Teaching Statistics in the 21th Century

Krystyna Karminska

Thomas Nelson Community CollegeHampton, VA

Teaching Statistics in the 21th Century

• Advantages • Potholes

Introduction

Why Teach Statistics?

I want my students to be statistically literate…

Statistical literacy is…

Being able to read and make sense of statistics in the news, media, polls, etc.” (Joan Garfield, University of Minnesota)

When teaching Statistics I keep reminding my students and myself that…

“Statistics is about understanding the world, not calculating a right answer”

(Richard De Vaux, Williams College, Ithaca, NY)

What is new in teaching Statistics?

Easy access to:• Internet to collect data, find

information, to connect with one another

• Software to crunch numbers and to teach, tutor and grade for us

• Computers (desktop, laptop, IPad, TV-set, cellphone, calculator…)

Technology and Internet:New dimension in teaching Statistics

• Class documents at a click (uploading, downloading to/from the platforms like Blackboard, Angel etc.)

• Our own data collected and shared on any virtual space (like GOOGLE Docs etc.)

• Browsing for any data or information has virtually no limits

• Distance learning is more appealing than ever (compare: the correspondence and TV courses in middle 20 century were to revolutionize teaching)

• Internet might soon replace paper textbook (a point: data often already outdated before the textbooks go to print)

• Software packaged with a textbook is a norm

Virtually all publishers offer computerized systems which include electronic (often interactive) textbook, educational applets, mini-videos, tutorials, and a ready to use bank of assignments for every chapter in the text.

All in comfort of your home.

Many millions of access codes to such systems are sold every semester.

Trouble with Technology • We, Stat Instructors, have to train

ourselves to use technological novelties (or are trained by the software selling publishers).

• Old and New mixed up: using modern technology AND still printing z-tables?

• Many blindly believe that computers are the Gurus in doing Stat, teaching and in assessing students’ work

“Technology offers an end to the tedious and laborious computations in data analysis, but it also offers the possibility of a total lack of feeling for what is being done in the analysis, and a blind assumption that if the computer or calculator has done it then it must be right.”(James Nicholson, Belfast Royal Academy)Proceedings of the 1996 IASE conferenceInternational Association for Statistical Education

http://iase-web.org/

For instance,

“EXCEL produces a wonderfully professional looking graph; however, EXCEL does exactly what you tell it, and cannot tell if the data makes sense, or if the type of graph chosen is appropriate.”

My experiences with computer as a teacher and a

grader:

Computer as a teacher• Fantastic illustrations, interactive

exercises, impossible to experience through paper textbook

• Tools to crunch numbers. Simulations• Comfort of studying anywhere, anytime

• Connection with instructor, tutors and peer students

• Immediate feedback to most of submitted work

Computer as a teacher – but…• Computer generated test bank

problems are often “one size fits most textbooks” (but not yours!), and might have little to do with your teaching outcomes and style.

• Some problems are tedious

• Computer unfair and particular with possible answers.

Computer as a teacher – but (cont.)• Not much (if any) room is left for student’s

creativity• Take-home tests and finals are becoming

popular, but proctoring students is HARD• HOMEWORK: The aides like “Show next

step” or “show example” promote “cookbookish” attitude with little if any lasting learning effect.Many answers can be simply guessed

Computer as a Teacher- but (cont.)

Many on-line (and not only on-line) students omit reading the text, viewing lecture notes, power-point presentations or mini-videos, and go straight to do homework…

And there – many prefer playing over studying…

So, I played one of such students…

After two random clicks – “Great job!”

Computer as a Grader

Computer graded homework vs.

final exam scores Question: did students whose homework was graded by computer retain enough knowledge to pass final (comprehensive) exam?

Data were obtained from 8 instructors and two colleges. In this presentation only Stat classes are discussed.

Following questions were asked:

• Are the scores for computer graded assignments and final exam scores correlated?

• Are they dependent?

At Thomas Nelson CC

Stat analyses were performed for 96 students from five sections of Statistics taught by three instructors in Fall 2010-Fall 2011. The instructors used their own syllabus and exam, but the text and coverage were common. Computer graded homework (CGH) was optional: could be replaced by final exam grade or make additional test grade.

