1. Math 20
Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
Gilligan, MOPE, and TiVo
Teaching activities at Harvard
Matthew Leingang
Harvard University
Department of Mathematics
University of California, Irvine
April 4, 2007
Matthew Leingang Gilligan, MOPE, and TiVo
2. Math 20
Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
Outline
Math 20
1
History
Current syllabus
Examples
Mathematical Online Placement Exam
2
History
Implementation
Lessons learned
The ALM in Mathematics for Teaching Program
3
History
Example: Bayesian Decision Making
Matthew Leingang Gilligan, MOPE, and TiVo
3. Math 20 History
Mathematical Online Placement Exam Current syllabus
The ALM in Mathematics for Teaching Program Examples
Outline
Math 20
1
History
Current syllabus
Examples
Mathematical Online Placement Exam
2
History
Implementation
Lessons learned
The ALM in Mathematics for Teaching Program
3
History
Example: Bayesian Decision Making
Matthew Leingang Gilligan, MOPE, and TiVo
4. Math 20 History
Mathematical Online Placement Exam Current syllabus
The ALM in Mathematics for Teaching Program Examples
Math 20: Introduction to linear algebra and
multivariable calculus
Taught since 2004
Original idea: stick
to the title
Almost no
applications
originally
Matthew Leingang Gilligan, MOPE, and TiVo
5. Math 20 History
Mathematical Online Placement Exam Current syllabus
The ALM in Mathematics for Teaching Program Examples
Math 20: Introduction to linear algebra and
multivariable calculus
Taught since 2004
Original idea: stick
to the title
Almost no
applications
originally
Matthew Leingang Gilligan, MOPE, and TiVo
6. Math 20 History
Mathematical Online Placement Exam Current syllabus
The ALM in Mathematics for Teaching Program Examples
Outline
Math 20
1
History
Current syllabus
Examples
Mathematical Online Placement Exam
2
History
Implementation
Lessons learned
The ALM in Mathematics for Teaching Program
3
History
Example: Bayesian Decision Making
Matthew Leingang Gilligan, MOPE, and TiVo
7. Math 20 History
Mathematical Online Placement Exam Current syllabus
The ALM in Mathematics for Teaching Program Examples
Syllabus for Math 20, Spring 2007
Foundational material
Systems of linear equations
Algebra
Gauss elim Inversion
Dot product
Vector Matrix Determinants
Eigenstuff
Function
Quad approx Partial derivative
Lin approx
Differentials
Matthew Leingang Gilligan, MOPE, and TiVo
8. Math 20 History
Mathematical Online Placement Exam Current syllabus
The ALM in Mathematics for Teaching Program Examples
Syllabus for Math 20, Spring 2007
Applications
Stationary points
Linear programming
Lag mult
Optimization
Game theory
Problems
Least squares
Assignment problem
Markov chains
Leontief
Matthew Leingang Gilligan, MOPE, and TiVo
9. Math 20 History
Mathematical Online Placement Exam Current syllabus
The ALM in Mathematics for Teaching Program Examples
Syllabus for Math 20, Spring 2007
Applications
Stationary points
Linear programming
Lag mult
Optimization
Game theory
Problems
Least squares
Assignment problem
Markov chains
Leontief
Matthew Leingang Gilligan, MOPE, and TiVo
10. Math 20 History
Mathematical Online Placement Exam Current syllabus
The ALM in Mathematics for Teaching Program Examples
Outline
Math 20
1
History
Current syllabus
Examples
Mathematical Online Placement Exam
2
History
Implementation
Lessons learned
The ALM in Mathematics for Teaching Program
3
History
Example: Bayesian Decision Making
Matthew Leingang Gilligan, MOPE, and TiVo
11. Math 20 History
Mathematical Online Placement Exam Current syllabus
The ALM in Mathematics for Teaching Program Examples
Some fun problems you can solve
(Economics) which is better: sales tax or income tax?
(Linear programming) can you eat a healthy meal at
McDonald’s?
