gilligan, mope, and tivo
DESCRIPTION
A survey of teaching activities from the past few yearsTRANSCRIPT
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
Gilligan, MOPE, and TiVoTeaching activities at Harvard
Matthew Leingang
Harvard UniversityDepartment of Mathematics
University of California, IrvineApril 4, 2007
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
Outline
1 Math 20HistoryCurrent syllabusExamples
2 Mathematical Online Placement ExamHistoryImplementationLessons learned
3 The ALM in Mathematics for Teaching ProgramHistoryExample: Bayesian Decision Making
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryCurrent syllabusExamples
Outline
1 Math 20HistoryCurrent syllabusExamples
2 Mathematical Online Placement ExamHistoryImplementationLessons learned
3 The ALM in Mathematics for Teaching ProgramHistoryExample: Bayesian Decision Making
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryCurrent syllabusExamples
Math 20: Introduction to linear algebra andmultivariable calculus
Taught since 2004Original idea: stickto the titleAlmost noapplicationsoriginally
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryCurrent syllabusExamples
Math 20: Introduction to linear algebra andmultivariable calculus
Taught since 2004Original idea: stickto the titleAlmost noapplicationsoriginally
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryCurrent syllabusExamples
Outline
1 Math 20HistoryCurrent syllabusExamples
2 Mathematical Online Placement ExamHistoryImplementationLessons learned
3 The ALM in Mathematics for Teaching ProgramHistoryExample: Bayesian Decision Making
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryCurrent syllabusExamples
Syllabus for Math 20, Spring 2007Foundational material
Vector Matrix
Function
Gauss elim
Determinants
Eigenstuff
Systems of linear equations
Inversion
Partial derivative
Lin approx
Quad approx
Differentials
Algebra
Dot product
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryCurrent syllabusExamples
Syllabus for Math 20, Spring 2007Applications
OptimizationProblems
Stationary points
Lag mult
Least squares
Markov chains
Leontief
Assignment problem
Game theory
Linear programming
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryCurrent syllabusExamples
Syllabus for Math 20, Spring 2007Applications
OptimizationProblems
Stationary points
Lag mult
Least squares
Markov chains
Leontief
Assignment problem
Game theory
Linear programming
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryCurrent syllabusExamples
Outline
1 Math 20HistoryCurrent syllabusExamples
2 Mathematical Online Placement ExamHistoryImplementationLessons learned
3 The ALM in Mathematics for Teaching ProgramHistoryExample: Bayesian Decision Making
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryCurrent syllabusExamples
Some fun problems you can solve
(Economics) which is better: sales tax or income tax?(Linear programming) can you eat a healthy meal atMcDonald’s?(Assignment problem) Match teaching fellows to time slotsto 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
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryCurrent syllabusExamples
A closed Leontief input-output system
Problem from Fall 2006 FinalConsider an island with a four-person economy:
Gilligan (agriculture) produces coconuts, palm fronds, andbamboo poles by collecting them.The Professor (manufacturing) produces shelter andequipment by consuming raw materials and with the helpof the Skipper.Mary Ann (service) takes coconuts and bakes deliciouscoconut cream pies, upon which the entire island subsists.The Skipper (labor) helps the professor with his projects.
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryCurrent syllabusExamples
Problem continuedThe distribution of products works like this:
Three-fourths of Gilligan’s raw materials go to theProfessor for his creations and the rest go to Maryann forher pies.Gilligan and the Skipper each use a sixth of the Professor’sinventions. Mary Ann and the Professor himself use a thirdapiece.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 theirproducts.
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryCurrent syllabusExamples
Solution
Find a solution to Ap = p, where
A =
Gilligan Professor Mary Ann SkipperGilligan 0 1/6 1/4 0
Professor 3/4 1/3 1/4 0Mary Ann 1/4 1/3 1/4 0Skipper 0 1/6 1/4 1
p =[1 3.3 1.8 1
]T works.
