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Journal Article

Threshold Concepts in the Development of Problem-solving Skills

Shelly Wismath, Doug Orr and Bruce MacKay
Teaching & Learning Inquiry: The ISSOTL Journal
Vol. 3, No. 1 (2015), pp. 63-73
Published by: University of Calgary on behalf of the International Society for the Scholarship of Teaching and Learning
DOI: 10.2979/teachlearninqu.3.1.63
Stable URL: http://www.jstor.org/stable/10.2979/teachlearninqu.3.1.63
Page Count: 12
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ARTICLES

Abstract

ABSTRACT

Problem-solving skills are often identified as a key component of 21st century education. This study collected data from students enrolled in a university-level Liberal Education science course called Problems and Puzzles, which introduced students to the theory and practice of problem solving via puzzles. Based on classroom observation and other qualitative data collected over three semesters, we have identified three significant changes in student behaviour at specific points in the course. These changes can be posited to reveal three underlying threshold concepts in the evolution and establishment of students' problem-solving skills.

KEYWORDS problem solving, threshold concepts, persistence, novice-to-expert transition, transformative experience, liminal state.

Author Information

Shelly WismathUniversity Of Lethbridge,

Shelly Wismath is a Professor at University of Lethbridge in the Departments of Mathematics and Computer Science and the Liberal Education Program.

Doug OrrUniversity Of Lethbridge,

Doug Orr is the Teaching Development Coordinator for the University of Lethbridge Teaching Centre.

Bruce MacKayUniversity Of Lethbridge,

D. Bruce MacKay is Assistant Professor and Coordinator of the Liberal Education Program in the Faculty of Arts and Science at the University of Lethbridge.

