Graphics Reference
In-Depth Information
We'll probably never know, but I wonder whether 10 years from now stu-
dents will remember this geology exercise. What will be remembered? If some
students had only read about the exploding volcano while others proceeded
through the entire exercise, I wonder which group would better remember
the lesson plan.
Here's an interesting experiment to test the power of multiple representa-
tions. First, write down a simple equation, say
y=1/x
. Written mathematical
equations are one way to depict a relationship between numbers. A second
medium is visual, drawing the equation on a two-dimensional graph.
Now let's image that you were to take this simple written equation to the
mall or your state legislature and ask several adults to solve the equation for
the value of “
x
.” Probably several people would know how an equation works.
They would know that to solve for
x
, you must be given the value of
y
(or vice
versa). If you were to tell them that in this case, the value of
y
was 2, they
could fairly easily calculate that the value of
x
would be ½.
How about if the same written equation were expressed in a new medium?
Let's assume you asked a person who successfully solved the written equation
to express its shape by drawing it on a graph. If you returned to the mall or
state legislature and asked random people to do this, probably very few people
would be able to readily express the written equation in a chart. Most of us
don't retain our high school or college math skills, one reason that among
applicants to MBA programs, the acceptable range of math GRE scores for
senior-level executives is much lower than the acceptable range for applicants
fresh out of college.
Some educational theorists speculate that the reason most people forget
their math lessons quickly after they leave school is because they learn math
in a single abstract medium. If students learned abstracts mathematical con-
cepts and then translated the concepts into different mediums, perhaps they
would gain greater mastery and recall. Translating an abstract concept between
different mediums requires skill and mastery. In my own experience, rote
memorization of abstract concepts got me through the exam but I quickly
forgot most of what I memorized after the test.
It's easier to teach and learn concepts in a single medium. Memorization
will get you through. However, real mastery hasn't necessarily taken place.
The problem is that most classroom education focuses on the page. However,
that's not necessarily what most people remember.
