# TEACHING AND LEARNING PROBLEM-SOLVING SKILLS PROJECT

DR. SHELLY WISMATH,
Professor,
Dept. of Mathematics and Computer Science,
and Liberal Education Program,
University of Lethbridge,
Lethbridge, Alberta,
e-mail: wismaths@cs.uleth.ca

CO-INVESTIGATOR:
DOUG ORR
Blended Learning Coordinator,
CRDC/CAETL, University of Lethbridge
Lethbridge AB.

RESEARCH ASSISTANTS:
Brandon Good, January 2010 - August 2010.
Maggie Zhong, Jaunary 2012 - August 2013.

BACKGROUND:

In 2010 I designed and taught a topics course called Problems and Puzzles, which is now offered as Liberal Education 2200. The core of this course deals with solving mathematical problems, including puzzles, games, and logic problems. We also look at problem solving from the point of view of other disciplines. Classes alternate between lectures on problem-solving tools and approaches, and actually working on problems. Assignments and tests similarly contain a balance of theory and hands-on work.

In conjunction with this course, I have carried out research on how students learn problem-solving skills.

What is problem-solving? In common language, a problem is an unpleasant situation, a difficulty. But in education, the first definition in {\textit Webster's Dictionary} - a question raised for inquiry, consideration, or solution" - is a more common meaning... Whenever you are thinking creatively and critically about ways to increase the quality of life (or to avoid a decrease in quality), you are actively involved in problem solving."
from Problem-Solving Skills in Education and Life, http://www.asa3.org/ASA/education/think/methods.html

As Kinsey and Moore write, Problem solving is a skill that you can apply to any situation or career, and mathematics is a very good place to work on it." (2002). (L. C. Kinsey and T. E. Moore, Symmetry, Shape and Space: An Introduction to Mathematics through Geometry, Springer, 2002.)

LINKS TO PUZZLES (AND A FEW JOKES): A list of good links.

BASIC RESEARCH QUESTIONS:

What are problem-solving skills?

How are they learned?

How can they best be taught or facilitated?

How can they be measured?

How can we tell if this course is helping students develop such skills?

INFORMATION on the Problems and Puzzles Course:

: Course Syllabus for Spring 2012; some changes will be made in the next offering in Spring 2013.

: List of topics covered for Spring 2012; some changes will be made in the next offering in Spring 2013.

FUNDING:

This project has been funded by the University of Lethbridge Teaching Development Fund, in 2010, 2011 and 2012.

RESEARCH PAPERS:

1. Shelly Wismath (2012). Shifting the Teacher-Learner Paradigm: Teaching for the 21st Century," College Teaching, Vo. 61 n0. 3, 2013, 88 - 89.

2. Shelly Wismath, Doug Orr and Brandon Good (2012). Metacogntion: Student Reflections on Problem Solving" Journal on Excellence in College Teaching, 2014, Vol. 25 no. 2, p. 69 - 90. \\

3. Shelly Wismath and Maggie Zhong (2012). Gender Differences in University Students' Perception of and Confidence in Problem-Solving Abilities." Journal of Women and Minorities in Science and Engineering, Vol. 20 Issue 1, 2014, pp. 1 - 10.

4. Shelly Wismath, Doug Orr and Bruce Mackay (2015). Transitions and Threshold Concepts in Problem Solving". Teaching and Learning Inquiry: The ISSOTL Journal Vol. 3, No. 1 (2015), pp. 63-73.

5. Shelly Wismath, Doug Orr and Maggie Zhong (2014). Student Perception of Problem-Solving Skills". Transformative Dialogues: Teaching and Learning Journal, Volume 7 Issue 3, November 2014. See https://www.kpu.ca/sites/default/files/Transformative%20Dialogues/TD7.3.5_Wismath_etal_Student_Perception.pdf

6. Shelly Wismath and Doug Orr. Collaborative Learning in Problem Solving: A Case Study in Metacognitive Learning". The Canadian Journal for the Scholarship of Teaching and Learning Volume 6, Issue 3 Article 10, Dec. 2015. See http://ir.lib.uwo.ca/cgi/viewcontent.cgi?article=1246&context=cjsotl_rcacea

CONFERENCE PRESENTATIONS:

1. Shelly Wismath, Maggie Zhong and Doug Orr (Nov. 2012). Teaching and Learning Problem-Solving Skills". One hour presentation at the MRU Symposium on the Scholarship of Teaching and Learning, Nov. 9, 2012.

2. Shelly Wismath and Maggie Zhong (Nov. 2012). Gender Differences in Confidence in Problem Solving". Poster presentation at the Mount Royal University Symposium on the Scholarship of Teaching and Learning, Nov. 9, 2012.

3. Shelly Wismath and Doug Orr (May 2013). Collaborative Learning in Problem Solving", One hour presentation at the University of Calgary Collaboration for Learning Conference.

4. Shelly Wismath and Doug Orr (Nov. 2013). Transitions and Threshold Concepts in Problem Solving". One hour presentation at Mount Royal University Symposium on the Scholarship of Teaching and Learning.

USEFUL REFERENCES:

George Polya, 1945, 1973. How to solve it: A new aspect of mathematical method. New Jersey: Princeton University Press.

Marcel Danesi, 2002. The puzzle instinct: the meaning of puzzles in human life. Indiana University Press.

Tim van Gelder: Teaching critical thinking: Some aspects from cognitive science. College Teaching, Winter 2005, Vol. 53, no. 1, pp. 41 - 46.

Janet E. Davidson and Robert J. Sternberg (Editors), 2003. The Psychology of problem solving. Cambridge: Cambridge University Press.