restoring essential numerical skills and thinking via ...d32ogoqmya1dw8.cloudfront.net/files/nnn/meetings/...Kate Brutlag Follette Dr. Don McCarthy Dr. Erin Dokter ... Through the

Re-Numerate restoring essential numerical skills and thinking via astronomy education

Kate Brutlag Follette

Dr. Don McCarthy

Dr. Erin Dokter

October 13, 2012

Can it be done?

Numbers are everywhere!

And yet…

Numbers are everywhere!

And yet…

² Motivation ² Study Basics ² Preliminary

Results ²  Implications

and Future Plans

Kate Follette University of Arizona NNN 2012 October 13, 2012

Innumeracy/Quantitative Illiteracy

Voters, Consumers, Citizens NASA’s 2011 Budget:

$18.724 billion

1 2 3 4 5

11%

29%

13%

8%

39%

Who Wants to be a Billionaire? Where is one billion on this scale?

1 trillion

E D C B A

US 2011 Budget: $3.630 trillion

Pseu

dos

cien

ce

“I have here in my hand a list of 205, a list of names that were made known to the Secretary of State as being members of the Communist party and who nevertheless are still working and shaping policy in the State Department”

Joseph McCarthy February 9, 1950 ² Motivation ² Study Basics ² Preliminary


and Future Plans




and Future Plans

Why

Intr

o Sc

ienc

e/A

stro

nom

y? ² Based on AIP survey: “introductory astronomy

enrollments have remained in the 180,000-190,000 range since 2004” (Nicholson and Mulvey, 2010)

² + community colleges, where “an estimated 100,000 students take Astronomy 101 in departments not covered by the AIP survey” (Fraknoi 2001).

² Bureau of Labor Statistics: 2.2 million people were enrolled in college in the US in Fall, 2010.

² >10% of college students eventually pass through the door of an “Astronomy 101” course in college.

“I have always heard a lot about science and math being related, but I have never actually used them together. I have finished an entire year of algebra, but there has never been any science in it. The same holds true in my science class. Frankly, I have never seen any connection between the two of them.”


Part

1: S

kill

Set

Numerical Skills ² Percentages and Fractions ² Multiplication and Division ² Simple Unit Conversions

² Powers and Area ² Estimation ² Error

² Graph Reading and Interpretation

Can you do Division? Divide a loaf by a knife - what's the answer to that? Through the Looking Glass



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You get a letter from your cable company saying that they will be raising your monthly rate by $5. Assuming that the rate does not change again, how much additional money will you be paying to the cable company over the course of the next three years? (a) $60 (b) $100 (c) $130 (d) $180

How confident are you in the answer you just selected? (a) very confident (b)Confident (c) not very confident (d) I guessed

Sam

ple

Que

stio

ns



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You begin by measuring out the peanut butter in a 2 cup glass measuring cup like that shown above. You fill it to the ¾ cup line. If you are to add the shortening to the same measuring cup on top of the peanut butter, which line should you fill it to? (a) the 1 cup line (b) the 1 ¼ cup line (c) the 1 1/3 cup line (d) none of the above



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Sam

ple

Que

stio

ns


Part

2: A

ttitu

de



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Prel

imin

ary

Surv

ey

0%

10%

20%

30%

40%

50%

60%

Very Confident

Confident Not Very Confident

Guessed

Confidence in Incorrect Answers

0%

10%

20%

30%

40%

50%

60%

Very Confident

Confident Not Very Confident

Guessed

Confidence in Correct Answers

Actual Score ~10% lower than Predicted Score



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Fall,

201

1 ² 2 classes ² 1 large (188 students)

² 1 small (26 students)



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Incl

usio

n C

rite

ria

² Completed both

² 18+ years

² Spent ≥10min on both

² Leaves ~55%: ² 102 in class 1

² 14 in class 2



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>-1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 >1

Normalized Gain Scores

Class 1

Class 2

Prel

imin

ary

Resu

lts



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Class 1 : 64% pre, 64% post Class 2: 68% pre, 73% post