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryCurrent syllabusExamples
Solution
Find a solution to Ap = p, where
A =
Gilligan Professor Mary Ann SkipperGilligan 0 1/6 1/4 0
Professor 3/4 1/3 1/4 0Mary Ann 1/4 1/3 1/4 0Skipper 0 1/6 1/4 1
p =[1 3.3 1.8 1
]T works.
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryCurrent syllabusExamples
Results so far
Very happy studentsVery high scoresPossible book in theworks someday
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryImplementationLessons learned
Outline
1 Math 20HistoryCurrent syllabusExamples
2 Mathematical Online Placement ExamHistoryImplementationLessons learned
3 The ALM in Mathematics for Teaching ProgramHistoryExample: Bayesian Decision Making
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryImplementationLessons learned
Status Quo
Pencil-and-paper examgiven on first day ofFreshman weekGrade Report is threenumbers and a coursecode: Math Xa, 1a, 1b,or 21a
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryImplementationLessons learned
Example placement information
HMPT1: 19 HMPT2: 10HMPT3: 6
Recommendation:Math XaAP Calculus BC: 5Recommendation:Math 21aCould be same person!
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryImplementationLessons learned
Example placement information
HMPT1: 19 HMPT2: 10HMPT3: 6Recommendation:Math Xa
AP Calculus BC: 5Recommendation:Math 21aCould be same person!
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryImplementationLessons learned
Example placement information
HMPT1: 19 HMPT2: 10HMPT3: 6Recommendation:Math XaAP Calculus BC: 5
Recommendation:Math 21aCould be same person!
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryImplementationLessons learned
Example placement information
HMPT1: 19 HMPT2: 10HMPT3: 6Recommendation:Math XaAP Calculus BC: 5Recommendation:Math 21a
Could be same person!
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryImplementationLessons learned
Example placement information
HMPT1: 19 HMPT2: 10HMPT3: 6Recommendation:Math XaAP Calculus BC: 5Recommendation:Math 21aCould be same person!
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryImplementationLessons learned
Example placement information
HMPT1: 19 HMPT2: 10HMPT3: 6Recommendation:Math XaAP Calculus BC: 5Recommendation:Math 21aCould be same person!
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryImplementationLessons learned
Example placement information
HMPT1: 19 HMPT2: 10HMPT3: 6Recommendation:Math XaAP Calculus BC: 5Recommendation:Math 21aCould be same person!
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryImplementationLessons learned
Disadvantages of Status Quo
Students descend upon advisors to interpret thesenumbers and give further guidanceSomewhat unnecessarily intimidating and impersonalHMPT was designed in an era when high school studentexposure to calculus was limited
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryImplementationLessons learned
Mathematical Online Placement Exam (MOPE)
Funded by Innovation Grant from the Provost’s Fund forInstructional TechnologyGoals
Give entering students more personal, more detailedinformation for choosing a math courseForm part of a student-friendly web presence
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryImplementationLessons learned
Outline
1 Math 20HistoryCurrent syllabusExamples
2 Mathematical Online Placement ExamHistoryImplementationLessons learned
3 The ALM in Mathematics for Teaching ProgramHistoryExample: Bayesian Decision Making
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryImplementationLessons learned
Features
Question database organized by mathematical topic andtype of questionA multitude of tests for qualification or masteryCan be taken any timeTopic-specific feedback, with granularityRetakes after refreshing are allowed
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryImplementationLessons learned
Portion of MOPE’s topic tree
Trigonometry
and circles
inverse trig
composingevaluating
arc length; sector area
radian measure
sign and range of trig fns
evaluting trig fns (radians)
evaluting trig fns (degrees)
and triangles
law of cosines
law of sines
trig fns from right triangles
trig identities
graphs
simplifying
sin2 + cos2 = 1
angle-addition
double-angle
sinusoidal
tan/cot
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryImplementationLessons learned
Screenshot of sample questionhttps://mope.dce.harvard.edu:10000/authentication/index.php?school=fas
1 of 1 8/22/05 9:21 PM
MATH PLACEMENT TEST TECHNICAL REQUIREMENTS
NAVIGATION HELP
FAQ
LOGOUT
TIME REMAINING: 43:56
QUESTION 9 22 questions left to answer SELECT YOUR ANSWER
TEST NAVIGATION
CLEAR YOUR ANSWER
NEXT QUESTION
PREVIOUS QUESTION
NEXT BLANK
FIRST QUESTION
GO TO QUESTION
1010
SUBMIT YOUR ANSWERS
and end the test
Answers: 0=>1 1=>4 2=>0 3=>2 4=>3 Correct answer: 1Question index: 779Question topic: 308
If vØ
=ÁËÈ
ËË5
1
˜¯˘
¯¯ and w
øØ=ÁËÈ
ËË
2
-3
˜¯˘
¯¯, what is the length of the vector v
Ø- wøØ
?
