Opening User Model Data for Motivation and Learning: The Case of

an Adaptive Multiplication Game

Angeliki Leonardou, Maria Rigou and John Garofalakis

Dept. of Computer Engineering and Informatics, University of Patras 26500, Rio Campus, Greece

Keywords: Learner Control, Self-regulated Learning, Open Learner Model, Engagement, Reflection, Educational Game,

Adaptive Learning, User Testing, Multiplication Table, Self-assessment.

Abstract: Multiplication table fluency is of core importance, as it consists a fundamental stage of mathematics

education. It is a common phenomenon that pupils face difficulties in perceiving this knowledge and achieving

multiplication skills. This paper presents an adaptive multiplication game for assessing and gradually

improving multiplication skills. The game also incorporates Open Learner Model elements which expose

parts of the learner model to the user through easily perceivable visualizations for improving self-reflection,

fostering self-regulated learning and increasing user motivation. The game has been tested with a

representative sample of primary school students and based on the data collected the game and the Open

Learner Model’s features have been received positively.

1 INTRODUCTION

It is a common place that both elementary and

secondary level of education are based on traditional

methods of teaching and assessing. Downing and

Haladyna (2006) claim that “teachers teach the way

they were taught and test the way they were tested”

(p. 291). Although alternative ways of assessment

(e.g. portfolios, performance) have been used in

curricula of other scientific domains (such as fine

arts), they are not typical in the mathematics

instructional procedure (Ford and Usnick, 2011). The

use of non-traditional ways of assessing was strongly

supported by the publication of Curriculum and

Evaluation Standards for School Mathematics

(National Council of Teachers of Mathematics,

2000). Specifically, multiplication table skills are

considered almost a student virtue. As this knowledge

is the heart of the majority of mathematical problem

solving, Gagne (1983) claims that the multiplication

table must be “not just learned, not just mastered, but

automatized” (p.18). Traditionally, the dominant

approach to teaching the multiplication table has been

the “rote memory” or “rote learning”, which is

defined as a memorization technique based on

repetition according to Davis (1984). However,

according to Caron (2007) “recent directions in

mathematics teaching and learning toward the need

for development of understanding in the uses of

calculations could not support the use of rote memory

alone” (p. 279). At the same time, the related

literature documents an urgent need for using

alternative approaches to mathematical concepts, as

rough use of drill and practise can make mathematics

unpleasant and uninviting (Gersten and Chard, 1999).

This tendency towards incorporating alternative

ways of teaching, practicing and assessing into

traditional instructional procedures is relatively

recent. There have been numerous efforts of software

applications documented in the corresponding

bibliography targeted at supporting the role of

teachers and increasing pupil attention and

participation to various lessons. Computer or

electronic games are among the dominant approaches

to this end.

Games in their primitive form are defined as

competitive interactions based on rules to achieve

specified goals that depend on skill, and often involve

chance and an imaginary setting (Cruickshank and

Teller, 1980). For years, playing games, even without

connection to a specific educational content has been

considered one of the fundamental forms of learning

(Huizinga, 1949) and is therefore not surprising that

games are closely linked to intrinsic educational

experiences. With technology rapidly developing in

graphics, sound, real-time video and audio, electronic

games have become more and more entertaining and

Leonardou, A., Rigou, M. and Garofalakis, J.

Opening User Model Data for Motivation and Learning: The Case of an Adaptive Multiplication Game.

DOI: 10.5220/0007735603830390

In Proceedings of the 11th International Conference on Computer Supported Education (CSEDU 2019), pages 383-390

ISBN: 978-989-758-367-4

383

enjoyable for kids, as well as adults. Among all the

kinds of games, educational games have one goal

beyond mere entertainment, and that is education.

In this paper we combine the notion of

educational games with a personalized approach and

an adaptive mechanism, with the innovative idea of

OLM. The intention is to support pupils in achieving

multiplication table fluency in a way that motivates

and engages them.

