Much of the great American genius starts with appreciating and utilizing what we find in nature and then improves on it, expanding the strengths and compensating for the deficits.  So when insulin and the pancreas cells that produce it were discovered in the 1920s, American scientists went to work, and American doctors put the research into practice.  Injectable human-analog insulin was derived first directly from beef or pork sources, then developed in lab cultures; nowadays nearly everyone uses a human-DNA replica, and more and more of us receive it through a pump.  When nature doesn’t work like it should (as in my body), we compensate for the deficit.

But the pump system still isn’t perfect, so I spent a few days in the hospital.  Even in small-town America, it was equipped with state-of-the-art technology, and excellent doctors and nurses.  The ER doctor recognized that I knew what I was talking about when I diagnosed my own DKA, and immediately started to resolve it–I was improving within an hour of triage.  The doctor on call for my family physician is young, fresh out of residency, extremely knowledgeable yet teachable enough to call my endocrinologist for a consult (she was in my room when he returned her call).  Took care of my relapse 24 hours later like an old pro.  And my family doctor sat down with me to try to determine the cause(s), is running tests to be forwarded immediately to the endocrinology office (50 miles from home), and will be the one to help me live out the endo orders.  He also ordered rest (pedicures and massages are restful…), thus easing my conscience about staying out of the classroom for the week, and made me laugh in the process.

Seeing how it all came together became food for thought, as I increasingly view the world through a Federalist lens.  We took what nature provided (a defective pancreas but an otherwise healthy constitution), employed superior knowledge, experience, and technology, called in experts as needed, and are in the process of restoring and hopefully improving that otherwise healthy constitution.

A Federalist enterprise if there ever was one.  And I’m at the center of the process.

My mom says she doesn’t know how in the world I manage all the competing demands on my time.  I don’t know that I have much choice; I obligate myself and then do what’s on the agenda.  I feel sometimes like a spinning top–if I cease spinning I’ll stop altogether.  I don’t know what will happen then, and I’m afraid.  I wish she wouldn’t say things like that.  i love her, and I know she’s expressing awe or admiration or some such, but it makes me doubt myself.

Am I too introspective?  too analytical?  too contemplative?

The T.A. walked in, threw a mess of equations on the board, said “First you take a derivative,” then continued with the mess of equations. I sat through the entire term wondering what the hell a derivative WAS! An economics professor a year later explained and demystified it–after that I could at least apply the concept .

When I was first asked to teach middle-school math, my goal was to demystify algebra for verbal kids with math anxiety. I did not want the current generation to undergo my travails unnecessarily. But I never gave much thought to what I did want for my students—after all, I was a social scientist recruited to teach math on the basis of all my statistics training in B-school. Thank heaven for AMSTI and Connected Math. This training is showing me new ways to teach math that fit my philosophy of education: Truth is always symphonic.

My preference in teaching history and government has always been to examine primary sources for original wording, and look for changes in interpretation, context nuances, cultural shifts, and so on. I try to point my students toward a goal, then let them figure out how to get there, discovering truths and constructing meaning along the way. Now I’m finally learning how to do that in math.

I feel like I’ve found the missing piece of my puzzle!

The Connected Math Project was developed and is maintained by Michigan State University.

My summer institute is sponsored by the Alabama Math, Science, and Technology Initiative, utilizing the CMP methods and materials.

Enjoy!

The topic under exploration is “Looking for Pythagoras,” and we trainees are all 8th graders. Yesterday we used a diagram of a city (called Euclid!) to figure out distances traveled by car vs. by helicopter. In the process we measured sides of triangles and figured out that the hypotenuse is always longer than either of the two other sides, but never longer than the two sides added together. Then we worked with graphing calculators, played, explored, experimented, etc., BEFORE we were given a task.

Today we found areas of squares, rectangles, figured out how to find the area of a triangle (half that of a rectangle), than applied that insight to areas of irregular polygons. After lunch we got to play with Calculator Based Rangers (basically motion sensors) that would hook to the graphing calculators (which hooked to the overhead projector). We got a random line graph and had 10 seconds to match it–by walking! We could try to match distance or velocity graphs, did OK on distance but couldn’t figure out how to match the velocity until after our time expired. I didn’t really want to do this, but wound up having a blast!

This week is getting “funner and funner” but its insights are also going deeper and deeper. I’ve needed some high quality math training for a long time, but I never expected to learn so much about my own philosophy of education in the process.

Every “investigation” has ACE questions at the end– application, connection, and extension. All work is done & discussed in groups unless the teacher says specifically to work alone. And NOT ONCE has the word “formula” been mentioned!

This strikes me as compatible with what little I know about both the Montessori approach and the Understanding By Design model. The teacher launches the lesson, presenting an interesting hook, then turns the students loose to see what they can do with it. S/he doesn’t answer their questions, but if they’re honestly stuck, may guide a group to a point where at least one member is beginning to see.

For the next two weeks I find myself in a workshop on inquiry-based mathematics education.  Math has never been my favorite subject, and while I’m a pretty good actress in convincing my students that math is interesting, I know I can’t fool all of the people all of the time.