(Assignment problem) Match teaching fellows to time slots
to maximize TF satisfaction
(Game theory) What percentage of the time should you say
“Merry Christmas” versus “Happy Holidays” to strangers?
(Markov chains) Will Detroit become an annular city?
Matthew Leingang Gilligan, MOPE, and TiVo
12. Math 20 History
Mathematical Online Placement Exam Current syllabus
The ALM in Mathematics for Teaching Program Examples
A closed Leontief input-output system
Problem from Fall 2006 Final
Consider an island with a four-person economy:
Gilligan (agriculture) produces coconuts, palm fronds, and
bamboo poles by collecting them.
The Professor (manufacturing) produces shelter and
equipment by consuming raw materials and with the help
of the Skipper.
Mary Ann (service) takes coconuts and bakes delicious
coconut cream pies, upon which the entire island subsists.
The Skipper (labor) helps the professor with his projects.
Matthew Leingang Gilligan, MOPE, and TiVo
13. Math 20 History
Mathematical Online Placement Exam Current syllabus
The ALM in Mathematics for Teaching Program Examples
Problem continued
The distribution of products works like this:
Three-fourths of Gilligan’s raw materials go to the
Professor for his creations and the rest go to Maryann for
her pies.
Gilligan and the Skipper each use a sixth of the Professor’s
inventions. Mary Ann and the Professor himself use a third
apiece.
Everyone shares Mary Ann’s pies equally.
All of the Skipper’s labor goes to the Professor.
Find the equilibrium prices each should charge for their
products.
Matthew Leingang Gilligan, MOPE, and TiVo
14. Math 20 History
Mathematical Online Placement Exam Current syllabus
The ALM in Mathematics for Teaching Program Examples
Solution
Find a solution to Ap = p, where
Gilligan Professor Mary Ann Skipper
Gilligan 0 1/6 1/4 0
A = Professor 3/4 1/3 1/4 0
Mary Ann 1/4 1/3 1/4 0
Skipper 0 1/6 1/4 1
Matthew Leingang Gilligan, MOPE, and TiVo
15. Math 20 History
Mathematical Online Placement Exam Current syllabus
The ALM in Mathematics for Teaching Program Examples
Solution
Find a solution to Ap = p, where
Gilligan Professor Mary Ann Skipper
Gilligan 0 1/6 1/4 0
A = Professor 3/4 1/3 1/4 0
Mary Ann 1/4 1/3 1/4 0
Skipper 0 1/6 1/4 1
T
p = 1 3.3 1.8 1 works.
Matthew Leingang Gilligan, MOPE, and TiVo
16. Math 20 History
Mathematical Online Placement Exam Current syllabus
The ALM in Mathematics for Teaching Program Examples
Results so far
Very happy students
Very high scores
Possible book in the
works someday
Matthew Leingang Gilligan, MOPE, and TiVo
17. Math 20 History
Mathematical Online Placement Exam Implementation
The ALM in Mathematics for Teaching Program Lessons learned
Outline
Math 20
1
History
Current syllabus
Examples
Mathematical Online Placement Exam
2
History
Implementation
Lessons learned
The ALM in Mathematics for Teaching Program
3
History
Example: Bayesian Decision Making
Matthew Leingang Gilligan, MOPE, and TiVo
18. Math 20 History
Mathematical Online Placement Exam Implementation
The ALM in Mathematics for Teaching Program Lessons learned
Status Quo
Pencil-and-paper exam
given on ﬁrst day of
Freshman week
Grade Report is three
numbers and a course
code: Math Xa, 1a, 1b,
or 21a
Matthew Leingang Gilligan, MOPE, and TiVo
19. Math 20 History
Mathematical Online Placement Exam Implementation
The ALM in Mathematics for Teaching Program Lessons learned
Example placement information
HMPT1: 19 HMPT2: 10
HMPT3: 6
Matthew Leingang Gilligan, MOPE, and TiVo
20. Math 20 History
Mathematical Online Placement Exam Implementation
The ALM in Mathematics for Teaching Program Lessons learned
Example placement information
HMPT1: 19 HMPT2: 10
HMPT3: 6
Recommendation:
Math Xa
Matthew Leingang Gilligan, MOPE, and TiVo
21. Math 20 History
Mathematical Online Placement Exam Implementation
The ALM in Mathematics for Teaching Program Lessons learned
Example placement information
HMPT1: 19 HMPT2: 10
HMPT3: 6
Recommendation:
Math Xa