2 BACKGROUND

The integration of games in formal or informal

learning scenarios has been an active field of research

at a theoretical, as well as a practical level, the last

decades with numerous experimental and commercial

applications worldwide. The scientific bibliography

of the domain is quite rich and addresses topics

ranging from the use of videogames in supporting the

learning process (Yee, 2006, Kirriemuir and

McFarlane, 2004, Mitchell and Savill-Smith, 2004,

Egenfeldt-Nielsen. 2007 Prensky, 2007), to learning

theories deployed by each learning genre, case studies

evaluating the effectiveness of electronic games as a

teaching and learning medium (Wong et al., 2007,

Smith, 2006, Blunt, 2007, Prensky, 2006), as well as

the traits of certain electronic games genres and the

respective educational potential they provide.

Adaptive games are games that offer an internal

mechanism that stores data about each individual user

and his/her interactions and is able to make inferences

regarding how to adapt to the needs and preferences

of this user. The idea of not only maintaining data

about the user and his/her interactions but also

exposing some of them in an adequate form, is a step

beyond adaptive educational gaming that leads to

Open Learner Modeling. Open Learner Modeling was

introduced as a notion in the domain of intelligent

tutoring systems and adaptive learning environments

for supporting personalized instruction to learners.

Traditionally, learners were not given any access to

the data maintained about them by the system in the

respective learner model. After realizing though the

educational value and benefits learner model data

could offer if they were exposed to learners and

instructors, this approach gradually changed (Self,

1990). More specifically, giving students access to

view some of their model’s aspects may improve self-

reflection, foster self-regulated learning, provide

better personalization transparency and increase user

motivation (Bull and Kay, 2007), (Hsiao et al., 2010),

(Mitrovic and Martin, 2007). Since then, various

information visualization techniques have been

extensively deployed in Open Learner Models

(OLMs) to represent in an easily perceivable way

learning data ranging from knowledge and skill

levels, to difficulties, misconceptions and other

dimensions of current learner status and recorded

activity (Law et al., 2017).

OLMs are learner models that can be viewed or

accessed in some way by the learner, or by other

stakeholders of the learning process (e.g. teachers,

peers, parents). Thus, in addition to the typical

purpose of a learner model (i.e. maintaining data to

enable adaptation according to individual current

learning needs), an OLM can also be of direct use by

the learner (Bull and Kay, 2010). In principle, any

type of learner model can be accessible to users, and

the method of presenting the learner model may

depend on the purpose of opening it, the target users,

the learning context and the learning tasks to be

performed (Bull and Kay, 2016). In addition, soon

after the introduction of the OLM concept,

researchers proposed the idea of Social OLMs

(OSLMs or OSSMs) (Bull and Kay, 2007; Bull et al.,

2007). OSLMs are defined as OLMs that integrate a

social dimension and thus “…enhance their cognitive

aspects with social aspects by allowing students to

explore each other’s models or an aggregated model

of the class and also provide guidance to appropriate

content topics” (Brusilovsky et al., 2016).

Visualization plays a central role in presenting the

adequate model contents to the intended users in an

easily perceivable way. As argued by Bull and Kay

(2016), learner model data simplification through

visual presentation is necessary, since in most cases

the internal learner model mechanisms and inference

logic is too complex to display to learners, teachers,

or parents.

OLMs can be visualized in various ways to

address the many usages and potential users that

access those models (Bull et al., 2010). Typically,

OLMs use fill, color, position or size to visually

represent level of understanding, degree of

competencies and acquired skills (Bull et al., 2016).

The most widely used types of visualizations

comprise bar charts, pie charts, radar plots,

scatterplots, tables, timelines, network diagrams, skill

meters, etc. (Leonardou et al., 2019). Systems

offering OLM features may support multiple

representations and research has shown that even

though some visualizations appear to be preferable

overall, there are users that often choose to use more

than one and prefer to change representations over

time (Xu and Bull, 2010, Mabbott and Bull, 2006,

Johnson and Bull, 2009). In the case of OSLMs,

visualizations may also include (apart from data about

CSEDU 2019 - 11th International Conference on Computer Supported Education

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the specific learner) data that allow comparison of the

current learner with individual peers, or a group of

learners (e.g. the best learner of the ‘class’, other

individual learner(s), or the average ‘class’

performance).

