You See it

1
You See it But Do You Believe It?Multiple
Representations and Misconceptions in Science
Instructional MaterialsHigh School Science
Teacher Forumfor North San Diego County Teachers

• Dr. Larry Woolf
• Larry.Woolf_at_ga.com
• www.sci-ed-ga.org (click on presentations)
• General Atomics
• Presented 1/11/05 at
• North County Professional Development Federation

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Please note

• 5. I am not a teacher.
• 4. I have never taught students.
• 3. I have no conception of the life of a teacher.
• 2. But I have been involved in the development
  and review of many science instructional
  materials for grades 7-12 and have given 100
  workshops to teachers.
• 1. I have had to teach many of my customers
  (who are easily bored) when giving presentations
  (20 per year).

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What do you or your students know about color?
4
Lets see what are the primary colors according
to expert sources
5
Authoritative approach

• Websters New World Dictionary
• color the primary colors of paints, pigments,
  etc. are red, yellow, and blue, which, when mixed
  in various ways, produce the secondary colors
  (green, orange, purple, etc.)

6
The gray scale approach(neither black or white)

• Art Fundamentals Theory and Practice
• There are three colors, however, which cannot
  be created from mixtures these are the hues,
  red, yellow, and blue. They are called the
  primary colors.
• A mixture of the three primaries should
  theoretically result in white actually this
  mixture produces a neutral grey which may be
  considered a darkened form of white.

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The 2 correct answers approach

• The Journal of Chemical Education
• students should identify the three colors
  needed to produce all the others as red, blue,
  and yellow. Most artists call these the
  fundamental colors, The correct subtractive
  colors, used by printers, for example, are cyan,
  magenta, and yellow.

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The parenthetical approach

• Color Printing Manual
• The primary process colors are Yellow, Red
  (Magenta), and Blue (Cyan).

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The loosely speaking approach

• Hewitts Conceptual Physics
• For this reason, cyan, magenta, and yellow are
  called the subtractive primary colors. In
  painting or printing, the primaries are often
  said to be red, yellow, and blue. Here we are
  loosely speaking of magenta, yellow, and cyan.

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What is meant by primary colors?
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What is meant by primary colors?

• You can make all other colors (not really)
• You cant make a primary color by mixing

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Using your colored films, lets do the
experiment Are the primary colors red, yellow,
blue?

• What colors can you make by mixing red, yellow
  and blue?
• What colors can you make by mixing cyan, magenta,
  and yellow?
• Which set of 3 produces the largest range of
  colors?
• Can you make any of these primary colors by
  mixing?
• What are likely candidates for the 3 primary
  colors? What cannot be the primary colors?

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Lets learn more about how we see color

• Basic simplifying assumptions
• 1. The color we see results from light of that
  color entering our eye.
• 2. This room is illuminated by uncolored (white)
  light

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Absorption of light by colored films

• Place C film over color wheel on white paper
• C film absorbs what color of light?
• Place M film over color wheel on white paper
• M film absorbs what color of light?
• Place Y film over color wheel on white paper
• Y film absorbs what color of light?
• Place C, M, Y films on top of each other over
  color wheel on white paper
• What happens? What does this mean?

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Absorption of light by colored films

• Place C film over color wheel on W paper
• C film absorbs R light
• Place M film over color wheel on W paper
• M film absorbs G light
• Place Y film over color wheel on W paper
• Y film absorbs B light
• Place C, M, Y films on top of each other
• All light (white light) is completely absorbed by
  the R light absorber,G light absorber, and B
  light absorber

How can these observations be written
mathematically? (R is red light, G is green
light, and B is blue light and W is white light)
See next page for guidance
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Consider the cyan film on white paper

• When cyan film is placed on white paper
• What color light do you start with?
• What color of light is subtracted?
• What color light remains after the subtraction?
• How can you write this mathematically?

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Color math
C
W
W
W
W R C
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Consider the magenta film on white paper

• When magenta film is placed on white paper
• What color light do you start with?
• What color of light is subtracted?
• What color light remains after the subtraction?
• How can you write this mathematically?

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Color math
M
W
W G M
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Consider the yellow film on white paper

• When yellow film is placed on white paper
• What color light do you start with?
• What color of light is subtracted?
• What color light remains after the subtraction?
• How can you write this mathematically?

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Color math
Y
W
W B Y
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Place cyan, magenta, and yellow films on top of
each other

• What happens and why?
• How do you describe this mathematically and
  pictorially?
• What does white light consist of?