2A.
5B.
3C.
260
- 130
D.
7E.
We would appreciate if you reported any technical difficulties or mathematical inaccuracies to [email protected].
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryImplementationLessons learned
Screenshot of sample questionhttps://mope.dce.harvard.edu:10000/authentication/index.php?school=fas
1 of 1 8/22/05 9:22 PM
MATH PLACEMENT TEST TECHNICAL REQUIREMENTS
NAVIGATION HELP
FAQ
LOGOUT
Your Receipt
Last Name: Strozek
First Name: Lukasz
Email address: [email protected]
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.
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 eagerto 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 placementexamination, 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
We would appreciate if you reported any technical difficulties or mathematical inaccuracies to [email protected].
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryImplementationLessons learned
Screenshot of sample question
You can take the test again in 1 hour. In the meanwhileyou may want to review: Analytic geometry, Vectors andplanes, Parametrization and vector fields, Optimizationand extrema, Directional derivatives, Double integrals,Differentiating functions of several variables, Gradientsin the plane, Gradient and path-independent fields, Lineintegrals, and Applications of multiple integrals.
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryImplementationLessons learned
“Result”
Average of Math 1a First MidtermHMPT1failed
HMPT1passed
all
MOPE failed 73.00 78.67 75.43MOPE passed 89.50 N/A 89.50
all 78.50 78.67 78.56
Unfortunately, N = 2 here
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryImplementationLessons learned
“Result”
Average of Math 1a First MidtermHMPT1failed
HMPT1passed
all
MOPE failed 73.00 78.67 75.43MOPE passed 89.50 N/A 89.50
all 78.50 78.67 78.56
Unfortunately, N = 2 here
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryImplementationLessons learned
Outline
1 Math 20HistoryCurrent syllabusExamples
2 Mathematical Online Placement ExamHistoryImplementationLessons learned
3 The ALM in Mathematics for Teaching ProgramHistoryExample: Bayesian Decision Making
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryImplementationLessons learned
Math on the Web
Very challenging problem!Originally we converted TEX to MathMLLater went to images (no MathML support)
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryImplementationLessons learned
Chicken-and-egg problem
can’t be more widely adopted without greater credibilitycan’t be more credible without better calibrationcan’t be calibrated without more datacan’t get more data without more people taking itcan’t get more to take it without being more widely adopted
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryExample: Bayesian Decision Making
Outline
1 Math 20HistoryCurrent syllabusExamples
2 Mathematical Online Placement ExamHistoryImplementationLessons learned
3 The ALM in Mathematics for Teaching ProgramHistoryExample: Bayesian Decision Making
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryExample: Bayesian Decision Making
Background of the ALM program
Goal: better K-12teachers in BPS andareaStarted in 2001 byD. Goroff and P. SallyDegree program since200335 participants andsoon to graduate firstMaster’s class
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryExample: Bayesian Decision Making
Objectives of the ALM program
Teach teachers the mathematics behind the rules, e.g.:0.9999.... = 1Division by zero is undefined
Give resources to challenge their studentsDemonstrate fun math learning activities
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryExample: Bayesian Decision Making
Outline
1 Math 20HistoryCurrent syllabusExamples
2 Mathematical Online Placement ExamHistoryImplementationLessons learned
3 The ALM in Mathematics for Teaching ProgramHistoryExample: Bayesian Decision Making
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryExample: Bayesian Decision Making
Bayes’s Theorem
Theorem (Bayes)Let Ω be a probability spacewith probability measure P.If A and B are events, then
P(B | A) =P(A | B)P(B)
P(A)
Proof.