Apart from whether an OLM visualization

incorporate elements from other learners’ models, it

can also be classified on the basis of its internal

structuring level, as highly-structured, medium-

structured and unstructured. This classification

regards whether the representation projects the

learner model on a visual view of the learning content

concepts and their relations (i.e. whether the domain

is represented within the visualization) (Bull et al.,

2016).

3 RELATED WORK

The developed educational tool deals with

multiplication tables. There are many sites that share

the same educational theme. Some indicative

examples can be found at https://www.timestables.

com/games, https://www.multiplication.com,

https://www.topmarks.co.uk/maths-games/7-11-

years/times-tables,https://www.mathsisfun.com/

timestable.html, https://www.free-training-tutorial

.com/times-tables-games.html, https://www.helping

withmath.com/resources/games/target_2x/2xtable.ht

ml. All these games use bright colors, impressive

graphics, movements and sound effects to captivate

user’s attention and to offer extra motivation for the

pupil to use them but none of them maintains user

model data nor do they support OLMs.

On the other hand, there are many efforts

documented for incorporating OLMs in the

instructive procedure of mathematics apart from

multiplication tables. One such characteristic

example is a tool on solving linear equations aiming

at 7

graders (Long and Aleven, 2013). Bull and

McKay (2004) presented Subtraction Master, a

learning environment with an OLM for two and three-

digit subtraction, which addresses schoolchildren.

Another tool is the “Point of View” (Bull et al., 2010),

which was designed for 10 to 11-year-olds and

involves learning science subjects (Earth, Sun, Moon;

Health & Teeth; Food Chains & Life Cycles).

Fraction Helper (Lee and Bull, 2008), is a

learning environment with an OLM aimed at helping

children to identify their problems with fractions and

their parents support them to overcome any

misconceptions.

CALMsystem (Kerly and Bull, 2008) opens the

learner model to students, allowing them to see the

representations of their current knowledge level as

assessed by the system, and their self-assessment for

each of the topics in the subject domain. The

CALMsystem environment is browser based,

operating independently of an ITS, and allows easy

access to users from a variety of platforms.

NEXT-TELL offers two example tools for

primary level math training targeted at school pupils.

First, a web-based multiplication trainer named 1×1

Ninja (http://next-tell.eu/portfolios/primary-level-

math-training/) for tablets or smart phones. Teachers

can retrieve a detailed summary of the competency

level of pupils. Based on the visualizations, they can

easily identify the low performers and, more

importantly, which competencies are lacking.

Secondly, Sonic Divider (http://next-tell.eu/

portfolios/sonicdivider/) is a tool designed for

practicing divisions both the classroom and as

homework. It supports practicing the formal sequence

of written divisions using a gamified approach. Pupils

receive competence-based feedback and they can

collect points, as well as compare their scores later.

Teachers can quickly access an overview about the

achievements, scores, and competency levels of their

pupils.

4 RESEARCH IDEA AND

RESULTS

The proposed approach is based on combining an

adaptive educational game on the multiplication table

(Leonardou and Rigou, 2016) with OLM elements.

The game incorporates adaptive behaviour, addresses

primary school pupils of 2

to 4

grade, concerns

self-assessing multiplication table skills and

gradually improving them. More specifically, the tool

aims to discover each pupil’s weaknesses and by

focusing on them, to help overcoming them. The

structure of the game includes 3 levels of increasing

difficulty, where information collected from level 1 is

used as feedback in level 2, and information from the

level 2 is the input for constructing level 3. In the

initial game version, the user could choose from 4

family numbers, an approach based on the idea of

Griffon (2005), where it is important to support

learners build networks from new to known

knowledge by building on and consolidating new

knowledge in a natural development and with

extensive practice. The game adaptation mechanism

used data about user performance collected during the

current session, without requiring setting up a

personal account. This was a limitation of the first

Opening User Model Data for Motivation and Learning: The Case of an Adaptive Multiplication Game

385

Figure 1: Level 1 indicative screenshot.

game version as it was not possible to monitor pupil

gradual progress and learning.