AP Calculus BC: 5
Matthew Leingang Gilligan, MOPE, and TiVo
22. Math 20 History
Mathematical Online Placement Exam Implementation
The ALM in Mathematics for Teaching Program Lessons learned
Example placement information
HMPT1: 19 HMPT2: 10
HMPT3: 6
Recommendation:
Math Xa
AP Calculus BC: 5
Recommendation:
Math 21a
Matthew Leingang Gilligan, MOPE, and TiVo
23. Math 20 History
Mathematical Online Placement Exam Implementation
The ALM in Mathematics for Teaching Program Lessons learned
Example placement information
HMPT1: 19 HMPT2: 10
HMPT3: 6
Recommendation:
Math Xa
AP Calculus BC: 5
Recommendation:
Math 21a
Could be same person!
Matthew Leingang Gilligan, MOPE, and TiVo
24. Math 20 History
Mathematical Online Placement Exam Implementation
The ALM in Mathematics for Teaching Program Lessons learned
Example placement information
HMPT1: 19 HMPT2: 10
HMPT3: 6
Recommendation:
Math Xa
AP Calculus BC: 5
Recommendation:
Math 21a
Could be same person!
Matthew Leingang Gilligan, MOPE, and TiVo
25. Math 20 History
Mathematical Online Placement Exam Implementation
The ALM in Mathematics for Teaching Program Lessons learned
Example placement information
HMPT1: 19 HMPT2: 10
HMPT3: 6
Recommendation:
Math Xa
AP Calculus BC: 5
Recommendation:
Math 21a
Could be same person!
Matthew Leingang Gilligan, MOPE, and TiVo
26. Math 20 History
Mathematical Online Placement Exam Implementation
The ALM in Mathematics for Teaching Program Lessons learned
Disadvantages of Status Quo
Students descend upon advisors to interpret these
numbers and give further guidance
Somewhat unnecessarily intimidating and impersonal
HMPT was designed in an era when high school student
exposure to calculus was limited
Matthew Leingang Gilligan, MOPE, and TiVo
27. Math 20 History
Mathematical Online Placement Exam Implementation
The ALM in Mathematics for Teaching Program Lessons learned
Mathematical Online Placement Exam (MOPE)
Funded by Innovation Grant from the Provost’s Fund for
Instructional Technology
Goals
Give entering students more personal, more detailed
information for choosing a math course
Form part of a student-friendly web presence
Matthew Leingang Gilligan, MOPE, and TiVo
28. Math 20 History
Mathematical Online Placement Exam Implementation
The ALM in Mathematics for Teaching Program Lessons learned
Outline
Math 20
1
History
Current syllabus
Examples
Mathematical Online Placement Exam
2
History
Implementation
Lessons learned
The ALM in Mathematics for Teaching Program
3
History
Example: Bayesian Decision Making
Matthew Leingang Gilligan, MOPE, and TiVo
29. Math 20 History
Mathematical Online Placement Exam Implementation
The ALM in Mathematics for Teaching Program Lessons learned
Features
Question database organized by mathematical topic and
type of question
A multitude of tests for qualiﬁcation or mastery
Can be taken any time
Topic-speciﬁc feedback, with granularity
Retakes after refreshing are allowed
Matthew Leingang Gilligan, MOPE, and TiVo
30. Math 20 History
Mathematical Online Placement Exam Implementation
The ALM in Mathematics for Teaching Program Lessons learned
Portion of MOPE’s topic tree
composing
evaluating
inverse trig
evaluting trig fns (radians)
arc length; sector a
simplifying
evaluting trig fns (degrees) and circles
radian measure
sin2 + cos2 = 1
trig identities
sign and range of trig fns
angle-addition
Trigonometry
double-angle
law of sines
and triangles sinusoidal
law of cosines
graphs
trig fns from right triangles tan/cot
Matthew Leingang Gilligan, MOPE, and TiVo
31. Math 20 History
Mathematical Online Placement Exam Implementation
The ALM in Mathematics for Teaching Program Lessons learned
Screenshot of sample question
https://mope.dce.harvard.edu:10000/authentication/index
MATH PLACEMENT TEST
TECHNICAL REQUIREMENTS FAQ
NAVIGATION HELP LOGOUT
TIME REMAINING: 43:56
QUESTION 9 22 questions left to answer SELECT YOUR ANSWER
Ø Á5˜ Ø Á 2˜
ø Øø Ø
If v = Ë ¯ and w = Ë ¯, what is the length of the vector v - w ?