P(B | A)P(A) = P(A ∩ B) = P(A | B)P(B)
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryExample: Bayesian Decision Making
Bayes and partitions
If Ω = H1 ∪ H2 ∪ . . . ∪ Hn is a partition, and E is any event, then
P(Hi | E) =P(E | Hi)P(Hi)
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
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryExample: Bayesian Decision Making
Bayes and partitions
If Ω = H1 ∪ H2 ∪ . . . ∪ Hn is a partition, and E is any event, then
P(Hi | E) =P(E | Hi)P(Hi)
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
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryExample: Bayesian Decision Making
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 knowP(Hj | Cα ∩O), too.Given a a “new” ω ∈ Ω \O, if we can find its observablesCαi, what is the likelihood of ω being in any particularstate?
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryExample: Bayesian Decision Making
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 )
!≈
(∏mj=1 P(Cαj | Hi)
)P(Hi)∑n
k=1
(∏mj=1 P(Cαj | Hk )
)P(Hk )
≈
(∏mj=1 P(Cαj | Hi ∩O)
)P(Hi | O)∑n
k=1
(∏mj=1 P(Cαj | Hk ∩O)
)P(Hk | O)
But everything at this stage is known.Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryExample: Bayesian Decision Making
Which brings us to TiVo
Ω is the set of all programs ontelevisionStates
Hj
are your attitudestoward programsObservables Cα aremetadata about the programsO is the set of shows youhave marked with thumbsup/thumbs down.
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryExample: Bayesian Decision Making
Preference Data from Math E-304 on March 6, 2006Title Like Dislike Neutral TotalKing of Queens 4 5 7 16How I Met your Mother 5 0 11 162 and a half Men 3 3 10 16Courting Alex 1 0 15 16CSI: Miami 4 2 10 16Wife Swap 3 3 10 16Supernanny 3 4 9 16Miracle Worker 0 0 16 16Deal or no Deal 4 3 9 16Apprentice 6 4 6 16Medium 3 1 12 1624 5 1 10 16Total 41 26 125 192Prob(each preference) 21.35% 13.54% 65.10% 100.00%
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryExample: Bayesian Decision Making
Probability of class attitudes for each show (P(Hk | O))
Title P(like) P(dislike) P(neutral) TotalKing 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
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryExample: Bayesian Decision Making
Frequency of attitude for each characteristic
Characteristic Like Dislike Neutral TotalDrama 12 4 32 48Comedy 13 8 43 64Reality 12 11 41 64Game Show 4 3 9 16Male Lead 22 16 42 80Female Lead 22 16 42 80Ensemble 9 2 21 32TV-PG 26 18 84 128TV-14 15 8 41 64Totals 135 86 355 576
Matthew Leingang Gilligan, MOPE, and TiVo
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryExample: Bayesian Decision Making
Conditional probability of each characteristic, givenattitude and observed (P(Cα | Hk ∩O))
Characteristic Like Dislike Neutral TotalDrama 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
Math 20Mathematical Online Placement Exam
The ALM in Mathematics for Teaching Program
HistoryExample: Bayesian Decision Making
(Posterior) probability of class attitudes for showsairing March 7, 2006
Title P(Like) P(Dislike) P(Neutral) TotalNCIS 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