In the new version, the underlying user model

maintains detailed information about pupils and their

progress during repetitive sessions and access to the

game is provided through personal accounts. The

database stores demographic and user account data,

information on each session concerning selected

multiplication table numbers to practise, number of

correct and wrong answers, as well as date and time

information.

This application based on Caron (2007) belief that

“practice over many times is all that is needed”

(p.281), maintains the structure of the previously

developed multiplication game and consists also of 3

levels. In the first, a set of multiplications is given,

each followed by 4 potential answers to choose from

(multiple-choice). In the second level, each question

comprises 4 multiplications and 4 answers and

players are asked to match each multiplication to its

correct answer by dragging-and-dropping answers on

frames with multiplication questions. In the last level

the player has to answer multiplications of a specific

number’s table, using the game onscreen keyboard to

enter the answer. Upon completing each level, pupils

are given the option either to move on to the next level

or see their accomplishments in the level they just

finished by accessing data of his learner model. After

completing the last level, they can also see their

overall progress in the current session.

From an implementation point of view, the game

was developed in Corona SDK

(https://coronalabs.com), a cross-platform framework

that empowers developers to create 2D games and

mobile applications for iOS, Android and Kindle,

desktop applications for Windows and OS X, and

connected TV applications for Apple TV and Android

TV. It uses integrated Lua layered on top of

C++/OpenGL to build graphic applications. Lua

(https://www.lua.org) is a lightweight programming

Figure 2: Level 2 indicative screenshot.

language designed primarily for embedded systems

and clients. Lua is cross-platform since it is written in

ANSI C, and has a relatively simple C API. For

building the database, SQLite

(https://www.sqlite.org/about.html) was used an in-

process library that implements a self-contained,

serverless, zero-configuration, transactional SQL

database engine.

4.1 Gameplay

Overall, and since the game addresses schoolchildren,

it is important to visually captivate their interest so that

they are willing to use it. Therefore, pleasant graphics,

bright colours, related sound effects and animation

have been deployed.

Initially an introductory welcome message

appears, while the player fills in a textbox with a

nickname to be used as identification and to associate

all recorded activity with. In the following screen the

player can select the number(s) of the multiplication

matrix to practice on. For extra support apart from

individual numbers, 4 number families are offered

according to the methodology of teaching

multiplication in the Greek formal public education.

The amount of multiplication questions is level 1 and

level 2 differs depending on the amount of the selected

numbers. Level 1 (Figure 1) randomly selects multiple-

choice questions from the group of the selected

numbers and the player has to click on the fish-object

marked with the correct answer/value. If the given

multiplication is answered correctly, a reward message

appears and the complete multiplication, for

educational reasons. If the answer is wrong the player

can try again (the wrongly pressed object disappears),

until the correct answer is provided.

The game is supported by an underlying adaptive

mechanism. According to this mechanism and among

the selected numbers, a ‘weak’ number is detected

based on an algorithm that compares the percentage of

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the wrong answered questions, the percentage of the

right answered questions and the amount of the given

questions for each number. This mechanism is

activated upon completion of levels 1 and 2, and the

‘weak’ number is passed on to level 2 and 3

correspondingly, so that the system adapts the

selection of next questions to this identified weakness

to provide the player with more relevant

multiplication questions and thus improve skills on

this number.

Upon completion of level 1, a screen with two

choices is given: the player can press one button to

continue to the next level or can see his/her progress

by accessing data stored in the respective user model.

If a choice is made to see the learner’s progress, a

screen appears projecting visually and textually the

score in each tested number by calculating the success

percentage (amount of right answered questions/

amount of total given multiplication for this number).

Specifically, a percentage less than 50% is assessed

as “not good” and is accompanied by a non-smiling

face, a percentage between 50% and 65% is assessed

as “good” and is accompanied by a smiley face,

whereas a percentage between 65% and 85% is

assessed as “very good” and a happy face appears.

