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

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.

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

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

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

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

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

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

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

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?

Worksheet Textbook

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

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?

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?

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”

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

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

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.

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. 241-254). 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), 8410-8415. doi:10.1073/pnas.1319030111 Lester, F., K., Jr. (2013). Thoughts About Research On Mathematical Problem-Solving Instruction. The Mathematics Enthusiast, 10(1&2), 245-278. 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.