Tuesday, April 8, 2014

Frenkel, Bressoud, Brights Spots, and the Implementation Era

David Bressoud recently wrote a post Age is Not the Problem in his MAA Blog Launchings.  There are several topics in his post in his response to Edward Frenkel's Op-Ed piece in the LATimes.

One topic I want to emphasize is that teaching and implementation aspect of the pieces.  There is this sense that the education community needs to wake up and get its act together, and this notion comes up implicitly in Frenckel's piece (and he may or may not have a strong opinion about this topic or have intended something by it).   Readers of his piece, however, may pick up on it, so I think this is a good opportunity to highlight the bright spots.

There are literally thousands of us who are working on implementing high quality, inquiry-based, student-centered methods of instruction that incorporates what we have learned from education research and experience.  Many of us in the community have heard the calls for change and are doing something about this.   There are people who are devoting their careers to address the majors issues in mathematics education.  We have bright spots to celebrate and to embrace as pillars for building real, long-term solutions.

Pointing fingers at "bad teachers" or "bad textbooks" or whatever else is one way to deal with education system issues, but it lacks a constructive outcome.  Truly great nations or communities go much, much further.  They look honestly at the problems, they evaluate and think about the evidence available, and they forge alliances and build systems that provide opportunities for the stakeholders to make good decisions and to do the long, hard job of building solutions to complex, long-term problems.  It's a big job to change a cultural activity like teaching.

Hence, this is the implementation era!  Implementation is a major if not the major challenge we face in education.  We have enough good ideas about how to teach effectively now.  It is worthwhile now to expand efforts and get these methods into our classrooms.  Are these methods perfect? No.  Do we need to do more work on improving our methods? Yes.  But we know enough that it's time to move so we can make differences in the lives of students today.  That's the implementation challenge!  Good ideas are on our shelves.  Lots of good ideas!  Now how do we get those good ideas into the classrooms implemented at a high level across the nation, globe?

If you're interested in engaging in this kind of work, please join the IBL community and AIBL (or NCTM or whatever  appropriate professional society for your area).   AIBL's mission is to help math instructors implement at a high level what we have learned.  We don't just talk about the issues, we implement them in our classrooms right now.   We can do more than point fingers and lament and complain.  We can take action and be movers and changers, and you're all invited.

Upward and onward!

Find AIBL at www.inquirybasedlearning.org
Dana Ernst has started a G+ community https://plus.google.com/u/0/communities/107762594334871181831

Saturday, March 22, 2014

Learning Zone Analysis Part 2: Evaluating Math Content

This is part 2 (of 3) of the Learning Zone Analysis (LZA) idea.  LZA Part 1 discusses how one can choose on a macro level the teaching methodology best suited to the specific goal.  In this post, I'll discuss how I use LZA to take apart a unit and use it to guide how I might construct problems.

Let's return to the integers unit for grade 6 (IBL Integers Unit).  The actual context doesn't really matter so much as the framework presented here, and as before I want to capture a wider audience.

We start with a traditional rote explanation of subtracting a number in traditional math settings.  I sometimes see subtracting an integer as (a) change the sign ($-(-1) = +1$), (b) remember to move right on the number line.  I personally experienced (a), when I was a student.  I was told when you see two minuses, you change it to a plus.   So I learned how to get to an answer, without having to learn the concepts that make things work.

I think it's easy to say that most of us agree that merely doing the computation in the ways presented above are a limited and not ultimately beneficial to students without a broader understanding of integers.  The IBL Integers Unit uses a context, includes a model for thinking, introduces zero pairs and mathematical equivalence, and requires students to write a justification why subtracting a negative is equivalent to adding.

Let's break things down...

LZA of the Traditional Integers content
  1. Computing how to subtract integers, skills practice
  2. A connection to the number line, but perhaps without conceptual grounding
LZA of the IBL Integers Unit
  1. Computing how to subtract integers, skills practice
  2. Context for problem solving
  3. Modeling numbers and equivalence (zero pair)
  4. Problem solving
  5. Argumentation and justification
It's immediately obvious the difference in the list.  One misconception in the general public is that the new teaching vs. old teaching is about style and that they are assumed to have the same goals and achieve the same ends.  It's clear that the goals are different, and that one is more sophisticated than the other.  Moreover, both instructors can say, "I covered integers."  The nature of the coverage is vastly different, and while one got through it faster, I'd like to say, "So what?"  What real math was learned if all we achieved is answer getting.

Once again cultivating dispositions is done more appropriately in the IBL setting than the traditional setting.  One can risk saying that a big missing piece in the general discussion about education reform is the difference in what the point of education is.  It makes me wonder if unacknowledged differences in "education axioms" may be a significant contributor to the friction in public discourse.

Another point worth mentioning is that there is an interaction between the method of teaching, teaching philosophy, and the content.  When we think of students as explorers and doers of mathematics, then we are more inclined to present to them tasks that are a different nature than if our view of teaching is focused on skills acquisition (or passing standardized tests).  So teaching isn't just a method.  It's a system.   What we value is important in education, our methods, how we assess, what we assess, our beliefs about what students are capable (and not capable of doing), and the goals of education all feed into what happens in the classroom.

One can argue that it is the case that one can lecture on concepts and conceptual understanding.  So the traditional content can be expanded to some degree.  I point out that the teacher explaining a concept is not equivalent to students actually demonstrating their conceptual understanding through a presentation or written work.  How content is covered and how students engage in it are important, intertwined factors.

A highly useful application of LZA is to use it when you're teaching out of a textbook.  An instructor can look at a section and make a quick list of the content and dispositions that students are likely to engage in.  Then using this list, an instructor will know the strengths and weaknesses of a unit, and fill the "gaps" appropriately.  Knowing students are good/not good at certain dispositions can also add valuable data for the instructor to consider.  When we say, "My students normally are not good at explaining/solving...," then there exists a set of tasks or problems that should be deployed.

Short story: Get your content.  Use LZA.  List what's there and not there.  Adjust.  Win!

Upward and onward!

Tuesday, March 11, 2014

MAA PREP IBL Workshops Summer 2014

Hello IBL Community!

This is a quick reminder that AIBL is offering two IBL Workshops under the MAA PREP umbrella.  Information about our workshops is available at www.iblworkshop.org  These workshops are for college math instructors, and early-career faculty are especially encouraged to register.

Registration for the workshop is handled by MAA through their registration portal

We hope to see you this summer!

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.