Ë¯ Ë¯
Ë¯ Ë¯
È1˘ È-3˘
A. 2
B. 5
C. 3 TEST NAVIGATION
0 0
CLEAR YOUR ANSWER
NEXT QUESTION
D. 26 - 13 PREVIOUS QUESTION
NEXT BLANK
E. 7 FIRST QUESTION
GO TO QUESTION
10
SUBMIT YOUR ANSWERS
and end the test
Answers: 0=>1 1=>4 2=>0 3=>2 4=>3
Correct answer: 1
Question index: 779
Matthew Leingang Gilligan, MOPE, and TiVo
Question topic: 308
32. Math 20 History
Mathematical Online Placement Exam Implementation
The ALM in Mathematics for Teaching Program Lessons learned
Screenshot of sample question
https://mope.dce.harvard.edu:10000/authentication/index.php?school=fas
MATH PLACEMENT TEST
TECHNICAL REQUIREMENTS FAQ
NAVIGATION HELP LOGOUT
Your Receipt
Last Name: Strozek
First Name: Lukasz
Email address: strozek@fas.harvard.edu
Test taken: Math-21a mastery
Test score: Your score is 7 out of 30
Placement: Placement not issued (test incomplete)
You can take the test again in 1 hours. In the meanhile you may want to review: Analytic geometry, Vectors and planes, Parametrization and vector fields, Optimization and extrema, Directional
derivatives, Double integrals, Differentiating functions of several variables, Gradients in the plane, Gradient and path-independent fields, Line integrals, and Applications of multiple integrals.
PRINT
CONTINUE
Results of this pilot version of the Online Placement Examination provide only one of several pieces of information to help you with course selection. The Mathematics Department is always eager
to meet you, to talk over your individual experience and goals, and to help formulate a plan that works for you. Please bring your scores on this and other tests (the pencil-and-paper placement
examination, SAT, AP, etc.) to any of the times and places specifically listed when advisors will be waiting to speak with you.
Anyone considering courses like Math 23 or Math 25 should especially plan on consulting with Professor Taubes during his office hours.
Aug 22 2005 21:22:30 #58791-60547-10506-01628
Matthew Leingang Gilligan, MOPE, and TiVo
33. Math 20 History
Mathematical Online Placement Exam Implementation
The ALM in Mathematics for Teaching Program Lessons learned
Screenshot of sample question
You can take the test again in 1 hour. In the meanwhile
you may want to review: Analytic geometry, Vectors and
planes, Parametrization and vector ﬁelds, Optimization
and extrema, Directional derivatives, Double integrals,
Differentiating functions of several variables, Gradients
in the plane, Gradient and path-independent ﬁelds, Line
integrals, and Applications of multiple integrals.