REFERENCES

  1. Adler-Kassner, L., Majewski, J. & Koshnick, D. (2012). The Value of Troublesome Knowledge: Transfer and Threshold Concepts in Writing and History. Composition Forum, 26, Fall 2012.
  2. Adawi, T. & Kabo, J. (2012, June). Exploring threshold concepts and liminal spaces using phenomenography: Engineering students' conceptions of technology as an example. Paper presented at the Fourth Bienniel Conference on Threshold Concepts: From personal practice to communities of practice. Trinity College, Dublin, 28-29 June 2012. Abstract retrieved from http://www.nairtl.ie/index.php?pageID=27&eventID=310
  3. Altheide, D.L., & Johnson, J.M. (1998). Criteria for assessing interpretive validity in qualitative research. In N.K. Denzin & Y.S. Lincoln (Eds.), Collecting and interpreting qualitative materials, pp. 283-312. Thousand Oaks, CA: Sage Publications.
  4. Barsch, J. (1991). Barsch learning style inventory. Novato, CA: Academic Therapy.
  5. Bloom, B.S. (Ed.) (1956) Taxonomy of Educational Objectives. NY: Longmans, Green.
  6. Conference Board of Canada. (2013) Employability skills 2000+. Retrieved from http://www.conferenceboard.ca/topics/education/learning-tools/employability-skills.aspx
  7. Diaz, M, Middendorf, J, Pace, D & Shopkow, L (2008). The history learning project: a department “decodes” its students. Journal of American History, March 2008, 1211 – 1224.
  8. Cousin, G. (2006). An introduction to threshold concepts. Planet, No. 17, Dec. 2006. pp. 4-5.
  9. Ericsson, A.K. (2003). The acquisition of expert performance as problem solving: Construction and modification of mediating mechanisms through deliberate practice, pp. 31-83 in Janet E. Davidson & Robert J. Sternberg (Eds.), The Psychology of Problem Solving. New York: Cambridge University Press.
  10. Flavell, J.H. (1979). Metacognition and cognitive monitoring: A new area of cognitive-developmental inquiry. American Psychologist, 34(10), 906 – 911.
  11. Flavell, J.H. (1987). Speculations about the nature and development of metacognition. In F. E Weinert & R. H. Kluwe (Eds.), Metacognition, Motivation and Understanding (pp. 21-29). Hillside, New Jersey: Lawrence Erlbaum Associates.
  12. Gregorc, A.F. (1979). Learning/teaching styles: Their nature and effects. In J. W. Keefe (Ed.). Student Learning Styles: Diagnosing and Prescribing Programs. Reston, VA: National Association of Secondary School Principals. 19-26.
  13. Hokstad, L.M., Flanagan, M.T., Zimmermann, M., Ackermann, G., Andersen, B. & Fradinho, M. (2012). A comparative academic/industrial professional development study of threshold concepts in project management. Paper presented at the Fourth Bienniel Conference on Threshold Concepts: From personal practice to communities of practice. Trinity College, Dublin, 28-29 June 2012. Abstract retrieved from http://www.nairtl.ie/index.php?pageID=27&eventID=310
  14. Janesick, V.J. (1998). The dance of qualitative research design: Metaphor, methadolatry, and meaning, pp.35-55. Thousand Oaks, CA: Sage Publications.
  15. Kay, K. (2010). 21st century skills: Why they matter, what they are, and how we get there. Foreword in: 21st Century Skills: Rethinking how students learn, J. Bellanca & R. Brandt (Eds.) Bloomington, IN: Learning Tree.
  16. Krathwohl, D.R. (2002). A revision of Bloom's Taxonomy: An overview. Theory Into Practice, 41(4), 212-218.
  17. Lesgold, A.M. (1998) Problem solving. In R.J.Sternberg & E. E. Smith (Eds.), The psychology of human thought (pp. 188-213). New York: Cambridge University Press.
  18. Mayan, M.J. (2009). Essentials of qualitative inquiry. Walnut Creek, CA: Left Coast Press Inc.
  19. Meyer, J.H.F. & Land, R. (2003). Threshold concepts and troublesome knowledge (1): Linkages to ways of thinking and practicing, in Rust, C. (Ed.), Improving Student Learning – 10 years on. Oxford: OCSLD.
  20. Middendorf, J. & Pace D. (2004). Decoding the disciplines: A model for helping students learn disciplinary ways of thinking. New Directions for Teaching and Learning, 98, 1-12.
  21. Pòlya, G. (1945, 1973) How to solve it: A new aspect of mathematical method. New Jersey: Princeton University Press.
  22. Pretz, J.E., Naples, A.J. & Sternberg, R.J. (2003). Recognizing, defining and representing problems. In Janet E. Davidson & Robert J. Sternberg (Eds.), The Psychology of Problem Solving, New York: Cambridge University Press.
  23. Savery, J. R. (2006). Overview of problem-based learning: De?nitions and distinctions. Interdisciplinary Journal of Problem-based Learning, 1(1). Retrieved from http://dx.doi.org/10.7771/1541-5015.1002
  24. Schwartzman, L. (2010). Transcending disciplinary boundaries: A proposed theoretical foundation for threshold concepts. In J.H.F. Meyer, R. Land & C. Baillie (Eds.), Threshold Concepts and Transformational Learning (pp. 21 – 44). Boston, MA: Sense Publishers.
  25. Wiggins, G. & McTighe, J. (2005.) Understanding by design (expanded 2nd ed.). Alexandria, VA: Association for Supervision and Curriculum Development.
  26. Wilkerson, L. & Gijselaers, W. (Eds.) (1996). Bringing problem-based learning to higher education: Theory and practice. New Directions in Teaching and Learning Series, no. 68. San Francisco: Jossey-Bass.
  27. Wismath, S., Orr, D., & Good, B. (2014). Metacognition: Student reflections on problem solving. Journal on Excellence in College Teaching.
  28. Wismath, S., Orr, D., & Zhong, M. (2014). Student perception of problem solving skills. Transformative Dialogues, 7(3), 1–17.
  29. Wismath, S. & Zhong, M. (2014). Gender differences in university students' perception of and confidence in problem-solving abilities. Journal of Women and Minorities in Science and Engineering, 20 (1), 1-10. doi: 10.1615/JWomenMinorScienEng.2013006530
  30. Zimmerman, B.J. & Campillo, M. (2003). Motivating Self-Regulated Problem Solvers, p. 233-262 in Janet E. Davidson and Robert J. Sternberg (eds.), The Psychology of Problem Solving, New York: Cambridge University Press.

