1. Mathematical Problem Solving and Active Learning: What, Why, and How
Kira Heater
Laramie County Community College

2. Hello Introduce yourselves at your table. Name Where you are from.
Something Unique about you.
Find one thing in common among those at your table.

3. Working in Groups Prioritize group work on day one!
Create a community of learners
Commit to making time in your schedule for group work
Stop using the chalkboard
Mix and Match

4. Your Class
What do you want your students to say about your class at the end of the semester?

5. The Courage to Teach
“…good teaching cannot be reduced to technique; good teaching comes from the identity and integrity of the teacher.” (Palmer 2010, p. 10)
Parker Palmer, The Courage to Teach

6. Teach from your Heart Good teaching comes in many flavors
Find your groove
Be Authentic

7. The Importance of Active Learning
In Freeman et. Al.’s (Freeman, Eddy et al. 2014) meta-analysis of 225 studies of college level STEM courses, in courses which used active learning techniques rather than traditional lecture students:
Were 1.5 times less likely to fail the class
(55% more likely to fail a class where only traditional lecture was used)
Saw a 6% increase in letter grades

8. Active Learning Defined
Freeman defined active learning through activities. Students engaged in active learning through:
Small group problem solving
In class worksheets
Use of personal response systems (clickers)
Classes using a workshop or studio model

9. Active Learning Activities in Higher Education
University of Minnesota’s Center for Educational Innovation: group discussions, problem solving, case studies, role plays, journal writing, and structured learning groups
California State University, LA: individual exercises, question and answer, critical thinking motivators, share/pair, cooperative learning exercise
Teaching Commons at Stanford: discussion during lecture (think-pair-share), problem or case-based research studies, small group critical analysis exercises, debate
The Center for Teaching Excellence at Cornell: one minute paper, think-pair-share, classroom response systems

10. My Approach to Active Learning
Live Slow, Think Fast
Mindfulness or Mindlessness
If I am bored, it’s a good thing
Use resources available: Textbook
Screen Clipping in Word is your friend
Who does the math?

11. Worksheet
Textbook

12. From:, Briggs & Cochran, Calculus Addison-Wesley 2010

16. Your Class
What do you want your students to learn in your class? What do you want students to know about Mathematics when they leave your class?

17. Mathematical Thinking
Does the task use multiple solution strategies?
Does the task encourage multiple representations?
Does the task demand explanation?
Does the task include finding patterns, conjecturing, or interpreting?
Does the task encourage questioning?

18. Mathematical Problem Solving
“…problem solving is an activity requiring an individual (or group) to engage in a variety of cognitive actions, each of which requires some knowledge and skill, and some of with are not routine.”(Lester 2013, p. 249)
Frank K. Lester, Jr., “Thoughts about Research on Mathematical Problem Solving”

19. Lester on Problem Solvers
A successful problem solver must:
Have much experience learning to solve problems
Strong content knowledge
An ability to use different representations
Understand how to recognize and construct patterns of inference
Be guided by intuition

20. What is a Problem?
“students’ own exploration of the problem is an essential competent in teaching through problem solving.”
J. Cai (2003), “What research tells us about teaching mathematics through problem solving.”
He suggests that problem solving problems include:
Open-ended problems which allow for multiple solution strategies
May allow for several correct answers
Create and opportunity for mathematical exploration
Allow students to “invent” their own strategies
Important mathematical ideas should be explored

21. Closing Thoughts Be thoughtful in your teaching
Create opportunities for both you and your students to learn
Be brave and bold
Laugh and have fun!
Enjoy your conference.

22. References
Briggs, W. L., Cochran, L., & Gillett, B. (2011). Calculus: Early Transcendentals: Pearson Boston.
Cai, J. (2003). What research tells us about teaching mathematics through problem solving. In J. F. K. Lester (Ed.), Reserach and issues in teaching mathematics through problem solving (pp ). Reston, VA: National Council of Teachers of Mathematics.
Freeman, S., Eddy, S. L., McDonough, M., Smith, M. K., Okoroafor, N., Jordt, H., & Wenderoth, M. P. (2014). Active learning increases student performance in science, engineering, and mathematics. Proceedings of the National Academy of Sciences, 111(23), doi: /pnas
Lester, F., K., Jr. (2013). Thoughts About Research On Mathematical Problem-Solving Instruction. The Mathematics Enthusiast, 10(1&2),
Palmer, P. J. (2010). The courage to teach: Exploring the inner landscape of a teacher's life: John Wiley & Sons.
Stewart, J. (2008). Calculus: Early Transcendentals. Thomson Brooks. Cole, Belmont.