Finally, for percentage more than 85% is assessed as

“great” and a very happy face with thumps up

appears. The choice of smiley faces for skill

assessment visualization was made since a smiley

face representation belongs to simple quantised

representation category, which is considered ideal for

schoolkids. Smiley face representation with scalar

variations depicts the level of knowledge or contrast

the current learner level with the level of peers. For

example, in Subtraction Master (Bull and McKay,

2004) the child views a series of simple smiley faces

representing the extent of their subtraction skills at

different levels of difficulty.

In level 2 (Figure 2) the player is presented with a

set of four multiplications in rectangular frames and

four results written on fishes and is asked to assign

them correctly so that each fish is dragged and placed

in the ‘cave’ that corresponds to its number. In the

case of some wrong assignment the fish is returned to

the center and the player can try again (all fish that

were placed correctly disappear). Completing this

level, the player has also the choice to move on to

level 3 or to see detailed score information before

doing so (Figure 3).

In level 3 (Figure 4), the player faces exclusively

the multiplication table of the number that the

previous level identified as the weakness. As this

level is the last one, its difficulty is higher.

Multiplications are given in sequence and the player

Figure 3: Progress screen.

needs to provide the answer with no help provided. In

case of a false answer, no second chance is given, but

the player is informed about the right answer. In this

level visually, the player helps the fish reach the

higher level of the rocks and avoid the shark. A right

answer moves the fish one position up, while a wrong

answer makes the fish slip to a lower position. The

level ends successfully if the upper point is reached

or ends unsuccessfully if the player uses the number

of allowed tries without reaching the target. At the

end of the game session the player can see level 3

scoring and overall game accomplishment.

5 CRITICAL ANALYSIS

The developed multiplication game was tested with

36 pupils (17 girls and 19 boys) of the primary school.

All pupils had prior experience with computer games

but only 5 of them had played educational computer

games in the past. Regarding ICT fluency, pupils

were experienced with web browsing and

smartphones apart from the typical ICT course they

are taught in school. The evaluation sessions took

place during the school year, while students are much

more active and ‘alert’. During each pupil session in

the game the database is filled with detailed

information about pupil activity and progress. Pupils

answered a questionnaire (a revised version of

Brusilovsky et al., 2016) about usability and

usefulness of the multiplication game and the OLM

elements available. Moreover, questions also focused

on the motivational value of the provided OLM

visualization. Table 1 presents the questions with the

average and standard deviation of the collected

answers. Values range from 1 (strongly disagree) to 5

(strongly agree).

Opening User Model Data for Motivation and Learning: The Case of an Adaptive Multiplication Game

387

Table 1: Subjective evaluation questions.

Questions

AVG

I enjoyed playing the

Multiplication Game (MG)

4.78

0.42

I liked the interface of the MG.

4.58

0.76

The given instructions were

enough to understand how to

play the MG.

4.28

1.33

I found it useful to see my

progress in MG.

4.17

0.99

Seeing my progress in MG

made me realize how well I

know the multiplication table.

4.53

0.99

Seeing my progress in MG

motivated me to plan for

specific homework.

3.92

1.16

It was useful to see my

progress in each level/different

type of questions.

4.28

0.96

I find the used visualization

(smiley faces) a good idea.

4.75

0.55

I believe MG is more a game

than a lesson.

3.81

1.45

Q10

I believe MG is more a lesson

than a game.

2.83

1.59

Q11

I would like to play MG at my

home PC, as well.

4.5

0.9

Q12

I would like to see the scores

of my peers.

4.17

1.28

Q13

I would like to see the class

average score.

4.11

1.22

Q14

I believe that seeing the

progress of others would

motivate me to work harder.

4.11

1.02

Q15

It is important for me to see

my rank among my peers.