REFERENCES

  1. Adler-Kassner, L., Majewski, J. & Koshnick, D. (2012). The Value of Troublesome Knowledge: Transfer and Threshold Concepts in Writing and History. Composition Forum, 26, Fall 2012.
  2. Adawi, T. & Kabo, J. (2012, June). Exploring threshold concepts and liminal spaces using phenomenography: Engineering students' conceptions of technology as an example. Paper presented at the Fourth Bienniel Conference on Threshold Concepts: From personal practice to communities of practice. Trinity College, Dublin, 28-29 June 2012. Abstract retrieved from http://www.nairtl.ie/index.php?pageID=27&eventID=310
  3. Altheide, D.L., & Johnson, J.M. (1998). Criteria for assessing interpretive validity in qualitative research. In N.K. Denzin & Y.S. Lincoln (Eds.), Collecting and interpreting qualitative materials, pp. 283-312. Thousand Oaks, CA: Sage Publications.
  4. Barsch, J. (1991). Barsch learning style inventory. Novato, CA: Academic Therapy.
  5. Bloom, B.S. (Ed.) (1956) Taxonomy of Educational Objectives. NY: Longmans, Green.
  6. Conference Board of Canada. (2013) Employability skills 2000+. Retrieved from http://www.conferenceboard.ca/topics/education/learning-tools/employability-skills.aspx
  7. Diaz, M, Middendorf, J, Pace, D & Shopkow, L (2008). The history learning project: a department “decodes” its students. Journal of American History, March 2008, 1211 – 1224.
  8. Cousin, G. (2006). An introduction to threshold concepts. Planet, No. 17, Dec. 2006. pp. 4-5.
  9. Ericsson, A.K. (2003). The acquisition of expert performance as problem solving: Construction and modification of mediating mechanisms through deliberate practice, pp. 31-83 in Janet E. Davidson & Robert J. Sternberg (Eds.), The Psychology of Problem Solving. New York: Cambridge University Press.
  10. Flavell, J.H. (1979). Metacognition and cognitive monitoring: A new area of cognitive-developmental inquiry. American Psychologist, 34(10), 906 – 911.
  11. Flavell, J.H. (1987). Speculations about the nature and development of metacognition. In F. E Weinert & R. H. Kluwe (Eds.), Metacognition, Motivation and Understanding (pp. 21-29). Hillside, New Jersey: Lawrence Erlbaum Associates.
  12. Gregorc, A.F. (1979). Learning/teaching styles: Their nature and effects. In J. W. Keefe (Ed.). Student Learning Styles: Diagnosing and Prescribing Programs. Reston, VA: National Association of Secondary School Principals. 19-26.
  13. Hokstad, L.M., Flanagan, M.T., Zimmermann, M., Ackermann, G., Andersen, B. & Fradinho, M. (2012). A comparative academic/industrial professional development study of threshold concepts in project management. Paper presented at the Fourth Bienniel Conference on Threshold Concepts: From personal practice to communities of practice. Trinity College, Dublin, 28-29 June 2012. Abstract retrieved from http://www.nairtl.ie/index.php?pageID=27&eventID=310
  14. Janesick, V.J. (1998). The dance of qualitative research design: Metaphor, methadolatry, and meaning, pp.35-55. Thousand Oaks, CA: Sage Publications.
  15. Kay, K. (2010). 21st century skills: Why they matter, what they are, and how we get there. Foreword in: 21st Century Skills: Rethinking how students learn, J. Bellanca & R. Brandt (Eds.) Bloomington, IN: Learning Tree.
  16. Krathwohl, D.R. (2002). A revision of Bloom's Taxonomy: An overview. Theory Into Practice, 41(4), 212-218.
  17. Lesgold, A.M. (1998) Problem solving. In R.J.Sternberg & E. E. Smith (Eds.), The psychology of human thought (pp. 188-213). New York: Cambridge University Press.
  18. Mayan, M.J. (2009). Essentials of qualitative inquiry. Walnut Creek, CA: Left Coast Press Inc.
  19. Meyer, J.H.F. & Land, R. (2003). Threshold concepts and troublesome knowledge (1): Linkages to ways of thinking and practicing, in Rust, C. (Ed.), Improving Student Learning – 10 years on. Oxford: OCSLD.
  20. Middendorf, J. & Pace D. (2004). Decoding the disciplines: A model for helping students learn disciplinary ways of thinking. New Directions for Teaching and Learning, 98, 1-12.
  21. Pòlya, G. (1945, 1973) How to solve it: A new aspect of mathematical method. New Jersey: Princeton University Press.
  22. Pretz, J.E., Naples, A.J. & Sternberg, R.J. (2003). Recognizing, defining and representing problems. In Janet E. Davidson & Robert J. Sternberg (Eds.), The Psychology of Problem Solving, New York: Cambridge University Press.
  23. Savery, J. R. (2006). Overview of problem-based learning: De?nitions and distinctions. Interdisciplinary Journal of Problem-based Learning, 1(1). Retrieved from http://dx.doi.org/10.7771/1541-5015.1002
  24. Schwartzman, L. (2010). Transcending disciplinary boundaries: A proposed theoretical foundation for threshold concepts. In J.H.F. Meyer, R. Land & C. Baillie (Eds.), Threshold Concepts and Transformational Learning (pp. 21 – 44). Boston, MA: Sense Publishers.
  25. Wiggins, G. & McTighe, J. (2005.) Understanding by design (expanded 2nd ed.). Alexandria, VA: Association for Supervision and Curriculum Development.
  26. Wilkerson, L. & Gijselaers, W. (Eds.) (1996). Bringing problem-based learning to higher education: Theory and practice. New Directions in Teaching and Learning Series, no. 68. San Francisco: Jossey-Bass.
  27. Wismath, S., Orr, D., & Good, B. (2014). Metacognition: Student reflections on problem solving. Journal on Excellence in College Teaching.
  28. Wismath, S., Orr, D., & Zhong, M. (2014). Student perception of problem solving skills. Transformative Dialogues, 7(3), 1–17.
  29. Wismath, S. & Zhong, M. (2014). Gender differences in university students' perception of and confidence in problem-solving abilities. Journal of Women and Minorities in Science and Engineering, 20 (1), 1-10. doi: 10.1615/JWomenMinorScienEng.2013006530
  30. Zimmerman, B.J. & Campillo, M. (2003). Motivating Self-Regulated Problem Solvers, p. 233-262 in Janet E. Davidson and Robert J. Sternberg (eds.), The Psychology of Problem Solving, New York: Cambridge University Press.