2. Learning As We Grow - Development and Learning
P. Comer, M.D., Yale University: There is the physical, the
social interactive, the psycho-emotional, ethical, linguistic, intellectual
cognitive. And it is development along all of those lines thats
really important. Up until recently, the school focused on the linguistic
and the intellectual cognitive. But it is growth along all those developmental
pathways that is important.
Linda Darling-Hammond: Good teachers
start where their students are and build upon what they are able to do.
But how do we know what our students are ready for and when? The concept
of the zone of proximal development helps us here.
Tharp, Ph.D, University of California, Santa Cruz: The zone
is an important concept because to teachers its absolutely vital,
because it helps the teacher understand what is the basic act of teaching.
And that is this to locate that point in the zone of proximal development
in which this learner needs the assistance and then to provide it. Good
teaching means constantly stretching, moving, rising in the developmental
process, and that means always providing more assistance.
Linda Darling-Hammond: Psychologist Jerome Bruner described a spiral curriculum that returns to important concepts at different stages when children can understand them more deeply.
In this half hour we will see three teachers guide
their students through an increasingly sophisticated understanding of
momentum. They provide wonderful examples of developmentally appropriate
Fe MacLean: This morning is just an introduction of several cycles which will help them understand concepts of motion, for example, uh, the relation of weight, or mass, with speed, the relation of incline, of a ramp to speed and momentum, or the relation of weight with momentum.
Fe MacLean: For these age of children
it is necessary that the material is chosen so that they see not just
the, the abstract time but they see it with their own eyes how the ball
rolls down the ramp. So I have a six-foot ramp instead of a small ramp
because I want to make sure the numbers are big enough to see a differences
with the children .
Fe MacLean: I want to make sure that
in their participation they are very clear of what we would call controlling
of variables. We would call it fair, so that it starts from the same place,
and we time it the same time until the end.
When we made the graphic organizer that I used while we were taking down
the data that the children are writing in there, that is a very abstract
way of representing what we were doing, so thats no longer concrete.
When I plan my activities or units of study, I make the activities or
the context rich enough so that it will benefit the children who are quite
competent and those, the children who are not quite so competent in certain
Fe MacLean : I want to make sure that children who have, are close to mastery will be able to have tasks that will them to be to that mastery and in their interaction with the children who are just entering the zone they will solidify or stabilize their competence, and the children who are entering will advance and become more stable in that zone.
Fe MacLean (interview): Hopefully in
the next investigation they will be at an even higher level and in the
zone its advanced.
The next thing were going to do is, is to look
at all of their drawings and what they wrote and their conclusions of
how many seconds it took for the balls to go down the ramp. So they will
discuss that, which is part of oral language and literacy.
Fe MacLean: When they have to write
it down they really have to think about it, and thats what we want
the children to do, not just in science, but to understand informational
text, which is what they really wrote this information about what they
Fe MacLean: When we use the long ramp,
thats a physical symbol of reality, which is the hill. So I think
of that as a concrete operational tool, and it is a symbolic tool, its
a physical tool representing something. When we made the representation
of that ramp, and the children drew illustrations of that, that then became
a higher level of symbolic tools inter
a graphic illustration or
a graphic representation. Which they did on their paper and on the chalkboard.
Fe MacLean: From my experience children
are not going to be able look at the data using numbers of measurement
to really understand the concept in this context of the level of the ramp
relative to the momentum, and that is how far the can will move
Fe MacLean: The tracing is more pictorial
and is more appropriate to their age.
Fe MacLean: I tried to relate it to
a to a form of a story, a narrative that hopefully can relate to their
own lives, for me to understand or to assess their understanding the concepts.
In one instance, for example, two children working together
They drew this picture
where one of them won the race with a snowboard, and the other one got
a bronze metal according to him, because he started from a lower hill
so he couldnt go as fast, and the other child who started on a higher
hill went faster. So to me they are understanding that the height of a
ramp, or the steepness is related to momentum or speed in this case.
Linda Darling-Hammond: Fe MacLean finds
many different ways to assist individual students within their zones of
George Mixon: I just wanted them to
look at a piece in calculating the acceleration of a free falling object,
getting the speed of that object, graphing that information and collecting
data and putting it in an organized manner into a data table.
