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Some
thoughts on using STELLA in Math and Science classes
Rob
Quaden
Waters Foundation Mentor
Carlisle (MA) Public Schools
It is Friday, a time I am released from teaching
math to help facilitate the use of system dynamics throughout the school. I
enter the eighth grade science class where the teacher is giving some last
minute instructions regarding a homework assignment. He then asks the students
to get out their lab books and look at the data from their ramp experiment. In
this experiment, students have run toy cars down a ramp and collected data.
Today, students will use their experience, along with a STELLA model, to deepen
their understanding of the physics of motion.
I turn on the computer and project onto the screen a STELLA model of a car
traveling down a ramp. The model looks complicated and the students are duly
impressed. A perfect set up for the first task: " Explain to your teammates why
the model really isn't as complicated as it looks."
The students are silent for a moment while they stare at the model and then
erupt in conversation. One by one the teams figure out what is going on: the
stocks and flows are similar to a model they built two days earlier in math
class. There the students were asked to build a model that would help them
figure out how long it would take a coin to hit the floor when dropped from a
height of three meters. Both models show how an object moves under the
influence of gravity.
I talk about today's model a bit and send each team of four students to a
computer where the ramp model has been loaded. After doing a number of
simulations, copying graphs, answering questions posed by the science teacher,
and checking predictions they made earlier in the week, the students are asked
to return to their seats. We run the distance graph on the computer and the
Science teacher asks the students to identify the point at which the car leaves
the ramp. Different teams make their prediction and a heated discussion ensues.
After some dialogue among the teams, the class narrows it down to two
possibilities.
There is some talk about what 'the answer' is but
students know better than to ask for it: in this class they have to figure it
out for themselves. One team suggests graphing the car's velocity and distance
graph on the same graph pad. After doing this a cheer goes up as a student
explains: "The car reaches its maximum speed at the same time that we predicted
earlier. The car goes fastest at the end of the ramp, so we were right..."
This class is a good illustration of how system
dynamics is used in our curriculum. By the time that students analyze the ramp
experiment, they have already made countless numbers of Behavior Over Time
Graphs in different subject areas to communicate their thinking. They have used
a systems component in every science lab this year. They have learned how to
navigate in the STELLA environment, and they have built a series of simple
models in math class to help solve word problems. Students see system dynamics
as another tool to get desired results: understanding and communicating complex
ideas that are part of the curriculum.
An
important stimulus in my desire to teach modeling with STELLA came from the
reappearance of simple ideas in different contexts. Consider word problems.
Like many Math teachers before me, I have put a lot of effort into developing
strategies to help students understand and solve word problems. While some
students thrive on the challenge of these problems, many find the process of
'translating' words to equations daunting. One of the reasons for this
difficulty is that the contextual story hides the underlying mathematical
structure.
It took me a while to appreciate that building simple STELLA models helps
students uncover these structures for themselves. STELLA allows students to
model what is described in the text, rather than abstract it. I believe that
this is what Barry called Operational Thinking. After a few introductory
lessons, my students are asked to model simple word problems, none of which
contain feedback. I looked for a good source of problems and ended up perusing
and using a variety of algebra texts. In the process of doing this it, it
became apparent to me that students could model well over half of the word
problems in a typical algebra book, all within the first month of the school
year! This was astounding, and reason enough for an algebra teacher to use
STELLA. I didn't have to convince students that many word problems are built
upon a similar underlying math structure - they discover that for themselves in
the process of building models.
It now is a recurring pleasure for me when students exclaim after modeling word
problems for a while, " Mr. Quaden, these problems are all the same." Indeed
they are...we are ready to move on!
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Rob
Quaden is a teacher in the Carlisle, Massachusetts, Public
schools, where he has taught math in grades six through eight. In addition
to teaching algebra, Rob currently is a Waters Foundation systems mentor for
the Carlisle Public Schools and in that capacity works with teachers and
students in grades three through eight. He is interested in developing
lessons and techniques that help teachers to integrate systems principles
into their curriculum. |
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