21%

42%

12%

4%

21% interesting

useful

useless

boring

hard

29%

46%

8%

4% 13%

16%

48%

2%

11%

23% 15%

56% 1%

11%

17%



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Mat

h is

…

Class 2 Pre

Class 2 Post

Class 1 Post Class 1 Pre




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Spri

ng, 2

012

•  6 classes •  4 small (25-35) •  1 large (100) •  1 very large (800+)

•  1000+ students •  Large research university +

community college


Step

1: D

ata

Ana

lysi

s ² NSF TUES ² Survey development

² Curriculum development

² Instructor training



and Future Plans


Step

2: S

kills

Val

idat

ion ²  Skills Survey

²  Area and Volume

²  Calculus (Integrals, Derivatives, Differential Eqns)

²  Dimensional Analysis* and Unit Conversions

²  Elementary Algebra

²  Error, Precision, Accuracy

²  Estimation

²  Exponents and Logarithms

²  Geometry and Trigonometry

²  Interpret Graphs (read, extrapolate, etc.)

²  Linear and Exponential Growth

²  Measurement and Units

²  Percent and Percent Change

²  Plotting/Making Graphs

²  Probability, Odds, Risk

²  Proportionality/Scaling and Relative Size/Scale

²  Ratios, Fractions, Decimals

²  Scientific Notation

²  Significant Figures

²  Simple Operations (+/-/×/÷)

²  Statistics (mean, median, mode, standard deviation)

²  Systems of Equations



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Step

3: C

urri

culu

m



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Step

3: C

urri

culu

m



and Future Plans


² Based on the following information, which environment do you think is more crowded, the Solar System or the space between galaxies?

² How many Earths would fit between the Sun and Earth? ²  The distance between the Sun and Earth

is 1.5 x 108 km. The diameter of the Earth is 1.3 x 104 km.

² How many galaxies would fit between the Milky Way and Andromeda? ²  The distance between the Milky Way

and Andromeda is about two million light-years. The diameter of the Milky Way is about 100,000 light-years.



and Future Plans


Exa

mpl

e: “

Em

pty

or

crow

ded?

” Th

ink-

Pair

-Sha

re q

uest

ion

² How many Suns would fit between the Sun and the next nearest star? ² The light travel time across the

Sun is ~4 seconds.

² The distance to alpha Centauri is ~4 light-years.

² The Milky Way and Andromeda galaxies will collide in a few billion years. Do you expect their stars to collide?



and Future Plans


Foll

owup

que

stio

n an

d co

ncep

t

² Graph Interpretation

² Powers of Ten

² Scientific Notation

² Unit Conversions

² Dimensional Analysis

² Fractions and Percentages

² Ratios

² Scale Factors



and Future Plans


Lect

ure

Tuto

rial

St

yle

Skill

Act

iviti

es

² Astronomical Society of the Pacific, 2011 ² Hilighted poster

² Contributed article to Mercury Magazine

² American Astronomical Society 2012

² Astronomical Society of the Pacific, 2012 ² Panel Discussion

² 1hr workshop

² American Astronomical Society ² 2hr workshop



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Step

4: F

acul

ty T

rain

ing

an

d A

war

enes

s

Sum

mar

y ² Motivation ² Study Basics ² Preliminary


and Future Plans

² Innumeracy has serious implications for science literacy, and students’ ability to spot pseudoscience in particular

² Intro science courses for non-majors captures an important innumerate demographic

² It is possible to change attitudes!

² It may be possible to improve skills, provoke awareness of need to improve Kate Follette

University of Arizona NNN 2012 October 13, 2012

THANK YOU!

[email protected]

www.katefollette.com/QL



and Future Plans


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restoring essential numerical skills and thinking via ...d32ogoqmya1dw8.cloudfront.net/files/nnn/meetings/...Kate Brutlag Follette Dr. Don McCarthy Dr. Erin Dokter ... Through the