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Color math
W
W R G B 0 W R G B
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Alternate model
W R G B 0 W R G B
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Place a cyan film over a magenta film
What color of light do you start with? What
colors of light are subtracted? What color of
light remains? How can you describe this
mathematically? How can you describe this
pictorially?
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Color math
B
(R G B) R G B
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Now use an alternate pictorial model to show what
happens
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Alternate pictorial model
(R G B)
-R
G B
-G
(G B)
B
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What color results from these pair of colored
film?
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What color results from these pair of colored
film?
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What is the one big idea that determines color?
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What is the one big idea that determines color?

• Color is determined by light absorption
• More generally, students will learn in subsequent
  physics classes the following big idea
• When light interacts with matter, it can be
  reflected, absorbed, or transmitted

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Color mixing

• We found that mixing cyan and magenta films made
  a blue film
• Mixing cyan film and yellow film makes a green
  film
• Mixing yellow and magenta makes a red film
• Now lets make a model that describes these
  results

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Color Wheel Model for Subtractive Colors
Y
M
C
What colors are between each of the subtractive
primaries?
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Color Wheel Model for Subtractive Colors
Y
R
G
Now lets deconstruct the model in terms of cyan,
magenta, and yellow components
M
C
B
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Deconstruct the model in terms of cyan, magenta,
and yellow components
Y
R
G
M
C
Now, how could you make this real?
B
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Put them together and see what happens- Do
you make a color wheel?
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Color Wheel Model for Subtractive Colors
Y
R
G
What are the limitations of this model? Does it
show all the possible colors? Does this model
explain how our eyes see color?
M
C
B
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A more sophisticated color model L a b color
space
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So What?

• Lets see what color mixing is good for
• Take a look at the colored magazines using the
  handheld microscope
• How are colored pictures made?

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Learning conceptually difficult subjectsFrom my
personal reflections, experience, science
education literature, and maybe this workshop,
need

• Interactive learning
• Learning cycle
• Engage (primary colors), explore (mixing
  experiments), explain (color math, diagrams,
  wheel), extend (printing)
• Converting between multiple representations
• Experimental, mathematical, pictorial, graphical,
  model, verbal, written
• Connected activities over time
• Relevance to students
• Underlying general scientific principles

Discuss with your fellow teachers agree or
disagree?
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Interactive engagement vs traditional instruction

• (a) "Interactive Engagement" (IE) methods are
  designed at least in part to promote conceptual
  understanding through interactive engagement of
  students in heads-on (always) and hands-on
  (usually) activities which yield immediate
  feedback through discussion with peers and/or
  instructors
• (b) "Traditional" (T) courses are those reported
  by instructors to rely primarily on
  passive-student lectures, recipe labs, and
  algorithmic problem exams
• Richard Hake, Emeritus Professor of Physics,
  Indiana University

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Scientific evidence interactive engagement is
more effective than passive lecture for
understanding of conceptually difficult subjects
Interactive-engagement vs traditional methods A
six-thousand student survey of mechanics test
data for introductory physics courses Richard R.
Hake Department of Physics, Indiana University,
From http//www.physics.indiana.edu/hake/
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Why is it hotter in the summer than the winter?
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Lets now watch part of the video A Private
Universe
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• Be very, very careful what you put into that
  head, because you will never, ever get it out.
• Thomas Cardinal Wolsey (1471-1530)
• From the Bad Science web site
• lthttp//www.ems.psu.edu/fraser/BadScience.htmlgt)

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What do you think about these questions?
Are the rays from the Sun ever indirect? Is
Earths orbit egg-shaped? At Earths surface, are
the Suns rays parallel? Can you make a scale
drawing of the Earth, Sun, and Earth-Sun
distance? Does the amount of atmosphere the
sunlight passes through contribute to the seasons
(i.e. more atmosphere to pass through in the
winter so less intense sunlight)?
Lets see what the experts say
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Misleading terms indirect rays and direct
rays
From A Private Universe Teachers Guide, p. 18
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From National Geographichttp//www.nationalgeogra
phic.com/xpeditions/activities/07/season.html
Misleading terms indirect rays and direct
rays

• Because the direction of the Earth's tilt
  changes in relation to the sun, the northern and
  southern halves of our planet get differing
  amounts of sunlight over the course of the year.
  When the Northern Hemisphere of the Earth is
  leaning toward the sun, it receives direct rays
  of sunlight and is warmer, while the Southern
  Hemisphere receives more indirect rays.
• When the northern part of the Earth is leaning
  away from the sun, the situation is reversedthe
  Northern Hemisphere gets cooler, more indirect
  sunlight while the southern half receives direct
  rays. Because of this, the seasons in the
  Northern and Southern Hemispheres are reversed,
  about six months apart from each other.

