Transcript 2014-06-17x

Engaging Students in a Large
Lecture: An Experiment using
Sudoku Puzzles
A
A
B
A
C
D
C
C
B
B
A
B
D
C
D
D
Caroline Brophy
National University of Ireland Maynooth
Collaborator
Lukas Hahn
Ulm University, Germany, 2008-13
Erasmus student at NUI Maynooth, Ireland, 2010-11
Current: Masters of Mathematics program in Statistics at the
University of Waterloo, Canada
Teaching large groups
• First year undergraduate classes
– First Science at NUIM currently  450
– Range of previous statistical experience
– Range of ability
• Data in class
– Textbook data sets
– Record personal information on students
• Hypothesis testing
The Sudoku experiment
1
The Sudoku experiment
2
5
1
6
4
4
5
2
6
1
4
3
1
2
5
5
4
2
• 9x9 grids would
take too long to
complete
6
5
• Mini 6x6 grids
used instead
The Sudoku experiment
A
B
Greek
Letters
Letters
C
Numbers
D
Random
symbols
Handout for students
•
•
•
•
Instructions on Sudoku puzzles
One of the four Sudoku puzzles
Space for recording completion time
Additional question
Have you ever played Sudoku before today?
Yes 
No 
Logistics
•
•
•
•
First lecture of the course
Printed handouts interleaved
Stopwatch on screen
Explain that students will need to
– Read instructions
– Complete puzzle
– Record the time it took to complete their puzzle
– Answer the question at end
– Maintain exam like conditions throughout
Logistics contd.
• Give out the handouts but instruct to keep
facedown
• Start the stopwatch and instruct all students
to start at the same time
• Collect the handouts when finished
• Manually record the data after class
The data
Sudoku
Type
.
.
.
Letter
Greek
Letter
Number
Number
Greek
Symbol
Greek
Greek
Symbol
Symbol
.
.
.
Correct
.
.
.
Yes
Yes
Yes
Yes
No
No
No
Yes
No
Yes
Yes
.
.
.
Time
.
.
.
170
218
436
74
255
472
245
102
424
390
410
.
.
.
Sudoku
Experience
.
.
.
Yes
Yes
No
Yes
No
No
Yes
Yes
Yes
No
Yes
.
.
.
Three
categorical
variables
One
quantitative
variable,
right censored
The data
Sudoku
Type
.
.
.
Letter
Greek
Letter
Number
Number
Greek
Symbol
Greek
Greek
Symbol
Symbol
.
.
.
Correct
.
.
.
Yes
Yes
Yes
Yes
No
No
No
Yes
No
Yes
Yes
.
.
.
Time
.
.
.
170
218
436
74
255
472
245
102
424
390
410
.
.
.
Sudoku
Experience
.
.
.
Yes
Yes
No
Yes
No
No
Yes
Yes
Yes
No
Yes
.
.
.
Explanatory
variables
Response
variables
Teaching opportunities
• Discussions on
– types of data
– hypotheses to address
– ideas on how to analyse the data
•
•
•
•
•
Descriptive statistics
Chi-square test for independence
ANOVA
Logistic regression
Survival analysis
Hypotheses
• Do Sudoku type and experience affect ability
to get the Sudoku correct?
• Do Sudoku type and experience affect the
length of time it takes to complete the
Sudoku?
First hypothesis
• Do Sudoku type and experience affect ability
to get the Sudoku correct?
Sudoku type
Chi-square test for
independence:
2= 4.62
df=3
p=0.2
Sudoku experience
Chi-square test for
independence:
2= 43.5
df=1
p<0.001
Logistic regression
Model probability of Sudoku being correct
Explanatory variables
Sudoku type
Sudoku experience
Interaction
LRT=4.8, df=3, p=0.189
LRT=36.1, df=1, p<0.001
LRT=4, df=3, p=0.262
First hypothesis
Do Sudoku type and experience affect the probability
of getting Sudoku correct? In summary:
• No evidence of interaction between Sudoku type
and experience
• No evidence of Sudoku type effect
• Sudoku experience has a strong effect
– No experience: pˆ  0.5
– With previous experience: pˆ  0.89
Second hypothesis
• Do Sudoku type and experience affect the
length of time it takes to complete the
Sudoku?
– ANOVA analysis on the correct Sudoku only time
to completion values (limited inference)
– Survival analysis on all completion times
– Details in paper
Concluding remarks
• Easy to implement with large groups
• Can illustrate the testing of real hypotheses
• Downsides
– Manual recording
– Analysis on the subset of correct Sudokus only has
inferential limitations that might be misunderstood
• Fun in-class activity and appears to help
students in an introductory class to engage
with Statistics