Doug Brutlag Professor Emeritus Biochemistry & Medicine (by courtesy)
restoring essential numerical skills and thinking via...
Transcript of restoring essential numerical skills and thinking via...
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
Results ² Implications
and Future Plans
Kate Follette University of Arizona NNN 2012 October 13, 2012
² Motivation ² Study Basics ² Preliminary
Results ² Implications
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.”
Kate Follette University of Arizona NNN 2012 October 13, 2012
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
² Motivation ² Study Basics ² Preliminary
Results ² Implications
and Future Plans
Kate Follette University of Arizona NNN 2012 October 13, 2012
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
² Motivation ² Study Basics ² Preliminary
Results ² Implications
and Future Plans
Kate Follette University of Arizona NNN 2012 October 13, 2012
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
² Motivation ² Study Basics ² Preliminary
Results ² Implications
and Future Plans
Sam
ple
Que
stio
ns
Kate Follette University of Arizona NNN 2012 October 13, 2012
Part
2: A
ttitu
de
² Motivation ² Study Basics ² Preliminary
Results ² Implications
and Future Plans
Kate Follette University of Arizona NNN 2012 October 13, 2012
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
² Motivation ² Study Basics ² Preliminary
Results ² Implications
and Future Plans
Kate Follette University of Arizona NNN 2012 October 13, 2012
Fall,
201
1 ² 2 classes ² 1 large (188 students)
² 1 small (26 students)
² Motivation ² Study Basics ² Preliminary
Results ² Implications
and Future Plans
Kate Follette University of Arizona NNN 2012 October 13, 2012
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
² Motivation ² Study Basics ² Preliminary
Results ² Implications
and Future Plans
Kate Follette University of Arizona NNN 2012 October 13, 2012
>-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
² Motivation ² Study Basics ² Preliminary
Results ² Implications
and Future Plans
Class 1 : 64% pre, 64% post Class 2: 68% pre, 73% post
Kate Follette University of Arizona NNN 2012 October 13, 2012
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%
² Motivation ² Study Basics ² Preliminary
Results ² Implications
and Future Plans
Mat
h is
…
Class 2 Pre
Class 2 Post
Class 1 Post Class 1 Pre
Kate Follette University of Arizona NNN 2012 October 13, 2012
² Motivation ² Study Basics ² Preliminary
Results ² Implications
and Future Plans
Spri
ng, 2
012
• 6 classes • 4 small (25-35) • 1 large (100) • 1 very large (800+)
• 1000+ students • Large research university +
community college
Kate Follette University of Arizona NNN 2012 October 13, 2012
Step
1: D
ata
Ana
lysi
s ² NSF TUES ² Survey development
² Curriculum development
² Instructor training
² Motivation ² Study Basics ² Preliminary
Results ² Implications
and Future Plans
Kate Follette University of Arizona NNN 2012 October 13, 2012
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
² Motivation ² Study Basics ² Preliminary
Results ² Implications
and Future Plans
Kate Follette University of Arizona NNN 2012 October 13, 2012
Step
3: C
urri
culu
m
² Motivation ² Study Basics ² Preliminary
Results ² Implications
and Future Plans
Kate Follette University of Arizona NNN 2012 October 13, 2012
Step
3: C
urri
culu
m
² Motivation ² Study Basics ² Preliminary
Results ² Implications
and Future Plans
Kate Follette University of Arizona NNN 2012 October 13, 2012
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.
² Motivation ² Study Basics ² Preliminary
Results ² Implications
and Future Plans
Kate Follette University of Arizona NNN 2012 October 13, 2012
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?
² Motivation ² Study Basics ² Preliminary
Results ² Implications
and Future Plans
Kate Follette University of Arizona NNN 2012 October 13, 2012
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
² Motivation ² Study Basics ² Preliminary
Results ² Implications
and Future Plans
Kate Follette University of Arizona NNN 2012 October 13, 2012
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
² Motivation ² Study Basics ² Preliminary
Results ² Implications
and Future Plans
Kate Follette University of Arizona NNN 2012 October 13, 2012
Step
4: F
acul
ty T
rain
ing
an
d A
war
enes
s
Sum
mar
y ² Motivation ² Study Basics ² Preliminary
Results ² Implications
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!
www.katefollette.com/QL
² Motivation ² Study Basics ² Preliminary
Results ² Implications
and Future Plans
Kate Follette University of Arizona NNN 2012 October 13, 2012