At Hampton University:

The other set of data was obtained from 132 students from six Statistics classes taught in the period Fall 2010 - Fall 2011. All these classes were taught by the same instructor using the same text, coverage, and similar final exams. CGH was required

Statistical tools used to analyze the data:

• linear regression analysis

• Pearson’s chi-square test for independence

• Test for Independence:

• H0: Grades for Computer Graded Homework and for Final Exam are statistically independent

• Ha: they are dependent

P-value: the smaller, the more evidence to reject H0 and support Ha

Regression Analysis and Test for Independence for Final Exam scores vs. Computer Graded Homework scores were performed three times (for each case):

1. for all students2. for students failing final exam (<70%;

“weak”) 3. for students passing final exam (≥70%;

“strong”)

Test for independence:P-value: 0.000Conclusion: Dependent

r=0.554R2=0.31

Final Exam vs. CGH at HU All students n=132

Final Exam vs. CGH Hampton U

r= 0.393R2=0.155

r=0.367 R2=0.134

Weak n= 79 Strong n=53

Weak n=79 Strong n=53

P-value: 0.00292 0.249

Conclusion: Dependent Independent

Test for Independence:

The evidence (P-value) is strong in all cases.

Final Exam vs. CGH TNCC All students

r=0.368R2=0.136

Test for independence:P-value: 0.0355

Conclusion: Dependent!

n=96

Final Exam vs. CGH TNCC

r= 0.286R2=0.082

r=0. 256R2=0.065

Weak n= 54 Strong n=42

Weak n=54 Strong n=42

P-value: 0.211 0.198

Conclusion: Inependent Independent

Test for Independence:

The evidence (P-value) is strong in all cases.

Final Exam vs. CGH TNCC

While such observations are NOT any

proof that CGH does not help students

to retain enough knowledge to pass the

final,

Change of Strategy:

Computer graded quizzes vs. Final exam scores

TNCC Statistics Fall 12 and Spring 13

72 students worked on CGH and took final exams

Final Exam vs. Quizzes F12+S13

(Lowest quiz was dropped in Spring but not in Fall)

Alln=72

r=0.5446 R2=0.2965

Final Exam vs. Quizzes F12+S13

STRONG n=40 r=0.5451 R2=0.2972

WEAK n=32 r=0. 491 R2=0.241

Computer graded Quizzes vs. Finals: ALL n=72 Weak n=32 Strong n=40P-value 0.0338 0.157 0.0114

Conclusions:Correlation, while still weak, is stronger for quizzes than for CGH. Grades for computer graded quizzes and finals are dependent for all and for strong students, and independent for weak students.

Observations so farComputer as a grader?

• So-so: graded homework with all options to aid student (“show me next step”, “show me an example” etc.)

• Better: graded timed quizzes, available only after completing homework: no aid available on line

• The best: Human touch!

Hand Graded Projects • Students take part in a survey: data are

collected on line (virtual space, in a spreadsheet).

• A small incentive (bonus points) for doing so.

• Final data collection is placed on the class website along with project questions summarizing Descriptive Statistics.

• The same data are used in Project 1 (Descriptive) and 2 (Inferential Stat)

• Students choose their tools and make their own conclusions, but having all students work out the problems in given order makes physically possible to grade their projects in a finite amount of time.

Note: For on-line quizzes R2=0.297

r=0.707R2=0.4999

Alln=72

Final Exams vs. Projects F12+S13

Final Exams vs. Projects F12+S13

Strong Students: r=0.763R2=0.582

Weak Students: r=0.239R2=0.057

For Finals and Projects the correlation is the strongest: R2=0.5!

Test for Independence:

The evidence (P-value) is much stronger.

What does not seem to work?• Leaving teaching to computers

• Leaving grading to computers

a Student said…“my problem is (that) some of my previous Math classes was a joke that allowed some of us to get by on homework and easier on test that focused more on an answer that how to actually do it. In fact most of my classes taught me how to enter things into a calculator and cheat rather than the vital processes needed to help us later in the future…”

A comment from another student:“For a student who is trying to master the Webassign material feels like a punishment. Since there is no focus on work done, the temptation to cheat is immense.”

Physics professor: please let your students know that the machine is looking at their answers, and the machine ain't flexibleAnother professor:Basically, in my opinion “right for the wrong reason” is no different than “wrong”.On the down side, I spend many more hours grading than my colleagues.

And what REALLY works?

PROJECTS!!! Learning by CREATING Also,

Stat classes are less boring when there’s an easy access to real and interesting to students data collected from the students by the students, and to software which can crunch numbers and make graphs.

If I still have the time to share this…

After grading Test 1 and Project 1 I perform regression analysis and share and discuss the results with students.

Learning about the relationship between the Projects and Test Grades help students to really start understanding regression

Example:Results Presented in Class After Test 1:(This presentation captures attention of the

entire class!)

Presented in class cont.The results Project 1 versus Test 1

Correlation coefficient r=0.85Coefficient of determination: R2=72%

Interpret! ………………………………….

Prediction line: Test-hat=1.316(project grade)+ 26.164What grade can one expect with a project score = 39? ………………

Please interpret the slope… Y-intercept……………………….Please find your expected test score, and your residual……………. What does it mean if your residual is positive? Negative?………………..

Dziekuje

Contact me: karminskak@tncc.edu