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It's Just About Learning the

Multiplication Table

Martin SchnLifeLongLearning

Graz University of

Technology

Mandellstrae 13, A-8010

Graz

+433168734931

martin.schoen@tugraz.at

Martin EbnerSocial Learning

Graz University of

Technology

Mnzgrabenstrae 35A/I, A-

8010

Graz

+433168738540martin.ebner@tugraz.at

Georg KothmeierSocial Learning

Graz University of

Technology

Mnzgrabenstrae 35A/I, A-

8010

Graz

+433168738540georg.kothmeier@tugraz.at

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Content1. Presumptions for 1x1

2. Experiences with developing an adaptive or

intelligent program

3. Surprises & future Contact for use thisapplications

Or: this is a story, how we began to think about a

teaching problem, how we tried to solve it

with a small application and how this leaded

us to Learning Analytics & Educational DataMining

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Task

Application to test the skills at the multiplication table.

Special: Algorithm for a somewhere intelligent procedure. Situation:

Pupil is introduced to a teacher. He/She tries to gain an overview of the

tasks the students can do reliable well in an optimal way .

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Basics

learning math starts before the school begins cultural differences, some obviously based on language

implications

linguistic competence is needed mathematic is the first non-native language

many children do not really understand reasons for crucial

aspects of the procedure

the most common and traditional way to learn the

multiplication table is drill and practice

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How to According to current neurological oriented

research results, but also based on a veryold educational tradition, teaching should

use tactile, optical and acoustic processing

methods in every single case intensively

when one observes deviations from the

mainstream. Learning / teaching multiplication tables

should not be reduced on a machine

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Program / Checklist

The system should estimate the competence grade of thelearner

The system should provide appropriate tasks according to

the competence grade of the learner.

Nevertheless the tasks should tend to be challenging.

The system should ensure that already well-done exercises

are repeated and practiced. After succeeding a problem the

probability for a repeated display decreases in two levels

(similar to a Leitner System )

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Checklist cont.

In general the system should be motivating and show thatlearning can be fun.

The system should record and safe fine-grained data of all

done exercises, test results and the current competence

grade of the learner in order to prepare the next sessions in

an adequate way.

It should relieve the teacher from this unsolvable task as an

information processing tool

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Checklist - Addon

during this spring we defined another goal:Today we are able to present a database for organizing

schools, classes and individuals with an interface for the

conventional desktop browsers and also for Android and

Apple mobile devices.

The web-application ist written in php/mysql

the apps in objectiveC (iPhone) &

JAVA (Android).

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Measurement

the goal is to generate a complete table to inform learnersas well as teachers about their competence in every single

task, in every single multiplication fact

(no probabilistic)

Teachers can talk about quantity:

I have 4 pupils who . And 6 who .

(Will teacher recognize.?)

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Algorithm

The presentation of the tasks is not only

randomly generated..

At the very first contact a moderate

problem is presented. According to the

results more or less difficult tasks arefollowing..

The competence level of the test subject

is then estimated and after every task

recalculated. This determines the

difficulty of the next tasks.

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Competence1. estimate the competence level:

2. After every new solved or unsolved problem we choose

a smooth way for adopting this first estimation of

competence to the experience during the sessions

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Difficulty

Without any empirical data we decided to use the rankingfor the tables as follows Youll find this hierarchy in mostdidactical concepts:

easy 1, 2, 4, 3, 5, 8, 6, 7, 9 difficult

we transformed these ranking in difficulty levels between1 and 0.

We discussed to integrate a statistical founded ranking, butat this point we fear, the teachers would be somewhereconfused about the results. Ill speak about this problem

later.

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Stored Data

The answers of the learners are marked with 0,1 or 2:1 shows that the user knew the correct answer once

2 indicates that the student had two consecutive correct

answers (this means a question is well known)0 indicates, the last answer was incorrect (or this item

was presented never before)

Additional we store: used time, result, task no., everpresented

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Selecting the next ItemWe use a random number between 0 and 1 ot decide, which

category is activited to generate the next multiplicationproblem: Therefore three cases are defined:

Case 1: If the random number is 0= 0.15 than a

known question marked with 1 is chosen.

Case 3: The random number is x > 0.15 than an

unknown question out of the extended and actual learningarea is chosen.

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Extended Area

Extended area means the idea, that wechoose items not only in the learning

area, that means under the level of

competence.