But these next two weeks may lead me to enjoy teaching math as a federalist enterprise!  We’re using a program called the Connected Mathematics Project, developed by Michigan State University (alma mater of my “brother,” “Hobbes21.”  I know he’ll be proud when he reads this!).  It’s designed to help students take math to levels not usually reached by America’s middle-school math classes.  Kids are encouraged to experiment , ask questions, help each other solve problems, and construct new insights into how math works and what we can do with it through hands-on and discussion activities.  The teacher serves as discussion leader and facilitator, “the guide on the side,” rather than lecturer, “the sage on the stage.”

This inquiry-based learning is built upon a solid foundation–they still have to know their multiplication tables COLD–but assessment is much deeper than solving problems on paper.  That’s what makes this whole process federalist:  the mind-set respects traditional background-building teaching, knowing the facts and manipulating them readily, but doesn’t rest there.  It draws its historic roots not from the traditional American classroom but from the Socratic method.  Assessment is based more upon what students can do with their learning than on what they know.

The process has cross-curricular implications, too.  Not only do students write in every lesson, they learn to apply their knowledge of math to science, social studies, art, music, phys ed, even English.  The math program takes a holistic view of the student’s education–also a Federalist notion.

I think the most important Federalist aspect of the Connected Math Project is that it provides students a tool with which to construct their own “worlds” based on solid principles of logic and sound judgment exercised corporately.  Students have to come together, each bringing his/her strengths and weaknesses to the table, to solve potentially–and often actually–real-world problems.  James Madison would be proud.

~Delores Dufner, OSB

Summoned by the God who made us
rich in our diversity
Gathered in the name of Jesus,
richer still in unity.

Refrain: Let us bring the gifts that differ
and, in splendid, varied ways,
sing a new church into being,
one in faith and love and praise.

Radiant risen from the water,
robed in holiness and light,
male and female in God’s image,
male and female, God’s delight.

Refrain

Trust the goodness of creation;
trust the Spirit strong within.
Dare to dream the vision promised,
sprung from seed of what has been.

Refrain

Bring the hopes of every nation;
bring the art of every race.
Weave a song of peace and justice;
let it sound through time and space.

Refrain

Draw together at one table,
all the human family;
shape a circle ever wider
and a people ever free

© Oregon Catholic Press

For me, federalism is fast becoming a way of viewing the world.  For example, I had a “federalist moment” immediately upon leaving Montpelier–at church, no less!  The closing song included the words “Sing a new church into being”; given the degree to which “words make worlds,” it could happen!

Fed moment # 2 (with background):  Both my sons are preparing to be teachers–the elder, 21, is farther along in several ways than his younger brother.  He’s studying math education, but is also profoundly interested in philosophy–including political philosophy (I can see him earning a PhD in the philosophy of integral calculus…).  I shared The Boxes with him yesterday, and he’s fascinated: the first thing he said to me this morning was “So how would you describe a blue-box federalist?”  Naturally this engendered quite a conversation!   We talked about federal education policy (including my anti-federalist assertion that the Department of Education is unconstitutional), and health-care policy (I’m all for nationalizing primary and critical care).   His response:  That makes sense–health-care is fundamental to life itself, in a way that education is not–it’s more a liberty-and-pursuit-of-happiness thing.  Not bad for a vacationing college student!

(BTW, the younger son, 19 and a future English teacher, is far too busy writing comic fantasy stories to converse–with me, he only debates, and I lack his youthful stamina!).

A friend who works for the same school system as I, and is in the inner-circle loop, suggested that enhancing my resume might be a good thing (even though I’m tenured in the system and have no desire to leave the classroom/library).

Another friend and I are discussing collaboration on a professional development program.

The workshop I attended two weeks ago helped me focus my planned doctoral studies.

The position in which I currently work is a fantastic learning experience, pointing me toward the program for my doctoral studies.  It also includes a reduced teaching load, giving me time to devote to my course work.

The National Academy gave me food for thought, a lot of ideas, and a fantastic support network of scholar-friends.  It also came at a very low time in my life, but my friends there encouraged me to be who I am: a smart, scholarly, persistent, caring, professional, family woman.  And they have become my family.  They’re now holding me accountable to enter my doctoral program in 2010.

Like a bunch of balloons tied together into a single bouquet, lots of signs are leading me into doctoral studies–and maybe beyond.  Likely there’s something I haven’t yet considered down the road.  And maybe Gerard Manley Hopkins was right: God draws straight with crooked lines.

There is even a quasi-spiritual dimension to this.  I’ve felt it off and on, but my awareness of it started while studying Scipio’s Dream (Cicero). There has been a decidedly different perspective permeating my thoughts. I’m finding it increasingly necessary to think constructively, compositionally, constitutionally in avenues of life other than history class–like I’m becoming more fully who I am….

Next question: what does this say about teacher education programs? Mine was woefully inadequate–or maybe I was. How do we recruit good students to become good teachers? How do we reach education profs and policy makers? How do we get the message across that constitutional thinking is the essence of a good education? How do we convince parents and principals, coaches and kids?

In other words, how do we reconstitute our education system?