Workshop
3 -- Conceptual Thinking
Download Workshop
3 in
PDF
This
workshop
will focus on concept maps as tools for helping students
learn. Joseph
Novak will explain how students learn by assimilating new
concepts
into their already existing frameworks, and will take a
teacher step-by-step
through the design and process of concept mapping. You will
see concept
maps being used in a variety of different ways in mathematics
and
science lessons, and will even have an opportunity to make
some concept
maps of your own.
Joseph
D. Novak
Professor of
Biological Science and Science Education recently retired
from Cornell
University, Joseph Novak is one of the seminal investigators
in the
research in children's ideas in science. He is the author of
Learning
How to Learn and a developer of the concept mapping
formalism. His
latest book, Learning, Creating, and Using Knowledge,
was published
in 1998. Teaching Science for Understanding,
co-authored with
Mintzes and Wandersee, was also published in 1998.
Workshop
3 Timeline
Getting
Ready
-- 30 Minutes
20
minutes
-- Moon Discussion
Examine
the Moon
Chart that you made in Workshop 1. In your observations of
the Moon
thus far, have you gathered any data that supports or
challenges the
information on the Moon Ideas list? Share and discuss your
information,
and update the chart.
Have you
or your
colleagues developed any new questions that you can add to
the Moon
Questions list? Consider where these questions came from.
What, specifically,
inspired the questions?
Now
that you
have thought about your own questions, think about your
students.
Where do you think they get their questions?
10
minutes
-- Concept Map Discussion
Have you
ever
used concept mapping in your classroom? How have you used
concept
maps (i.e., for what purpose)? What kinds of things have your
students
mapped?
Remember to update the Moon and Learning
Charts.
Watch
the Workshop
Video -- 60 Minutes
Going
Further
-- 30 Minutes
30
minutes
--Making Concept Maps
In
pairs, have
one person construct a concept map about teaching while the
other
person makes one about learning. After you have made the two
concept
maps, compare them. What are the similarities? The
differences? Did
the word "teach" appear in the learning concept
map? Did
"learn" appear in the teaching map? How do you
believe teaching
and learning should be connected?
Save
your concept map -- you will need it again in Workshop 8.
Note:
You can
assess your students' prior knowledge of a particular topic
by having
them make concept maps before you prepare and introduce the
lesson
on that topic. You might have them make concept maps again at
the
end of the lesson, and compare the before and after maps to
see what
they've learned.
For Next
Time
Homework
Assignment
Using the materials of your choice, make two pendulums
(e.g., hand-held,
taped to a table edge, free-standing) with the following
specifications:
- Pendulum 1: a period of 15 swings in 10 seconds
- Pendulum 2: a period of 30 swings in 30 seconds
Please bring
your pendulums with you to Workshop 4.
Reading
Assignment
In
preparation
for Workshop 4, please read "Assessing 'Imperfect'
Conceptions" by
Hubert Dyasi. (All readings are included in the
Appendix.)
Moon
Journal
Here are
more suggestions
for your Moon Journal:
- Does the Moon's position change over time?
- If you want to record the Moon's exact position in the
sky in
your journal, what information do you need?
- Where do you predict the Moon will be positioned in the
sky tomorrow
night during your regular observing time? One week from
now?
Suggested Activity
Measuring
the Elevation of the Moon
One
piece of information helpful in describing the Moon's
position is
its height in angles (angular height) above the horizon. The
horizon
is the line along which the sky and land -- or sea -- appear
to meet.
You can determine the Moon's height above the horizon if you
know
the angle between the line from your eyes to the Moon and the
line
from your eyes to a point on the horizon directly below the
Moon.
Measuring
with Fists
You
can estimate the Moon's angular height by simply using your
hands.
Stretch one arm out straight and make a fist with the hand on
your
outstretched arm. From the horizon to the highest point in
the sky
is one quarter of a circle or 90 degrees. If you measure with
fists,
putting one fist on top of the other, nine fists will about
equal
this angle -- one (adult) fist is roughly the same as 10
degrees.
To
measure the angular height of the Moon at any given time,
stretch
one arm out straight and make a fist with the hand on your
outstretched
arm. Close one eye and adjust your sight so the outstretched
fist
is aligned with the horizon. Make a fist with your other hand
and
stack it on top of the first. Continue stacking your fists,
one on
top of the other, until the Moon appears to be covered by one
of the
fists. The number of fists you stacked indicates the angular
height
of the Moon. For example, if you counted six fists, the
angular height
of the Moon above the horizon would be approximately 60
degrees.
Measuring
with a Clinometer
A
clinometer is a tool that can help you to measure the angular
height
of the Moon more accurately than with your fists.
Materials: Protractor
template,
Cardstock, Paste or glue, Drinking straw, Clear tape,
Scissors, 30
cm fishing line or kite string, Metal washer or weight with
hole,
Tack or pin
Building
a Clinometer
- Adhere the
Protractor template to a piece of cardstock and cut along
the
dotted lines.
-
Center
the straw lengthwise along the edge of the template
directly above
the straight side of the protractor. Secure it in this
position
with tape.
- At
the
point where the protractor's center line (0 degrees)
meets with
the line that runs parallel to the straw, use a tack or
pin to
make a hole.
-
Thread
one end of the fishing line or kite string through the
hole so
that approximately 2 cm extends out the back side of the
protractor.
Secure this portion of string to the back side of the
protractor.
-
Tie the
metal washer to the opposite end of the fishing line or
kite string.
The string and washer should swing freely along the front
side
of the protractor.
Using
a Clinometer
-
Position
the Clinometer straw-side up so the straw is parallel to
the ground
and the string hangs parallel to the 0 degree marking on
the protractor.
- Look through
the straw and adjust the position of the Clinometer until
you
sight the horizon directly below the Moon (while keeping
the straw
parallel to the ground).
-
While looking
through the straw, tip the entire Clinometer upward until
you
can sight the Moon through the straw.
- As
you
move the Clinometer, the string moves along the
protractor. By
noting the position of the string along the protractor,
you can
determine how many degrees you are tipping the Clinometer
to sight
the Moon. This measurement is the angular height of the
Moon.
Extensions
To
measure the height of an object that makes a right angle with
the
land, such as a tree or a building, sight the top of the
object through
your clinometer and walk towards the object until the
clinometer measures
45 degrees. By mentally tracking from your observation point
to the
base of the object to the top of the object and back to your
observation
point, you will make an isosceles triangle. Given that two
sides of
an isosceles triangle are equal, you can determine that the
distance
from the observation point to the object itself will be equal
to the
height of the object.
Adapted
from:
Coyle,
H.P., Gregory, B., Luzader, W.M., Sadler, P.M., and Shapiro,
I.I. (1993).
Project STAR: The universe in your hands. Kendall/Hunt
Publishing
Co.: Dubuque, Iowa.
Education
Development Center, Inc. (1968). Where is the moon?
Webster
Division, McGraw-Hill Book Co.: New York.
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