Friday, January 27, 2006

Habits of Mind in Math Learning and Teaching

I was thinking about math and the students who are so "quick.” Many of them have to talk themselves out of being "impulsive," while so many of us have to talk ourselves into persevering without losing confidence.
Somehow in math we don't draw on the habits of mind we might readily apply when writing an essay or reading for deeper comprehension. Why not? Have they not been modeled?
Surely many students exhibit the habits of mind they need in writing and reading and in thinking about big ideas in history.....
why don't they automatically transfer them to math?
Is it the environment of math class? Is it a setting where students compare themselves and judge their success in comparison to others?
What are the questions we should be asking ourselves to bring clarity to this?

Sometimes parents approach me because they are convinced their children have a problem understanding mathematics. Often the whole thing isn't a problem understanding mathematics at all. It is something deeper but it fascinates me because we see this time and time again. (This is especially documented in girls during their MS years).

I fault the way we teach and the institution of school and want to figure out how we can change- so that all students can feel successful.
This shouldn't happen in math or any other subject.

One response to this problem (of some kids being so quick while other lose confidence even with what they know) is to give more problem solving to students at an early age....... (at my elementary school we have been doing this regularly) i.e., we are trying to expose our students to problems that no one will readily that all our students deal with the space of not knowing.
Then it is interesting to see how they react. ...define and see themselves....accept and push themselves......or simply give up

Certainly it is where we can all grow...(whether we must control our
impulsivity or learn strategies for persevering)

Facing the unknown
in the broadest of all about being human
and learning is so much about
asking questions
that can't even be answered....

(what do we really know anyhow?)
But back to math

How do we assess understanding? How young are children when they begin to form this misconception that getting the "answer" quickly means you are a better math thinker? How do we as teachers, perpetuate this myth? We have witnessed intuitive math thinkers and applaud them but why does that have to undermine those whose minds are meandering, wandering, and thoroughly enjoying exploring their way....following another type of intuition....the
foundation of discovery!

Sometimes kids have "test skills" but they can't apply that knowledge in a problem- solving situation.....They can test to prove quickness, but what does that really tell us about their thinking? I've had kids who can't memorize their facts (rote) and yet they show strong higher order thinking skills...which I place a much greater value on . Often these very strong thinkers are slammed in MS in 5th and 6th grade for not having that rote ability, where rote procedural and memorization skills are constantly assessed as if they are measures of understanding.

How do we overcome our own blocks? Our own triggers (or tendencies) to
freeze and lose confidence?

Over time, I have come to appreciate that:

When I understand something, I feel calmness in the air around me.
When I don't understand something, and I think I should, I get upset. (I think this happens to kids all the time in school)
The key, however, has been for me to learn that: When I don't understand something --- I believe and trust that I will come to understand it in time, and therefore, I am fine....

even if that time, is mine and mine alone...

To arrive at the last stage, takes maturity and confidence in oneself-
Are our school's fostering that type of growth?

Rilke’s over-quoted quote is worth quoting again:

Be patient toward all that is unresolved in your heart.
Try to love the questions themselves like locked rooms
and like books written in a very foreign tongue.
Do not seek now the answers, which cannot be given to you because
you would not be able to live them.
And the point is, to live everything.
Live the questions now....perhaps you will then gradually, without noticing it, live along some distant day into the answer...

Life long learners trust the process of living the questions.

Thursday, January 26, 2006

How Do We Help Create Life-Long Learners?

Two terms that always get me going are "life long learners" and "risk takers". If there is anything that has kept me going as a teacher and a learner it is the hard lessons I learned at Hampshire College. There I had to struggle through the process of describing the "mode of inquiry" I used to complete a project, and the actual topic of the project came second in importance. I had to prove that I understood how to solve problems or do research in an area of study before I presented the actual project. This requirement is why I can learn new things, take on new projects, and conceptualize on a big scale -- I am always looking at what is behind the idea or the concept - - perhaps I should say the big idea rather than focusing simply on the content. This is the gift I believe we are supposed to be sharing with students. This is the gift that leads to life-long learning.

I work with kids who are both potential life-long learners and risk-takers (in a good way) -- kids who are jumping out of their skin to move forward and desperate for the next thing to do and might be willing to struggle with deeper meanings or the messy process of focusing how to learn. So often, however, because of their competitive instincts (or parental pressure) these students become satisfied by succeeding where ever rote response is required and become learners who are fine with learning superficially as long as they maintain their "top of the class" label. We should challenge these kids to reach beyond and try to really comprehend the underbelly of everything they learn, rather than rewarding them for success by letting them think they are "winning" for rote or formulaic responses. In truth, they will never be truly satisfied because deep inside they really know that there is more to it than this.

I think it is the responsibility of schools to educate life-long learners and risk takers, rather than to focus on rewarding those who achieve the highest mark, however easily or cheaply obtained...