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e-status: a Problem-based Learning Web Tool Powered by R

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e-status: a Problem-based Learning Web Tool Powered by R J. A. Gonz lez, L. Marco, L. Rodero, J. A. S nchez Statistics and Operations Research Dept. – PowerPoint PPT presentation

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Title: e-status: a Problem-based Learning Web Tool Powered by R


1
e-status a Problem-based Learning Web Tool
Powered by R
  • J. A. González, L. Marco, L. Rodero, J. A.
    Sánchez
  • Statistics and Operations Research Dept.
  • Technical University of Catalonia, Barcelona

2
Outline
  • Introduction
  • Motivation
  • Architecture
  • Example
  • The feedback issue
  • Testing e-status
  • Conclusion
  • (What)
  • (Why)
  • (Where)
  • (How)
  • (Who)
  • (Is it)
  • ()

3
Introduction
  • e-status is a web-based tool (http//ka.upc.es/).
  • It helps the students with exercises corrected
    automatically.
  • R is the engine working behind
  • for computations,
  • for graphics,
  • for some management.

4
What it is not
  • e-status is neither
  • a static list of problems
  • Problems can (have to) be very dynamic.
  • a statistics course or an online textbook
  • Related materials may be linked to the problems,
    they are not structural components.
  • a demonstration tool (like applets collection)
  • Focus is put on the students, so that they play
    the active role.

5
Why a problem-oriented tool?
  • Statistics is conceptually hard to learn
  • uncertainty, randomness,
  • Hands-on techniques (PBL, CooperativeL) are
    effective to reach highest capabilities.
  • However, lack of numeracy skills is a matter of
    concern
  • Students are not even used to managing data or
    making simple computations

6
Why a problem-oriented tool? (2)
  • Introductory problems are usually solved in the
    classroom
  • Content-overloaded courses!
  • Great demand of sample problems.
  • Lists published null flexibility.
  • Teachers cannot revise all the students
    exercises, if check requested.
  • Scarce information about their performance.

7
In the beginning
  • 2003 All-in-one

MS OS MS IIS MS SQLServer java PHP
e-status server
Web
User
8
Architecture 2007
Linux Apache Cake-PHP
MySQL
any internet browser
9
Highlights
  • Distributed architecture
  • one server for e-status and web,
  • one server for DataBase,
  • one server for authentication optional,
  • one server for R.
  • R runs in the background, responding to the
    application requests
  • RServe is used as communication software.
  • The PHP client-side implementation was developed
    for e-status.

10
An example
Two urns with yellow and blue balls. One coin to
choose the urn. The mix of colors is random, so
questions like You flipped a coin, and a blue
ball was drawn from the selected urn. Find the
probability that the coin is heads. have a
different solution each time.
11
The example in depth
  • As data is not fixed in the problem, one has
  • to create the data, and
  • to compute the answers.
  • R allows to resolve both points.

Deciding the composition of the urns h
sample(12,1) h1 heads on left n
sample(415,2,repl1) number of balls left,
right m1 sample(2(n1-1),1) yellow on
left m2 sample(2(n2-1),1) yellow on right
12
The example in depth (2)
Finding the probability P(heads blue), using
Bayes Theorem t 3-h n_B.H nh -
ifelse(h1,m1,m2) P_B.H n_B.H/nh P_B
P_B.H0.5 (nt - ifelse(h1,m2,m1))/nt0.5 P
_H.B P_B.H0.5/P_B The exact solution is
P_H.B the students answer has to be compared
with this value (within some tolerance, chosen by
the teacher).
13
The example in depth (3)
In this case, the problem includes a descriptive
picture too q1 c(rep(7,m1),rep(4,n1-m1)) q2
c(rep(7,m2),rep(4,n2-m2)) q1 sample(q1) q2
sample(q2) x c(1,3,5,7,9,2,4,6,8,3,5,7,4,6,5)
T sqrt(3) y c(1,1,1,1,1,rep(1T,4),
rep(12T,3),rep(13T,2),14T) X1
x1n1 Y1 y1n1 X2 15x1n2 Y2
y1n2 bxc(-1,-1,11,11) byc(y151,0,0,y15
1)
graphini_imagen(500,250) oppar() par(marc(0.5
,0.5,0.5,0.2)) plot(c(-5,30),c(0,10),typen,
asp1, axes0,xlab,ylab) symbols(X1,Y1,circ
rep(1,n1),bgq1,asp1,inc0,add1) symbols(X2,Y2
,circrep(1,n2),bgq2,asp1,inc0,add1) lines(b
x,by) lines(15bx,by) text(5,10,labmonh,cex2)
text(20,10,labmont,cex2) par(op) fin_imagen()
14
Typically, an exercise looks like this
15
The Feedback issue
  • Feedback allows and improves learning.
  • Short-term the student verifies the correctness
    of answers
  • Sometimes, the system can give a clue.
  • Long-term everything is saved. These records can
    show strengths and weaknesses
  • particularly, for the student,
  • in general, for the teacher.

16
Example résumé
17
Example marks analysis by question
Gasp! Very bad results for 7th question Rephrase
it?
18
R as a controller
R model
questions
19
R as a controller (2)
  • First release compared answers with the (unique)
    solution.
  • At present, the check with R allows richer
    assessment of the answers.
  • Example Given a random variable X following the
    law N(120, 20), enter an interval a, b such
    that P(a lt X lt b) be between 1/4 and 1/3.
  • Solution p pnorm(b,120,20)-pnorm(a,120,20)
  • result p gt 1/4 p lt 1/3

20
Testing
  • e-status has been experimentally tested
  • 2006, Dentistry School (University of Barcelona)
  • 94 participants from 120 enrolled
  • 2 parallel groups six problems each at the end
    of the year, before the final exam
  • subject contents were split up

Block A
Block B
21
Testing (2)
  • 2008, Engineering School (Technical University of
    Barcelona)
  • 210 assigned 197 made the exam 145 used
    e-status actively
  • 2 parallel groups two common blocks, plus one
    specific per group, during the year
  • the assignation involves

2 samples tests, independent
gt2 samples tests, blocked
Block 2
Block 1
2 samples tests, blocked
gt2 samples tests, independent
22
Outcomes
  • 2006
  • The final exam included six questions, three
    related to A and three related to B.
  • Single evaluator.
  • Compared the difference in mark within student
  • YA YB
  • It is expected that the difference is positive
    for A and negative for B (average).
  • 2008
  • Four questions (one for each item of the 3rd
    block).
  • Two evaluators (no confusion 2 samples tests
    and gt2 samples tests).
  • Each mark modelled with a linear mixed-effects
    model (group A or B, and student).
  • It is expected that A and B effects are
    statistically significant.

23
Results
  • 1442 exercises the students performed mainly
    during the holiday period (decreases interaction).

7500 exercises the students performed mainly
before deadlines less activity in third block.
24
Results (2)
The measured effect of e-status exercising was
0.96 points (95 CI 0.20-1.72) on a ten-point
scale. Among those 94 students who employed
e-status, the effect size was 1.27 (95 CI
0.35-2.19). We assumed one effect (not one
for A and one for B)
The model failed to find differences among all
the students. Taking only active participants,
there is some evidence just for group B
(estimation 0.7 points), but not for group
A. An explanation complex subject -?complex
experiment. Incidental uncertainties could have
increased the noise in the outcome.
25
Conclusion
  • e-status has been clearly enriched with R
  • powerful and simple.
  • In accordance with EHEA
  • active learning method,
  • utensil to measure student effort.
  • ITs it is not an added value by itself
  • committed to promoting IT tools for getting the
    students motivated and to awaken their interest
    in statistics.
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