To produce some dynamic and thechance to get a higher level, we add

now .15 to the actual estimation of the

degree of competence of the student

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Prototype

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mathe.tugraz.at

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Register (is simple!)

If you want to test this application you can use noschool for an individual registration.If you want to administer a whole school and classlists you should askmartin.ebner@tugraz.atto send you an administration-account.

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Infomationprocessing

The matrix at the left shows the history: The beige colour

indicates well known results, the brown is one rightanswer. The rabbit comes from left to right to the carrot

and catches one - if the pupil produces consecutive right

answers.

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DetailsIf you point over with the mouse on

the matrix, you see themultiplication fact behind the

symbol.

Download:

1. http://mathe.tugraz.at/ -

2. http://itunes.apple.com/at/app/1x1

trainer/id452707340?mt=8 -3. https://market.android.com/detail

s?id=at.tugraz.einmaleinstrainer

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Study first research study was carried out at a primary school in Austria.

Begin: summer semester 2011

42 pupils of the primary school Laubegg (age: 9-10).

at least 4 weeks. Some of the learners ignored this time restriction andplayed the game again and again over months.

Learners learned on computers at the school as well as on their

personal computers at home.

12.926 answers where given which means that on average each learneranswered 308 questions- they did 3.4 times the whole multiplicationtable.

Bearing in mind that there was no real pressure from teachers sideusing the program it is a considerable pleasant high number.

Furthermore it can be stated that pupils seemed to enjoy using theapplication or at least get not bored.

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Highscores

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We dont know

More than half of the learners did not reach the 100 percent level

(= 90 items are well-known). Therefore we have to think aboutthis group of learners: Perhaps they

didnt get used to / have problems with the interface

do not know the necessary operations; are not able to solve

the learning problem correctly

misinterpret an assignment

are distracted by the environment

are badly concentrated for several reasons.

Could we gather more information to know more?

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Analyses

Ill show here some graphs of the collected statstical data.

We made the experience, that the teachers in our interviews

are interested in very short compact information,

overviews.

We fear, that if we would produce too much information the

teacher would than reject the entire system .

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Demotivated learner

One learner with a weak

performance attracted our attentionbecause of a very high number of

trials (513). A detailed inspection

showed that he did not work very

intensively. In the first two tasks

he/she failed, then eleven tasks

were ok, his performance rose

abruptly. However, afterwards, hecontinued approximately 400 times

to wait the whole answering time

without doing anything but asking

for a new assignment.

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Motivated Captain

The most diligent learner.

In the beginning, theassignments were solved

correctly, then some mistakes

occurred, afterwards a

learning process can berecognized and finally with

some occasional mistakes the

learner works on a high

performance level.Obviously, the learner was

highly motivated to deal with

the assignments given by the

program.

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Medium LearnerIn the beginning, the learner made

mistakes in every second

assignment (0.5), followed by 7mistakes consecutively. This is the

reason for the big decrease (0.15).

Afterwards, the learner gave a

number of right answers and the

rate of correct answers increased

back to 0.5. In the following phase

an up and down can be seen till a

number of right consecutive

answers helps to reach a level of

0.7. But then the number of

mistakes rose again and the rate

went down to about 0.5.

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Medium Learner 2

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Weak Learner

Classified as 2 id156

0

2

4

6

8

10

111

21

31

41

51

61

71

81

91

101

111

121

131

141

151

161

171

181

191

201

211

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Summary

It is as easy as never before to collect data

We perceive much more details about the

learners the learning process as never

before!!

Teacher get precise information (class lists

are coming soon)

This application was designed to test. Now

we see, it can be effectivly used for learning

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Future Work

closer look at the learners: perhaps more intelligentanalyses of the data? more data more concepts?

Hints for Learners?

Special Results for Teachers

Alerts for Teachers

AND we are already working on the Mathe-Multi-Trainer

(multi digit

multiplication:http://mathe.tugraz.at/~mickname/access/login

)

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Acknowledgements

We express our gratitude to the teachers of the

primary school in Laubegg (Styria, Austria) as well

as all participating school children.

We are equally indebted to our funding agency

Internet Foundation Austria (IPA) for supporting

our ideas and helping us to work on the future of

education.

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Thank you!

Martin Schn

TU Graz Austria

martin.schoen@tugraz.at