Matthew Leingang Gilligan, MOPE, and TiVo
34. Math 20 History
Mathematical Online Placement Exam Implementation
The ALM in Mathematics for Teaching Program Lessons learned
“Result”
Average of Math 1a First Midterm
HMPT1 HMPT1
all
passed
failed
MOPE failed 73.00 78.67 75.43
MOPE passed 89.50 N/A 89.50
all 78.50 78.67 78.56
Matthew Leingang Gilligan, MOPE, and TiVo
35. Math 20 History
Mathematical Online Placement Exam Implementation
The ALM in Mathematics for Teaching Program Lessons learned
“Result”
Average of Math 1a First Midterm
HMPT1 HMPT1
all
passed
failed
MOPE failed 73.00 78.67 75.43
MOPE passed 89.50 N/A 89.50
all 78.50 78.67 78.56
Unfortunately, N = 2 here
Matthew Leingang Gilligan, MOPE, and TiVo
36. Math 20 History
Mathematical Online Placement Exam Implementation
The ALM in Mathematics for Teaching Program Lessons learned
Outline
Math 20
1
History
Current syllabus
Examples
Mathematical Online Placement Exam
2
History
Implementation
Lessons learned
The ALM in Mathematics for Teaching Program
3
History
Example: Bayesian Decision Making
Matthew Leingang Gilligan, MOPE, and TiVo
37. Math 20 History
Mathematical Online Placement Exam Implementation
The ALM in Mathematics for Teaching Program Lessons learned
Math on the Web
Very challenging problem!
Originally we converted TEX to MathML
Later went to images (no MathML support)
Matthew Leingang Gilligan, MOPE, and TiVo
38. Math 20 History
Mathematical Online Placement Exam Implementation
The ALM in Mathematics for Teaching Program Lessons learned
Chicken-and-egg problem
can’t be more widely adopted without greater credibility
can’t be more credible without better calibration
can’t be calibrated without more data
can’t get more data without more people taking it
can’t get more to take it without being more widely adopted
Matthew Leingang Gilligan, MOPE, and TiVo
39. Math 20
History
Mathematical Online Placement Exam
Example: Bayesian Decision Making
The ALM in Mathematics for Teaching Program
Outline
Math 20
1
History
Current syllabus
Examples
Mathematical Online Placement Exam
2
History
Implementation
Lessons learned
The ALM in Mathematics for Teaching Program
3
History
Example: Bayesian Decision Making
Matthew Leingang Gilligan, MOPE, and TiVo
40. Math 20
History
Mathematical Online Placement Exam
Example: Bayesian Decision Making
The ALM in Mathematics for Teaching Program
Background of the ALM program
Goal: better K-12
teachers in BPS and
area
Started in 2001 by
D. Goroff and P. Sally
Degree program since
2003
35 participants and
soon to graduate ﬁrst
Master’s class
Matthew Leingang Gilligan, MOPE, and TiVo
41. Math 20
History
Mathematical Online Placement Exam
Example: Bayesian Decision Making
The ALM in Mathematics for Teaching Program
Objectives of the ALM program
Teach teachers the mathematics behind the rules, e.g.:
0.9999.... = 1
Division by zero is undeﬁned
Give resources to challenge their students
Demonstrate fun math learning activities
Matthew Leingang Gilligan, MOPE, and TiVo
42. Math 20
History
Mathematical Online Placement Exam
Example: Bayesian Decision Making
The ALM in Mathematics for Teaching Program
Outline
Math 20
1
History
Current syllabus
Examples
Mathematical Online Placement Exam
2
History
Implementation
Lessons learned
The ALM in Mathematics for Teaching Program
3
History
Example: Bayesian Decision Making
Matthew Leingang Gilligan, MOPE, and TiVo
43. Math 20
History
Mathematical Online Placement Exam
Example: Bayesian Decision Making
The ALM in Mathematics for Teaching Program
Bayes’s Theorem
Theorem (Bayes)
Let Ω be a probability space
with probability measure P.
If A and B are events, then
P(A | B)P(B)
P(B | A) =
P(A)
Proof.
