Pilar Muñoz, José-Antonio González, Erik Cobo, Lluis Jover JORNADES D’INNOVACIÓ DOCENT A LA...

Pilar Muñoz, José-Antonio González, Erik Cobo, Lluis Jover

JORNADES D’INNOVACIÓ DOCENT A LA UPC: Presentació de

resultats dels projectes MQD

ICE 28/06/07

Avaluació experimental de la millora de l’aprenentatge en

estadística

2

PRESENTACIÓ DE RESULTATS MQD

Outline

1. Aims and motivation

2. Model & subjects

3. Results

4. Conclusions and future work

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Outline

1. Aims and Motivation

2. Model & subjects

3. Results


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• To improve student learning

• To provide to students an automatic IT which generates and solves individual exercises

• To apply statistical theory to formally measure its effects

• To employ real examples in teaching

Motivation

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Learning Model

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Factors to be efficient in the teaching process

TrainingPractice of methods and techniques with realistic cases

Instant feedback for students Immediate marking of work

Evaluation of knowledge gained Evaluation of effort

Feedback for teachersTo monitor progress

(globally or individually)

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The tool: e-status (1)

• Learning by practicing:– The exercise can be repeated– Initial data are always different

• Immediate feedback providing:– Right answer– Error reason (if predicted)

• Students’ assessment:– Any criteria (best answer, average, …)

• Students’ follow up:– Both individual data and group summaries

• Broad range of problems: based on R

• Web-based tool

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The tool: e-status (2)

More information on e-status: Gonzalez & Muñoz (2006)

(CAEE, 14(2): 151-159)

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How e-status looks

Wording

Question

AnswerGrading

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e-status previous experience

• Experience since 2003:

– Four schools:

– About 10 subjects

– More than 2000 students

– About 25000 executions

• High positive correlation between e-status use and exam performance… but

…experience is not experiment

• Computer Science

• Maths and Stat

• Medicine

• Dentistry

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Outline


2. Model & subjects

3. Results


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• Biostatistics course in the Dentistry School of the University of Barcelona

• Prior experience in 2004/2005 academic course

• Duration of the stat subject: 35 hours

• Teachers:

– theoretical classes: 1

– lab groups: 3

• Experiment: 2005/2006 year (fall)

• Outcome: written final examination

Setting

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Operation

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Two “topics”

A

• Descriptive statistics and graphical representation

• Agreement

• Inference about one proportion

• Comparison of two means

• Comparison of two proportions

B

• Probabilities with Normal distribution

• Interval estimation of proportion and mean

• Assessment of sample size

• Inference about one mean

• Goodness of fit chi-square

Every student had access to e-status

Students were randomly allocated to group 1 or 2

Each group only had access to e-status exercises on only one topic

Final exam contained questions about both topics A and B

Stat course content was divided in two ‘balanced’ topics

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Outcome

Exam

TopicProblems in the practical exam

e11 e12 e21 e22 e31 e32

A

B

Score Yt A

i

Score Yt B

i

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Participants & allocation

• All students (N =121) enrolled in the course

• Random assignment to 1 or 2 balanced with respect to Lab group and new/old profile

• Teacher was not involved in randomization neither data analysis

• Final exam evaluator was masked to allocation group

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Hypothesis

Yt j i stands for the exam performance:

• by student i

• assigned to intervention, t=1, 2

• in topic j=A, B

Hypothesis:

If e-status is effective, students in group 1 (2)trained with e-status exercises in topic A (B)should get better exam results in topic A (B)

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Ytji = µ + t + πj + Φi + ij

t: fixed effect of intervention t=1, 2

• πj: fixed effect of exam topic j=A, B

• Φi: random effect of student i

ij: measure error assessing performance in student i for question j

Assumptions:• Access to e-status topic A(B) has no effect on exam topic B(A).• Error independence between students

Statistical model

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Statistical analysis

Let D1 i (D2 i) be the difference of scores in part A and B for the

student i receiving intervention 1(2):

DD1i1i = Y = Y1Ai1Ai – Y – Y1Bi1Bi = (µ + = (µ + ττ11 + + ππAA + + ΦΦii + + iAiA)-(µ + )-(µ + ππBB + + ΦΦii + + iBiB) = ) = ττ11 + + ππAA - - ππBB+ + iAiA- - iBiB

DD2i2i = Y = Y2Ai2Ai – Y – Y2Bi2Bi = (µ + = (µ + ππAA + + ΦΦii + + iAiA)-(µ + )-(µ + ττ2 2 + + ππBB + + ΦΦii + + iBiB) = - ) = - ττ22 + +ππAA - -ππBB+ + iAiA- - iBiB

E(DE(D1i1i)= )= ττ11 + + ππAA - - ππBBAs

E(DE(D2i2i)= )= --ττ22 + + ππAA - - ππBB

V(DV(Djiji)= )= V( V(iAiA- - iBiB) = 2) = 2σσ22εε

nnn

222 422

DD

DD

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221

VE 1

Then

50 students per group 50 students per group provide 80% power to highlight an effect equal to 80% power to highlight an effect equal to

0.7x σ0.7x σ (α=0.05) (α=0.05)

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Outline


2. Model & subjects

3. Results


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Main results

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The random model, fitted with R, replicated the results

SΦ = 2.81 (CI95%: 2.43 to 3.24)

Sε = 1.48 (CI95%: 1.31 to 1.68)

Linear Mixed-Effects Model

Fitted values

Sta

nd

ard

ize

d r

esi

du

als

-2

-1

0

1

2

2 4 6 8

Standardized residuals

Qu

an

tile

s o

f sta

nd

ard

no

rma

l

-3

-2

-1

0

1

2

3

-2 -1 0 1 2

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Outline


2. Model & subjects

3. Results


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+1. It is feasible to evaluate interventions in teaching with formal

experiments Random allocation Masked evaluation Without interfering in course development

+2. e-status improves student exam performance

In an exam over 10 points, e-status improves performance by

0.96 points (CI95%: 0.20, 1.72)

Conclusions

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What did the students do when they had no access to e-status?

That is, what is the reference for the intervention?

a) Did they not study statistics at all?

b) Did they spend their time on another kinds of exercises?

If a, the estimated e-status effect is mediated by an increase in the

time spent by the student to study.

If b, e-status increases learning efficiency, since it improves the

amount of learning with respect to the alternative method.

Interpretation (1)

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If e-status influences advanced capabilities, such as motivation or

statistical reasoning, there may be some contamination between

interventions A and B: that is, intervention 1 (2) employing e‑status

on set A (B) would have some learning effect τ‘1 (τ‘2) on set B (A),

and then

E( ) = (τ1 + τ2 ) – (τ‘1 + τ‘2 ) = (τ1 - τ‘1) + (τ2 - τ‘2 )

If so, this design estimates e-status direct effect minus delayed,

cross-over, effects

If τ‘ positive, this design underestimates overall effects on learning

Interpretation (3)

DD 21

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1. Repeat the randomized experiment many times in many courses

You are invited to do it!

2. Also you are invited:- to use it in your teaching work

http://key.upc.es/estatus

3. To share your ideas with [email protected], [email protected],[email protected]

Future work

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Thanks for your attention

Q & A

Pilar Muñoz, José-Antonio González, Erik Cobo, Lluis Jover JORNADES D’INNOVACIÓ DOCENT A LA...

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