Engaging Students in a Large Lecture: An Experiment using Sudoku Puzzles

Caroline Brophy National University of Ireland Maynooth

A B

C D

A B

C D

A B

C D

A B

C D

Collaborator

Lukas Hahn

Ulm University, Germany, 2008-13Erasmus student at NUI Maynooth, Ireland, 2010-11Current: 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

• 9x9 grids would take too long to complete

• Mini 6x6 grids used instead

2     6   4

    4 5    

5 2 6 1 4  

  3 1 2 5 6

    5 4    

1   2     5

The Sudoku experiment

Greek Letters

Numbers

A B

C D

Letters

Randomsymbols

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 dataSudoku

Type Correct TimeSudoku

Experience. . . .. . . .. . . .

Letter Yes 170 YesGreek Yes 218 YesLetter Yes 436 No

Number Yes 74 YesNumber No 255 No

Greek No 472 NoSymbol No 245 Yes

Greek Yes 102 YesGreek No 424 Yes

Symbol Yes 390 NoSymbol Yes 410 Yes

. . . .

. . . .

. . . .

Three categorical variables

One quantitative

variable,right censored

The dataSudoku

Type Correct TimeSudoku

Experience. . . .. . . .. . . .

Letter Yes 170 YesGreek Yes 218 YesLetter Yes 436 No

Number Yes 74 YesNumber No 255 No

Greek No 472 NoSymbol No 245 Yes

Greek Yes 102 YesGreek No 424 Yes

Symbol Yes 390 NoSymbol Yes 410 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: – With previous experience:

89.0ˆ p5.0ˆ p

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