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Misleading use of terms contributes to
misconceptions

• Direct Proceeding in a straight line or by the
  shortest course straight undeviating not
  oblique
• Indirect Not direct in space deviating from a
  straight line
• (Also misused strong and weak rays)
• All the rays from the Sun are direct rays!

Words which are used should be as close as
possible to those in our everyday language, or as
a minimum requirement, they should be the very
same words used by scientists Richard Feynman,
1965 (in Perfectly Reasonable Deviations from the
Beaten Track, p.453) (these are not new thoughts!)
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Bully for Brontosaurus by Stephen Jay Gould (p.
166)

• I can only conclude that someone once wrote the
  material this way for a reason lost in the mists
  of time, and that authors of textbooks have been
  dutifully copying ever since.
• evidence indicates that cloning bears a
  discouraging message. It is an easy way out, a
  substitute for thinking and striving to improve.

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Misleading statements from scientist experts

• slowly increasing amounts of sunlight after the
  winter solstice are due to Earths egg-shaped
  orbit around the sun.
• National Weather Service forecaster Steven
  Vanderburg (San Diego)
• in North County Times, December 21, 2005, page
  A-4
• Actually, Earths orbit is very nearly circular
  see poster. Why do you think he believes that
  Earths orbit is egg-shaped?

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Critically analyze this figure
http//csep10.phys.utk.edu/astr161/lect/time/seaso
ns.html
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Misleading scales and diagramsOverly distorted
Sun position and elliptical orbit
http//csep10.phys.utk.edu/astr161/lect/time/seaso
ns.html
Note egg-shaped orbit. This type of diagram is
common in Earth and space science texts. Even
though the text of this figure states it is not
to scale, we only remember the incorrect
misleading image!
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Critically analyze this figure
http//hea-www.harvard.edu/ECT/the_book/Chap2/Chap
ter2.html
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Misleading scales and diagrams Earth is larger
than the Sun, the Sun emits rays in two opposite
directions, all the rays are parallel, Earth is 3
diameters from the Sun
http//hea-www.harvard.edu/ECT/the_book/Chap2/Chap
ter2.html
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Dinosaur in a Haystack by Stephen Jay Gould
(p.249)

• an important principle in the history of
  science the central role of pictures, graphs,
  and other forms of visual representation in
  channeling and constraining our thought.
  Intellectual innovation often requires, above all
  else, a new image to embody a novel theory.
  Primates are visual animals, and we think best in
  pictorial or geometric terms. Words are an
  evolutionary afterthought.

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Conflicting models for the suns rays
Suns rays are parallel
From GEMS The Real Reasons for Seasons p. 92
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Conflicting models for the suns rays
Suns rays are not parallel
From What is Light and How Do We Explain It by
Bill G. Aldridge Scope Sequence and Coordination
High School Project of NSTA, 1996
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What are students taught about the rays from the
Sun?

• When studying the seasons, the rays are perfectly
  parallel.
• When studying solar and lunar eclipses, the rays
  are not parallel at all, but are highly angled.
• Students are taught completely contradictory
  views, each with no justification.
• This is science by belief, not science by
  evidence

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Lets make a correct scale model for the Suns
rays

• The standard approach is difficult to visualize
  and conceptualize (e.g. from GEMS The Real
  Reasons for Seasons p. 46)
• Earth 0.25 cm dia.
• Sun 28 cm dia.
• Earth-Sun distance 30 meters !!!
• Better to use a model that can be visualized and
  used to understand physical situations such as
  seasons and eclipses
• Earth 8000 mi dia. ---
  10,000 mi 104 mi
• Sun 865,000 mi dia. ---
  1,000,000 mi 106 mi
• Earth-Sun distance 93,000,000 mi ---
  100,000,000 mi 108 mi
• So Sun dia Earth dia. 1001
• And Earth-Sun distance Sun dia. 1001

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Correct scale model for the Suns rays

• So if we make the Earth a very small but visible
  dot
• Earth dia. 0.1 mm
• Sun dia. 10 mm
• Earth-Sun distance 1000 mm 1 m
• This scale is useable and can be visualized!
  draw this (or see poster)
• Draw rays from the outer parts of the Sun to
  Earth
• Are the rays parallel?
• Is the use of parallel rays a good approximation?