P(B | A)P(A) = P(A ∩ B) = P(A | B)P(B)
Matthew Leingang Gilligan, MOPE, and TiVo
44. Math 20
History
Mathematical Online Placement Exam
Example: Bayesian Decision Making
The ALM in Mathematics for Teaching Program
Bayes and partitions
If Ω = H1 ∪ H2 ∪ . . . ∪ Hn is a partition, and E is any event, then
P(E | Hi )P(Hi )
P(Hi | E) =
P(E)
P(E | Hi )P(Hi )
=
P(E | H1 )P(H1 ) + · · · + P(E | Hn )P(Hn )
Matthew Leingang Gilligan, MOPE, and TiVo
45. Math 20
History
Mathematical Online Placement Exam
Example: Bayesian Decision Making
The ALM in Mathematics for Teaching Program
Bayes and partitions
If Ω = H1 ∪ H2 ∪ . . . ∪ Hn is a partition, and E is any event, then
P(E | Hi )P(Hi )
P(Hi | E) =
P(E)
P(E | Hi )P(Hi )
=
P(E | H1 )P(H1 ) + · · · + P(E | Hn )P(Hn )
If P(E) and P(E | Hj ) can be estimated, then so can P(Hi | E).
Matthew Leingang Gilligan, MOPE, and TiVo
46. Math 20
History
Mathematical Online Placement Exam
Example: Bayesian Decision Making
The ALM in Mathematics for Teaching Program
Observations and Observables
Suppose O ⊂ Ω is a “representative” sample:
P(E | O) ≈ P(E) for all events E.
Suppose we know what P(Hj | O) are.
Suppose also we have sets {Cα } and we know
P(Hj | Cα ∩ O), too.
Given a a “new” ω ∈ Ω O, if we can ﬁnd its observables
{Cαi }, what is the likelihood of ω being in any particular
state?
Matthew Leingang Gilligan, MOPE, and TiVo
47. Math 20
History
Mathematical Online Placement Exam
Example: Bayesian Decision Making
The ALM in Mathematics for Teaching Program
Don’t look at this all at once
P(Hi | Cα1 ∩ Cα2 ∩ . . . ∩ Cαm )
P(Cα1 ∩ Cα2 ∩ . . . ∩ Cαm | Hi )P(Hi )
= n
k =1 P(Cα1 ∩ Cα2 ∩ . . . ∩ Cαm | Hk )P(Hk )
m
j=1 P(Cαj | Hi ) P(Hi )
!
≈
n m
| Hk ) P(Hk )
j=1 P(Cαj
k =1
m
| Hi ∩ O) P(Hi | O)
j=1 P(Cαj
≈
n m
| Hk ∩ O) P(Hk | O)
j=1 P(Cαj
k =1
But everything at this stage is known.
Matthew Leingang Gilligan, MOPE, and TiVo
48. Math 20
History
Mathematical Online Placement Exam
Example: Bayesian Decision Making
The ALM in Mathematics for Teaching Program
Which brings us to TiVo
Ω is the set of all programs on
television
States Hj are your attitudes
toward programs
Observables {Cα } are
metadata about the programs
O is the set of shows you
have marked with thumbs
up/thumbs down.
