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A Scientific Investigation of Science Instructional Materials

SDSC TeacherTECH Program

Dr. Larry WoolfLarry.Woolf@ga.com

www.sci-ed-ga.org (click on presentations)General AtomicsPresented 1/17/08

San Diego Supercomputer Center

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Topics• Color

-Multidisciplinary and crossdisciplinary– Different “truths” taught in art and science class

• Seasons– Poster child for misconceptions and science

instruction– Private Universe project

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Part I: Color MixingWhat 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 white is black approach

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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The red (or vermillon), green, blue (or intense blue or violet), cyan (or cyan blue or blue), magenta (or red), and yellow multi-colortural approach

Barron’s Art Handbooks: Mixing Colors 1. Watercolor

Danger: Same model for light and pigment colors!

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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 (absorbed)?– 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 = 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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Why are CMY called the Subtractive Primaries?

• Cyan film absorbs a single primary color of light– Red

• Magenta film absorbs a single primary color of light– Green

• Yellow film absorbs a single primary color light– Blue

They each “subtract a primary” color of light

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How Can We Understand These Ideas in a Way That Connects to

a “Big Idea?”

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Concept Map for ColorEnergy is conserved

Energy is conserved when light interacts with matter:

R+T+A=1

Subtractive color results from selective absorption of visible

light

W-R=C W-B=YW-G=MW=R+G+B

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Concept Maps are useful for hierarchical organization of knowledge

• Hyperphysics– http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

• AAAS Atlas of Science Literacy– http://www.project2061.org/publications/atlas/default.htm

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Color mixing

• We found that mixing cyan and magenta films made a blue film

• Mixing cyan and yellow films makes a green film

• Mixing yellow and magenta films 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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Color Cube Model for Subtractive (and Additive!) Colors

www.colorcube.com

Color difference: distance between colors

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Industrial strength color model: L* a* b* color space

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So What?

• What is subtractive color mixing good for?

• Take a look at colored magazines using a handheld microscope

• How are colored pictures made?

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What happens when you mix different color of light?

We already did this!

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Additive Color Mixing

• What is it good for?

• Let’s use two computers to verify

• Consider how TVs, computer monitors, and all display devices work

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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

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Part II: 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”

15:19 – 17:43

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A Private Universe

• What confused Heather?

• What images were presented to her?

• What science terms were presented to her?

• What were the root causes of her misconceptions and private theory?

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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

Commonly used 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.”

Commonly used 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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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!

60http://hea-www.harvard.edu/ECT/the_book/Chap2/Chapter2.html

Critically analyze this figure

61http://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.”

63From GEMS: The Real Reasons for Seasons p. 92

Sun’s rays are parallel

Conflicting models for the sun’s rays

64From: “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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See Seasons Poster (Block 5)

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Can we semi-quantitatively understand why we have seasons?

• How can we demonstrate analytically what are the reasons for the seasons?– Do we have data that is related to seasons?

• Hint: This information would be useful if you are buying a solar panel for your home

– What is our theory for why we have seasons? What factors are involved?

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Seasons data: Solar INSOLATION (INcoming SOLar radiaTION)

http://www.apricus.com/html/solar_collector_insolation.htm

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Seasons Theory

• Change in sun angle reduces intensity of incoming solar radiation by factor of sine of maximum sun angle above horizon

• Change in number of daylight hours during which sun is shining

How would a theory account for 2 factors that are both proportional to the solar insolation?

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Sun angle data

http://aa.usno.navy.mil/data/docs/AltAz.php

Sine of these data is related to solar intensity

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Daylight Hours Data

http://www.timeanddate.com/worldclock/aboutastronomy.html

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Relative change of Raw Data and Theory

Both sine (sun altitude) and number of daylight hours both affect solar insolation, so need to multiply these effects

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Relative Change of Data and Model

Our model agrees with data!!!

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Qualitative reason 1 for seasons

Note: Correct perspective, shows summer and winter, shows entire Earth - so more context and opportunity for connections

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Qualitative reason 2 for seasons

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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

80From: 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– in winter?– in summer?

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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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“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

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GA References

• This and other presentations are at:– http://www.sci-ed-ga.org/GASEFPresentations.html

• It’s a Colorful Life and Season’s module:– http://www.sci-ed-ga.org/modules/index.html

• Educational Materials:– http://www.sci-ed-ga.org/modules/materialscience/color/materials.html