George Mixon: With this age group you
have to start these kids off with something thats a little more
concrete and more solid for them to understand and then you can kind of
branch them off into the abstract and get them to formulate ideas and
almost, what I call taking intellectual risks.
George Mixon: I think I started them
with the ramp primarily because its kind of like, most of these
kids sled, they all snowboard.
George Mixon: I toss a lot of variables
at the kids because I think one of the goals as a scientist is that theyre
going to be bombarded with variables that will hinder experiments or procedural
steps, and they have to learn how to control those and identify what is
an independent and whats dependent variable.
George Mixon: I think when they, when
they realize that, they can say I need to control this, control this,
control this, to test for just the one thing that I need to test for.
George Mixon: If I gave them the table,
they dont think. They need to be able to figure out ways in which
to formulate and organize their information. That shows me how well theyre
George Mixon: I think if you can get
kids active, and motivated, and involved, and get their hands in stuff,
theyre focused. I think thats what kind of pulls them in and
kind of gets them motivated, plus just knowing who they are and having
a relationship with them.
George Mixon: I sometime have to go
outside my realm, and you know, the kids have to understand too, that
there some, they can be flexible in their thought process, and formulating
data tables, because not every kid is going to think alike.
George Mixon: Kids have unique ways
in which to organize information and collect data and control certain
variables. Its just a matter of how well theyre able to collaborate
with a group to come up with that ultimate goal.
George Mixon: I just kind of wanted
to see if they could make that transition and see that connection, and
I think some of them did. But I still, there is something that something
that you have to revisit to make sure that they understand it.
Linda Darling-Hammond: George Mixon
pushes his students' thinking by asking questions that get them to analyze
data and test their hunches with one another.
Roland Tharp: Vygotsky pointed out that
that kind of assistance that will help development in the zone can come
from more capable peers. It doesnt really matter where the assistance
comes from. And the most competent teachers, I think, provide the assistance
themselves when they need to, make sure that a good, rich diet of assistance
is available from other class members, and outside resources, and the
web, and wherever assistance can be provided to make sure thats
available to the student. Thats the orchestration of excellent teaching.
Linda Darling-Hammond: At the Detroit High School for the Performing Arts, Ken Gillams physics students study the same concepts, drawing on even higher levels of abstract reasoning. Through experimentation they move into evaluating evidence, drawing inferences, and predicting outcomes.
Ken Gillam: I started what I knew as
prior knowledge for them. We had done situations, we worked in situations
where they had the opportunity to evaluate velocity, acceleration of a
ball rolling on a ramp.
Ken Gillam: Their initial thought was,
its going to be the same lab again, well, it really wasnt
going to be the same lab again, because the minute I put a barrier there
and crashed it, they said this is not going to be the same. So the hook
was I think its going to be, no its not. And so I hooked them
by getting, giving them something they knew, but then giving them something
new to look at.
Ken Gillam: They are ready to go into
But in a lot of ways they are still just kids and they like
to see things that happen.
Ken Gillam: So if you give them something
on a concrete basis, this is concrete, you can take this car, you can
roll it down this ramp, and you can make informational observations, you
can collect data, you can use that data to develop information that is
solid, meaningful in a problem solving sense.
Ken Gillam (interview):
Girl: It moved back a little.
Ken Gillam: Once you see them beginning
to fall into this pattern that says were all beginning to get this,
then its time to challenge them again. Move them up a level.
Ken Gillam : So
you take the solid concrete, then you take them into the problem solving
area and into the analytical, analyze what youve seen. Then, once
you begin to analyze it, how are you going to use this information in
a real world? How do you build this meta skills of thinking? How do you
think in a broader context?
Ken Gillam: And you begin to put together
a structure, a pattern into not only abstract, but into, not only being
able to bring it all together and synthesize something that may be totally
unique in their analysis.
James Comer: And so understanding that
you are really an instrument of learning, and that you can help the child
grow all the developmental pathways, and that growth along all the developmental
pathways is what makes academic learning most possible. If you can think
that, then you will find all kinds of opportunities to help children grow,
and develop, and learn, both what it takes to be successful in school
and as an adult, and to get the academic material they need to be successful
Linda Darling-Hammond: Fe MacLean, George
Mixon and Ken Gillam taught similar concepts using similar materials,
but adapted their lessons to the developmental needs of their students.They
created intellectual challenges to support increasingly complex thinking.
Return to the Support Materials for Session 2