Matthew Leingang Gilligan, MOPE, and TiVo
49. Math 20
History
Mathematical Online Placement Exam
Example: Bayesian Decision Making
The ALM in Mathematics for Teaching Program
Preference Data from Math E-304 on March 6, 2006
Title Like Dislike Neutral Total
King of Queens 4 5 7 16
How I Met your Mother 5 0 11 16
2 and a half Men 3 3 10 16
Courting Alex 1 0 15 16
CSI: Miami 4 2 10 16
Wife Swap 3 3 10 16
Supernanny 3 4 9 16
Miracle Worker 0 0 16 16
Deal or no Deal 4 3 9 16
Apprentice 6 4 6 16
Medium 3 1 12 16
24 5 1 10 16
Total 41 26 125 192
Prob(each preference) 21.35% 13.54% 65.10% 100.00%
Matthew Leingang Gilligan, MOPE, and TiVo
50. Math 20
History
Mathematical Online Placement Exam
Example: Bayesian Decision Making
The ALM in Mathematics for Teaching Program
Probability of class attitudes for each show (P(Hk | O))
Title P(like) P(dislike) P(neutral) Total
King of Queens 25.00% 31.25% 43.75% 100.00%
How I Met your Mother 31.25% 0.00% 68.75% 100.00%
2 and a half Men 18.75% 18.75% 62.50% 100.00%
Courting Alex 6.25% 0.00% 93.75% 100.00%
CSI: Miami 25.00% 12.50% 62.50% 100.00%
Wife Swap 18.75% 18.75% 62.50% 100.00%
Supernanny 18.75% 25.00% 56.25% 100.00%
Miracle Worker 0.00% 0.00% 100.00% 100.00%
Deal or no Deal 25.00% 18.75% 56.25% 100.00%
Apprentice 37.50% 25.00% 37.50% 100.00%
Medium 18.75% 6.25% 75.00% 100.00%
24 31.25% 6.25% 62.50% 100.00%
Prob(each attitude) 21.35% 13.54% 65.10% 100.00%
Matthew Leingang Gilligan, MOPE, and TiVo
51. Math 20
History
Mathematical Online Placement Exam
Example: Bayesian Decision Making
The ALM in Mathematics for Teaching Program
Frequency of attitude for each characteristic
Characteristic Like Dislike Neutral Total
Drama 12 4 32 48
Comedy 13 8 43 64
Reality 12 11 41 64
Game Show 4 3 9 16
Male Lead 22 16 42 80
Female Lead 22 16 42 80
Ensemble 9 2 21 32
TV-PG 26 18 84 128
TV-14 15 8 41 64
Totals 135 86 355 576
Matthew Leingang Gilligan, MOPE, and TiVo
52. Math 20
History
Mathematical Online Placement Exam
Example: Bayesian Decision Making
The ALM in Mathematics for Teaching Program
Conditional probability of each characteristic, given
attitude and observed (P(Cα | Hk ∩ O))
Characteristic Like Dislike Neutral Total
Drama 8.89% 4.65% 9.01% 8.33%
Comedy 9.63% 9.30% 12.11% 11.11%
Reality 8.89% 12.79% 11.55% 11.11%
Game Show 2.96% 3.49% 2.54% 2.78%
Male Lead 16.30% 18.60% 11.83% 13.89%
Female Lead 16.30% 18.60% 11.83% 13.89%
Ensemble 6.67% 2.33% 5.92% 5.56%
TV-PG 19.26% 20.93% 23.66% 22.22%
TV-14 11.11% 9.30% 11.55% 11.11%
Totals 100.00% 100.00% 100.00% 100.00%
Matthew Leingang Gilligan, MOPE, and TiVo
53. Math 20
History
Mathematical Online Placement Exam
Example: Bayesian Decision Making
The ALM in Mathematics for Teaching Program
(Posterior) probability of class attitudes for shows
airing March 7, 2006
Title P(Like) P(Dislike) P(Neutral) Total
NCIS 23.98% 9.87% 66.14% 100.00%
The Unit 22.24% 2.80% 74.96% 100.00%
Amazing Race 14.58% 14.46% 70.96% 100.00%
According to Jim 19.30% 14.67% 66.03% 100.00%
Sons & Daughters 18.47% 4.29% 77.24% 100.00%
Boston Legal 25.33% 2.45% 72.22% 100.00%
Joey 19.30% 14.67% 66.03% 100.00%
Scrubs 21.20% 3.79% 75.00% 100.00%
Law & Order: SVU 25.33% 2.45% 72.22% 100.00%
American Idol 20.69% 6.59% 72.72% 100.00%
House 27.40% 8.69% 63.92% 100.00%
Matthew Leingang Gilligan, MOPE, and TiVo
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