anastasia Filippoupoliti. Edinburgh: MuseumsEtc.Google Scholar
  17. 17.
    Rothenberg, M. and Hart, J. (2006) Analysis of Visitor Experience in the Exhibition Connections: the Nature of Networks at the New York Hall of Science. Northampton, MA: People, Places & Design Research.Google Scholar
  18. 18.
    Dancu, T., Gutwill, J., and Sindorf, L. (2009) Geometry Playground Pathways Study. San Francisco, CA: Exploratorium.Google Scholar
  19. 19.
    Laibowitz, M. (2004) Meaning Density and Other Attributes of Deep Engagement MIT Media Lab report. Cambridge, MA: Massachusetts Institute of Technology.Google Scholar
  20. 20.
    Pugh, K., Linnenbrink-Garcia, L., Koskey, K., Stewart, V. and Manzey, C. (2010), Motivation, learning, and transformative experience: A study of deep engagement in science. Science Education, 94. New York: Wiley and Sons. 1.Google Scholar
  21. 21.
    Crick, R, (2012) Deep Engagement as a Complex System: Identity, Learning Power and Authentic Enquiry. in: Sandra L Christenson, S Reschly, C. Wylie (eds) Handbook of Research on Student Engagement. New York: Springer. 675.CrossRefGoogle Scholar
  22. 22.
    Cohen, B., & Cohen, E. (1991). From groupwork among children to R&D teams: Interdependence, interaction and productivity. In E. Lawler, B. Markovsky, C. Ridgeway, & H. Walker (Eds.), Advances in group processes,Vol. 8. West Yorkshire: Emerald Publishing. 205.Google Scholar
  23. 23.
    Webb, N. (1992). Testing a theoretical model of student interaction and learning in small groups. In R. Hertz-Lazarowitz & N. Miller (Eds.), Interaction in cooperative groups: The theoretical anatomy of group learning. New York: Cambridge University Press. 102.Google Scholar
  24. 24.
    Garland, D., O’ Connor, M., Wolfer, T., and Netting, F. (2006) Team-based Research Notes from the Field. Qualitative Social Work Volume: 5 No. 1. Thousand Oaks: Sage Publications. 93.Google Scholar
  25. 25.
    Hsu, L., Lee, K. and Lin, C, (2010) A comparison of individual and team research performance: A study of patents in III, Picmet 2010 Technology Management For Global Economic Growth, Phuket. 1.Google Scholar
  26. 26.
    National Research Council. 2015. Enhancing the Effectiveness of Team Science. Washington, DC: The National Academies Press. Scholar
  27. 27.
    Blansky, D., Kavanaugh, C., Boothroyd, C., Benson, B., Gallagher, J., Endress, J., and Sayama, H. (2013). Spread of academic success in a high school social network. PLOS ONE, Vol. 8, No. 2. e55944.CrossRefGoogle Scholar
  28. 28.
    Faux, R. (2014) Summer Workshop Evaluation Report. Boston, MA: Davis Square Research Associates.Google Scholar
  29. 29.
    Faux, R. (2015) Evaluation of the NetSci High ITEST Project: Summative Report. Boston, MA: Davis Square Research Associates.Google Scholar
  30. 30.
    Daniel, Wayne W. (1990). “Kolmogorov–Smirnov one-sample test”. Applied Nonparametric Statistics (2nd ed.). Boston: PWS-Kent. pp. 319–330.Google Scholar
  31. 31.
    Harrington, H., Beguerisse-Díaz, M., Rombach, M., Keating L, and Porter, M. (2013) Teach network science to teenagers. Network Science, Vol.1, No. 2. Cambridge: Cambridge University Press. 226.Google Scholar
  32. 32.
    Sanchez, A., Brandle, C. (2014). More network science for teenagers. arXiv:1403.3618.Google Scholar
  33. 33.
    NetSciEd (2018) NetSciEd Symposia ( Accessed 1/1/18.
  34. 34.
    Cramer, C., Porter, M., Sayama, H., Sheetz, L. and Uzzo, S. (2015) What are essential concepts about networks? Journal of Complex Networks. Vol. 3 No. 4 Oxford: Oxford University Press.Google Scholar
  35. 35.
    NetSciEd (2015) Network Literacy: Essential Concepts and Core Ideas. ( Accessed 1/1/18.
  36. 36.
    NGSS Lead States. (2013). Next Generation Science Standards: For States, By States. Washington, DC: The National Academies Press.Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Catherine B. Cramer
    • 1
  • Lori Sheetz
    • 2
  1. 1.Data Science Institute, Columbia UniversityNew YorkUSA
  2. 2.Center for Leadership and Diversity in STEM, Department of Mathematical Sciences, U.S. Military Academy at West PointWest PointUSA

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