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You See it – But Do You Believe It?Multiple Representations and Misconceptions in

Science Instructional Materials

High School Science Teacher Forumfor North San Diego County Teachers

Dr. Larry Woolf

Larry.Woolf@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?

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Let’s see what are the primary colors according to expert sources

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Authoritative approach

Webster’s 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.)”

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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

Hewitt’s 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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• You can make “all” other colors (not really)

• You can’t make a primary color by mixing

What is meant by “primary colors?”

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Using your colored films, let’s 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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Let’s 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

W W W C

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

W M

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

W Y

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

(R +G +B) – R – G = B

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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• 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

What is the one big idea that determines color?

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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 let’s 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

R

Y

M

B

G

C

Now let’s deconstruct the model in terms of cyan, magenta, and yellow components

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R

Y

M

B

G

C

Deconstruct the model in terms of cyan, magenta, and yellow components

Now, how could you make this “real?”

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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

R

Y

M

B

G

C

What are the limitations of this model?Does it show all the possible colors?Does this model explain how our eyes see color?

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A more sophisticated color model: L* a* b* color space

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So What?

• Let’s 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 subjects:From 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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• (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

Interactive engagement vs traditional instruction

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From: http://www.physics.indiana.edu/~hake/

“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,

Scientific evidence: interactive engagement is more effective than passive lecture for understanding of conceptually difficult subjects

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Why is it hotter in the summer than the winter?

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Let’s 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:<http://www.ems.psu.edu/~fraser/BadScience.html>)

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Are the rays from the Sun ever *indirect*?

Is Earth’s orbit egg-shaped?

At Earth’s surface, are the Sun’s 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)?

What do you think about these questions?

Let’s see what the experts say …

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From: A Private Universe Teacher’s Guide, p. 18

Misleading terms: “indirect rays” and “direct rays”

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From National Geographichttp://www.nationalgeographic.com/xpeditions/activities/07/season.html

“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 reversed—the 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.”

Misleading terms: “indirect rays” and “direct rays”

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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 “…Earth’s 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, Earth’s orbit is very nearly circular – see poster. Why do you think he believes that Earth’s orbit is egg-shaped?

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http://csep10.phys.utk.edu/astr161/lect/time/seasons.html

Critically analyze this figure

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Misleading scales and diagramsOverly distorted Sun position and elliptical orbit

http://csep10.phys.utk.edu/astr161/lect/time/seasons.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!

55http://hea-www.harvard.edu/ECT/the_book/Chap2/Chapter2.html

Critically analyze this figure

56http://hea-www.harvard.edu/ECT/the_book/Chap2/Chapter2.html

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

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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.”

58From GEMS: The Real Reasons for Seasons p. 92

Sun’s rays are parallel

Conflicting models for the sun’s rays

59From: “What is Light and How Do We Explain It” by Bill G. Aldridge; Scope Sequence and Coordination High School Project of NSTA, 1996

Sun’s rays are not parallel

Conflicting models for the sun’s rays

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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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Let’s make a correct scale model for the Sun’s 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. = 100:1

– And Earth-Sun distance: Sun dia. = 100:1

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Correct scale model for the Sun’s 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

64From: Earth Science Seventh Edition by Tarbuck and Lutgens

Incorrect Explanations?

According to this Earth Science textbook, the amount of atmosphere the sunlight passes through is a cause of the season: true?

Does the atmosphere deplete the solar energy more in winter than summer because rays pass through more atmosphere in winter than summer?

WINTER at 40°

SUMMER at 40°

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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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Clear Sky Ground Insolation/Top of Atmosphere Insolation for 40 degrees North

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1 2 3 4 5 6 7 8 9 10 11 12

Month

Cle

ar s

ky

gro

un

d i

nso

lati

on

/to

p o

f at

mo

sph

ere

inso

lati

on

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.

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Relative monthly averaged Top of Atmosphere (TOA) insolation (black lines) and relative monthly averaged clear sky ground insolation (red lines)

versus month for the various latitudes shown

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

0.900

1.000

1 2 3 4 5 6 7 8 9 10 11 12

Month

Rel

ativ

e In

sola

tio

n

0º

-20º

-40º

-60º

-80º

80º

60º

40º

20º

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 can’t 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 Bohren’s 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– Galileo’s 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 You’re 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– Life’s Matrix: A Biography of Water by Philip Ball– Napolean’s Buttons: 17 Molecules That Changed History by Penny Le Couteur and Jay Burreson

• Biology– Bully for Brontosaurus by Stephen Jay Gould– Full House by Stephen Jay Gould– The Blind Watchmaker by Richard Dawkins– The Double Helix by James WatsonSee also: http://scilib.ucsd.edu/spotlight/amsci100.htm

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“A Private Universe” Resources • General Information

www.learner.org/channel/workshops/privuniv/intro.html• A Private Universe video: Harvard students explaining the seasons

www.learner.org/resources/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