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Incorrect Explanations?According to MSNBC, NOAA,
and NASA, the amount of atmosphere the sunlight
passes through is a primary cause of the seasons.
Is this true?
From http//www.msnbc.com/news/251727.asp
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Incorrect Explanations? According to this Earth
Science textbook, the amount of atmosphere the
sunlight passes through is a cause of the season
true?
WINTER at 40
Does the atmosphere deplete the solar energy more
in winter than summer because rays pass through
more atmosphere in winter than summer?
SUMMER at 40
From Earth Science Seventh Edition by Tarbuck
and Lutgens
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Is the amount of atmosphere that sunlight passes
through a significant factor contributing to the
seasons?

• Yes, according to MSNBC/NASA
• No, according to GEMS/NASA
• It is of importance according to the Earth
  Science Seventh Edition by Tarbuck and Lutgens
• What is the answer?
• It apparently has never been calculated or
  estimated, so I decided to do it (see next two
  slides)
• If it is significant, how would you expect the
  following to vary over the year
• daily solar energy at ground/daily solar energy
  above the atmosphere

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Data indicate that the amount of atmosphere that
sunlight passes through is not a major cause of
the seasons
L. Woolf, 2005, unpublished analysis
The amount of atmosphere does not substantially
change the amount of solar energy striking the
ground.
67
More complete data that indicate that the amount
of atmosphere that sunlight passes through is not
a major cause of the seasons
L. Woolf, 2005, unpublished analysis
The amount of atmosphere does not substantially
change the amount of solar energy striking the
ground.
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To eliminate impediments to learning

• No misleading and confusing terminology
• Realistic and understandable diagrams so that
  students have a visual image to anchor their
  understanding
• Materials must be scientifically correct
• Evidence for scientific validity should be
  presented or described

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Misc. topic 1 The Importance of Writing and
Talking Across the Curriculum

• Because I never wrote or talked about science in
  my science classes, I never really learned the
  topic well. In industry, you are always writing
  or talking about your work proposals, reports,
  presentations, etc.
• Writing and talking improves your conceptual
  understanding of science. Example instead of
  having students solve a physics problem, have
  them write about why they are using the equation
  and how they are solving the problem
• If you have to talk or write about science, you
  cant just aimlessly make diagrams or write down
  equations
• Some districts lacks formal writing programs
  using books such as The Elements of Style or The
  Write Way

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Misc. topic 2 The Importance of Reading Across
the Curriculum

• There are excellent popular science books.
• These books provide insight and excitement that
  textbooks do not provide. Students should be made
  aware that quality, interesting, informative
  non-fiction exists. Non-fiction books are rarely
  read in school. I learned more about optics from
  Craig Bohrens Clouds in a Glass of Beer than my
  undergraduate Optics textbook.
• Suggestion Have your students read a non-fiction
  science book or chapter or essay and write a
  report or give a presentation about it for both
  English and Science class

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I have learned a lot from reading excellent
popular science books

• They show scientific ways of thinking and
  analyzing situations that do not occur using
  standard textbooks. Consider collaborating with
  your language arts teachers.
• General
• Galileos Finger The Ten Great Ideas of Science
  by Peter Atkins
• Chaos Making a New Science by James Gleick
• A Short History of Nearly Everything by Bill
  Bryson
• Collapse How Societies Choose to Fail or Succeed
  by Jared Diamond
• Physics
• Clouds in a Glass of Beer by Craig Bohren
• What Light Through Yonder Window Breaks by Craig
  Bohren
• Surely Youre Joking Mr. Feynman by Richard
  Feynman
• What Do You Care What Other People Think by
  Richard Feynman
• The Meaning of it All by Richard Feynman
• Empires of Light Edison, Tesla, Westinghouse,
  and the Race to Electrify the World by Jill
  Jonnes
• Chemistry
• Uncle Tungsten Memories of a Chemical Boyhood by
  Oliver Sacks
• Lifes Matrix A Biography of Water by Philip
  Ball
• Napoleans Buttons 17 Molecules That Changed
  History by Penny Le Couteur and Jay Burreson
• Biology
• Bully for Brontosaurus by Stephen Jay Gould

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A Private Universe Resources

• General Information
• www.learner.org/channel/workshops/privuniv/i
  ntro.html
• A Private Universe video Harvard students
  explaining the seasons www.learner.org/res
  ources/series28.html
• Minds of Their Own video MIT students making
  simple circuits www.learner.org/resources/
  series26.html
• Using A Private Universe video with high school
  students
• www.learner.org/teacherslab/pup/usinghs.html
  
• Private Universe activities
• www.learner.org/teacherslab/pup/
• Modeling workshops to learning how to teach
  inquiry in high school
• http//modeling.asu.edu