3.94

1.41

All participants enjoyed playing the game (q1),

89% enjoyed the application’s interface (q2) and 81%

felt that there is no need for extra instruction on how

to play the game (q3). 78% found useful the opening

of the model for seeing their progress (q4), 89%

believe that opening the model supports self-

reflection (q5) and 67% believe that opening the

learner model is a factor of self-motivation (q6). 75%

considered it significant to see their progress after

completing each level and thus watching their

progress in different types of questions (q7), 94%

agreed with the usage of smiley faces as the type of

visualization provided (q8) and 64% felt that the

application has more of an entertaining than an

educational role (q9), whereas 47% didn’t agree with

the opinion of a more educational than entertaining

role (q10). 83% would like to have the opportunity to

play again the game at home (q11), which gives an

extra support of the assumption that pupils enjoyed

interacting with the tool. 78% were interested in the

idea of social OLM (q12). This finding is interesting

as providing access to score of others seems

motivating to competing pupils. 69% would like to

see the average progress of their classroom (q13).

72% believed that OSLM would offer self-motivation

(q14), thus the ability of seeing peers progress will

contribute in self-directing their study. 69% would

like to see their rank among their classmates (q15)

and thus to contrast their level of efficiency with all

classmates.

Questionnaire responses suggested that pupils

had positive reactions towards the OLM approach, as

well as the idea of OSLM. They consider it easy and

pleasant to interact with and didn’t underestimated

the educational role it plays.

Many of the game testers after completing

specific levels chose not to see their progress: only

38% choose to see Level 1 progress, 44% Level 2

progress and 38% Level 3 progress. On the other

hand, the vast majority (88%) chose to see the total

progress of the activity at the end of the game. When

asked, pupils stated that they preferred to keep on

playing because they were amused by the process and

wanted to see their overall score at the end, an

approach that is considered logical for their age group

and the purpose of the application. In addition, this is

also supported by the answers received on the q7

where pupils considered the application a game rather

than an educational activity.

6 CONCLUSIONS

This paper presented the design and implementation

of an adaptive educational game addressing primary

school students for practicing and mastering

multiplication table skills. The game incorporates

OLM characteristics as it maintains in a properly

structured database information about the pupils and

their activity and progress. Based on the data

collected during the testing sessions, there is strong

indication that both the ideas of OLM and OSLM

were perceived positively. It was observed that

participants enjoyed playing and faced no difficulty

in understanding the way the game works.

Regarding future plans for extending this work,

the application is going to be expanded with social

OLM elements, as it will open not only to the user

himself but also to peers and teachers. In the new

version currently under development, users will be

able to access specific anonymous information of

peers and watch a summative view of the class

CSEDU 2019 - 11th International Conference on Computer Supported Education

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progress, whereas the teacher will be able to access

detailed pupil data.

In the current version for each selected number,

the system maintains the sum of multiplications

given, the sum of the right answered multiplication

and the number of wrong answered multiplications.

An idea for improving the application is to maintain

a 2-dimension table with the specific wrong answered

multiplication combination so that the teacher can

reach safer pupil assessment decisions and the system

can better match each pupil practise needs.

One of the limitations of the current analysis is

restricted number of test participants when

considering the number of pupils per grade as well as

the narrow time frame. It has been planned to

examine the effectiveness of this tool in real

classroom conditions during the school year with

more pupils per grade, so as progress would be more

thoroughly recorded and safer results could be

reached. The pupils are expected to use the

application in school using the computer laboratory

class, either with the presence of the teacher, who will

guide them on the numbers to be selected for the

practise (according to the stage of the instruction

procedure and progress), or either as part of the

computer lesson, where the pupils will be able to play

the game in an unsupervised mode.

Among the experimental ideas is to check the

application in two versions, that is with and without

the OLM elements, as we believe that this comparison

will provide interesting results. Such experiments

will allow for the comparative analysis of OLM and

non-OLM game versions on the basis of learning

outcome as well as student preference, metacognition

and motivation.

Another idea expanding the game features is to

give pupils the option to become more active

(Himmele and Himmele, 2011) by tailoring the game

interface elements (such as the background image, the

image objects, and the kind of visualizations)

according to their preferences.

The last direction in our plans is to introduce to

the game a stronger instructional parameter in the

form of graphical explanatory feedback that will help

pupils understand calculations that explain answers

they failed to calculate correctly (Harries and

Barmby, 2007).

ACKNOWLEDGEMENTS

The authors would like to thank the elementary

school teachers who helped in the educational design

of the game and the pupils who participated in the

game evaluation testing.

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