Wednesday, February 26, 2014

IBL Best Practices Poster Session, MathFest 2014

Hello IBLers!  Please consider presenting a poster at the IBL Best Practices Poster Session, at MathFest  2014.  Poster sessions are a great way to interact with people directly who are interested in similar courses or ideas.   Please join us, share your ideas, and contribute to the IBL community!

This poster session is co-organized by
Angie Hodge, University of Nebraska Omaha, AIBL Special Projects Coordinator
Dana Ernst, Northern Arizona University, AIBL Special Projects Coordinator
Stan Yoshinobu, Cal Poly San Luis Obispo, Director of AIBL

Friday, February 21, 2014

Learning Zone Analysis Part 1: Dispositions and Skills

How do you know when to use a specific teaching method or technique?  This is a question that all teachers deal with, and I believe that a general tool for sorting some of this out can be very helpful.  One idea I have been working on is a framework called "Learning Zone Analysis" or LZA for short.   In this post, I'll discuss one aspect of LZA, which is useful for deciding when to use active learning and when one can get away with a mini lecture or flipping a topic outside of class.

Zone 1 contains dispositions.  Dispositions include (but not limited to) problem-solving ability, learning to read and write proofs, positive attitudes about mathematics, being willing to experiment, searching for counterexamples, advanced techniques, communicating ideas, utilizing effective practices in the study of mathematics.  

Zone 2 contains basic skills, factual knowledge, connecting Math to other subjects (or other disciplines within Math), motivation, organizing information or a unit of work that students have just presented proofs on, etc.

LZA can be represented in a diagram:

For Zone 1, it can be argued that it is most appropriate to use active, student-centered methods, such as IBL.  Zone 1 is about dispositions, habits of mind, and cultivating higher-level skills.  Such dispositions must be developed by students for themselves through sustained practice and reflection in a supportive environment.  Dispositions cannot be learned by listening to others, and this is fundamentally why actively solving challenging problems is necessary.

Zone 2 can be effectively and efficiently covered through lectures or mini lectures.  Learning about where your office is shouldn't be a problem-solving experience.  Similarly, students could learn that Fourier Series can be applied to signal processing on their own, but it's much more motivating and useful if the instructor presents a succinct, clear exposition of the connections, providing value and motivation.  Further I can envision setting the context of a unit, what students are responsible for learning outside of class, students' roles, and and should be done via direct instruction.

Motivation actually exists in both zone 1 and zone 2.  In zone 2, the instructor can give explicit motivation for mathematical concepts.  A different kind of motivation can be addressed by the instructor in the form of encouragement and praise.  Encouragement and praise should be regular and clearly positive.

Motivation in Zone 1 is tacit.  It is through individual successes over long time periods that students become ever more confident and motivated to learn mathematics.   It is also arguable the the motivation from being successful at solving hard math problems is more authentic and long lasting compared to pep talks.   Motivation from mentoring or coaching and from success are both necessary.

How does this all work in the practical world?  For a specific topic, list the goals of the lesson(s) into zone 1 and zone 2.  Then select IBL or teacher-centered to cover each zone.  A rule of thumb is 75% IBL and 25% teacher-centered is a good place to start, with variation class-to-class to suit the specific mathematical landscape and how students are getting on with the material.

There exist other ways to use LZA.  We could evaluate lessons or curricula to see how much higher-level thinking vs. factual or skills knowledge is present.  LZA can also be used in class observations to measure how much of the visible work is in zone 1 or 2, and the relative effectiveness of lecture vs. IBL.  More on these other uses in future posts.

Friday, February 7, 2014

Student Testimonial: Nora Ortega

Nora Ortega is a math major in the teaching option at Cal Poly San Luis Obispo.  Nora has taken several IBL Math courses, including Intro to Proofs (Math 248), Euclidean Geometry (Math 442), and Modern Geometry (Math 443).  Nora intends to become a high school math teacher.

One of my favorite parts of this video starts at around 6:15, when Nora is asked about the impact her experiences in IBL classes have had on her intended career choice.  Nora discusses how seeing her instructors take a risk has left an impression upon her to do more.


Saturday, February 1, 2014

IBL Workshops in 2014

AIBL is offering two IBL Workshops in summer 2014 for professors and instructors of undergraduate mathematics courses.  The 4-day workshops are built around hands-on, interactive sessions focused on the skills, practices, and concepts necessary for successful implementation of IBL methods.  Participants are supported for one calendar year via a follow-up mentoring program, and invited into in the IBL community.

Workshop 1 will be hosted at Kenyon College, Gambier OH, June 23-26, 2014.
Workshop 2 is a pre-MathFest workshop in Portland, OR, August 3-6, 2014.

More information is available on the IBL Workshop website.

Both workshops have identical programs and are designated MAA PREP workshops.  The workshops are funded with generous support from the National Science Foundation, The Educational Advancement Foundation, and the Academy of Inquiry Based Learning.