This was the best Learning Adventure because it showed us how allow learners to tackle perceived big, unsolvable, off limits, whole entity problems.

Not sure how to post the artifact as the discussions were lengthy and the collaborative work of our Cadre went above and beyond the normal limitations of classroom “assignments.”

Check it HERE.

All in all there were some very impressive codes, graphs, and conjectures posted on the Collatz conjecture.

I had my fun with 2n-1 almost making some “big” breakthroughs.

So here are some graphs, emails, and thoughts:

Preferred paths

Preferred paths

collatz1

REFLECTION:

I can’t remember when I first stumbled upon Perkins, probably senior year at UCSD during a mundane visual arts class.  Unlike my “sage on the stage” professor, Perkins offered a refreshing approach to thinking about art in The Intelligent Eye: Learning to Think by Looking at Art , The Getty Center for Education in the Arts, 1994.

Furthermore, his ideas on peace education have struck me as both intelligent, noble and plausible so when I saw “Making Learning Whole” on your blog I put it my Amazon shopping cart….(I like books.)

For anyone interested here’s his first 7 principles.  Principle #7 in particular, answers Gary’s question for me:

RE:  So, what do you think was the “point” of the 3N Learning Adventure?  What are some lessons that emerge?

1. Play the whole game. If you’re a baseball player step up to the plate.  If you’re a jazz musician get up on the stage.  If you’re a scientist don’t learn science by reading about it (“aboutitis”), DO IT.  In the Collatz conjecture we (along with children) were attempting high caliber “math conference” problems and we had fun doing it (or gained awareness about our learning styles/apprehensions).  Ultimately, by approaching the big picture we understood how the elements fit instead of banking up knowledge step by step before we were ready to tackle a monster problem.  In this sense, the whole game was effective and refreshing.

2. Make the game worth playing. Some of us are still not clear why we are doing these adventures.  I wasn’t until about up to the Comedian…Say what you will about the Socratic method but it does get you thinking and as I began to uncover the “why and how” the meaning behind the learning adventures connected to the real world.  As such, this course, this Masters program, and the effects it will have in my life grows more and more valuable.

3. Work on the hard parts. We all have different perspectives so we must dig deep to uncover our underlying biases, assumptions and apprehensions.  Some of us consulted experts and friends to help with us with this conjecture and in the process were able to reflect more critically and work on our supposed “weaknesses.”

4. Play out of town.  3n and Microworlds EX was a novel approach to mathematics, programming, and learning for me.  Getting out of our comfort zone keeps us from becoming crusty, stale, teachers.  Tackling foreign challenges makes us exciting, multi-dimensional lifelong learners.

5. Uncover the hidden game. For me, the 3N adventure was a real breakthrough as it fit together social constructivism, public education, and my personal objectives in pursuing a Master’s degree.  I.E. Just as public education was ultimately helpful in remedying some social ills of the 20th century (illiteracy, segregation) 21st century education must address how we learn knowledge building in a more technologically advanced society.  How will we create imaginative, inventive, effective leaders who shape our world instead of merely being shaped by it?

6. Learn from the team . . . and the other teams. This is kind of the backbone of Vygotsky’s ZPD (zone of proximal development) and social constructivism in general.  I thought we all learned from each other but also were able to research what had already been done regarding the Collatz conjecture.  Learning from the team lead to my repetitive “atta boys” as I sat in the dugout watching Joy, Cramer, Nick, Dillon, Mike, Kevin (who am I forgetting?) hit home run after home run.   Their efforts gave me more confidence when it was my turn at the plate.

7. Learn the game of learning. This is the big one.  If you examine how we all learned on this project we can apply it to other genres such as foreign languages or art design (i.e. graphs).  Learning how to learn is the most valuable principle I garnered from the Learning Adventures taken as a whole.

Cramer,

What if my “blue” and you’re “blue” are two entirely different things?

Sorry, but I’m becoming a radical constructivist.

Math is subjective.  Numbers are a cultural phenomenon and therefore unreliable.

Radical Constructivism – ‘What is radical constructivism? It is an unconventional approach to the problem of knowledge and knowing. It starts from the assumption that knowledge, no matter how it is defined, is in the heads of persons, and that the thinking subject has no alternative but to construct what he or she knows on the basis of his or her own experience. What we make of experience constitutes the only world we consciously live in. It can be sorted into many kinds, such as things, self, others, and so on. But all kinds of experience are essentially subjective, and though I may find reasons to believe that my experience may not be unlike yours, I have no way of knowing that it is the same. The experience and interpretation of language are no exception.’

p.1 – ‘Growing Up Constructivist’, in, ‘Radical Constructivism – A Way of Knowing and Learning’.