Collecting and Analysing Learners Data to Support the Adaptive

Engine of OPERA, a Learning System for Mathematics

Marisa Oliveira

, Alcinda Barreiras

, Graça Marcos

, Hermínia Ferreira

, Ana Azevedo

and Carlos Vaz de Carvalho

Institute of Engineering of Porto, Porto, Portugal

Porto Accounting and Business School, Porto, Portugal

GILT - Institute of Engineering of Porto, Porto, Portugal

Keywords: Mathematics, Active Learning, Adaptive Learning Systems, Computer Aided Learning.

Abstract: Learning mathematics has always been (and still is) a major issue. Many students fail to understand the basic

concepts and/or are unable to apply them. These students end up moving to other subject areas or simply

dropping out. One of the major reasons for this problem is the fact that the educational system is only prepared

to apply standardized teaching methods that do not respect or fit the individual characteristics of each student.

This paper presents the OPERA learning adaptive system that provides the foundations for further

mathematics learning while addressing the diversity of the users/learners. OPERA collects learner interaction

data to monitor the learning process in an active and contextualized way and to identify the users’ difficulties

and achieved knowledge in each stage. Based on the data analysis, OPERA then reorganizes the sequence of

contents and provides the precise information needed to progress which makes learning much more efficient.

1 INTRODUCTION

Like many other Western countries, Portugal is

confronted with a declining number of students in

science, mathematics, engineering and technology

(STEM) careers. This problem will hamper the future

country development if no measures are taken.

Different approaches have been suggested to increase

the motivation of students to learn mathematics and

follow STEM careers and the use of technology to

support learning has been one of them. According to

Folden (2012) technology-based learning (e-learning)

has its roots in the so called teaching machines that

emerged in the beginning of the twentieth century.

Computers became the natural environment for the

teaching machines and, with the advent of digital

communications and the Internet, the first virtual

learning environments where adopted throughout

organizations (Folden, 2012; Peres, Mesquita, and

Pimenta, 2015).

Nowadays, technology based learning

environments are typical in organizations, and

adaptive systems are gaining momentum. Adaptive

learning systems dynamically change the contents or

the way they are presented, based on the user’s

preferences, responses, and activities, in order to

facilitate the learning process and to optimize the

students’ performance (Oxman and Wong, 2014;

Paramythis and Loidl-Reisinger, 2004; Wilson and

Scott, 2017).

OPERA is an adaptive learning system that

addresses the mathematics topic of operations with

real numbers. The strategy is based on an adaptive

model in which students solve exercises through a

progression scheme adjusted to their level of

knowledge and performing skills. OPERA collects

data, analyses it and evaluates the performance of the

student and when a lack of knowledge is

acknowledged the application proposes additional

learning, through video-tutorials or documentation.

OPERA is mainly aimed at students from

secondary schools and initial courses of higher

education. It is also thought for students over 23 years

of age that have to do a mathematics exam in order to

access higher education. The topic “operations with

numbers” is one of the topics that is evaluated in this

exam and it is fundamental for other mathematics

matters.

2 OPERA CONCEPT

Mathematics is many times perceived as a difficult

and abstract subject, which involves learning a lot of

Oliveira, M., Barreiras, A., Marcos, G., Ferreira, H., Azevedo, A. and Carvalho, C.

Collecting and Analysing Learners Data to Support the Adaptive Engine of OPERA, a Learning System for Mathematics.

DOI: 10.5220/0006389806310638

In Proceedings of the 9th International Conference on Computer Supported Education (CSEDU 2017) - Volume 1, pages 631-638

ISBN: 978-989-758-239-4

631

processes and formulas that seem irrelevant to the

students' lives. Therefore, students develop a negative

attitude towards mathematics and lack of confidence

in ‘being good at it’ which later affects their career

choices.

Besides that, improving the students' motivation

to learn mathematics is also crucial to the economy

and so aiming for a high proportion of graduates’

students in technology areas is a very important

objective. Appropriate learning methods can develop

students' level of understanding mathematical rules

and procedures, helping them develop a deeper

interest, engagement and motivation.

2.1 Learning with Technology

The emerging computer and network technologies

have changed the way we live, work, teach and learn.

The learning paradigm took advantage of the new

technologies in the development of different

education models, changing the teaching-learning

process. Over the last years the learning systems have

also embraced new educational technologies. The

creation of new and innovative teaching and learning

resources supported the use of new pedagogical

methodologies that are beneficial for teachers and

learners. The concept of Open Educational

Resources, in spite of the identified problems, has

been widely adopted (Vaz de Carvalho, Escudeiro,

Caeiro Rodriguez, & Llamas Nistal, 2016). Different

initiatives and projects were developed involving

interactive web sites, learning applications, online

training activities, intelligent tutoring environments

and many others. Serious games have also been

identified as excellent learning tools (Andrade,

Gouveia, Nogueira, Russo, & Vaz de Carvalho,

2015).

However, most of the learning systems still

provide the same inputs and similar learning

resources to all students not taking into consideration

their different characteristics. In those systems all the

students have the same learning path, independently

of their distinct background knowledge, different

needs, individual methods or preferences.

To be effective, the learning environment must be

student-centred and the student’s differences should

be contemplated. In a student-centred learning

system, the student builds his/her knowledge by

interacting with correctly chosen learning objects that

suit his/her skills and previous performance. This

increases the effectiveness of the learning and the

learner´s motivation since the system converges to

his/her needs. Several categories of adaptation can be

identified, and one of the most used, named as

Adaptive Course Delivery, is designed in order to

obtain courses tailored to each one of its users, fitting

the course contents to the users characteristics as

much as possible (Paramythis and Loidl-Reisinger,

2004).

An adaptive system can be considered as similar

to a biological system, which changes its behavior in

response to its environment, and this change is

relevant to achieving a certain goal (Brusilovsky and

Peylo, 2003; Michalewicz, Schmidt, Michalewicz,

and Chiriac, 2007; Wilson and Scott, 2017).

According to Paramythis and Loidl-Reisinger

(2004) four types of models can be typically found in

adaptive learning systems, namely: i) the domain

models, which is a representation of the course being

offered including contents and possible learning

paths; ii) the learner models, which maintains

diversified information about the user; iii) the group

models, which identifies similar students to

dynamically create groups of learners; and iv) the

adaptation model, which defines what, can be adapted

and when and how it can be adapted. Oxman & Wong

(2014) consider that there are three core elements

above which adaptive learning systems are built,

namely, the content model, which is similar to the

domain model referred by Paramythis and Loidl-

Reisinger (2004), the learner model, similarly to the

leaner model of Paramythis and Loidl-Reisinger

(2004), and the instructional model, which is similar

to the adaptation model of Paramythis and Loidl-

Reisinger (2004). Wilson and Scott talk about the

“knowledge of the domain (the domain model),

knowledge of teaching strategies (the pedagogic

model), knowledge of the learner (the learner model),

and rules for interaction (the communication model)”

(2017, p. 3).

The instructional or adaptation models uses a set

of data about the user, and can be rule-based, with if-

then statements and heuristics, or algorithm-based,

with advanced mathematical formulas and applying

machine learning techniques, such as data mining

(Medina-Medina and García-Cabrera, 2016; Oxman

and Wong, 2014; Paramythis and Loidl-Reisinger,

2004). This can be considered as Prescriptive

Analytics. “One can view analytics as the process of

developing actionable decisions or recommendations

for actions based upon insights generated from

historical data” (Sharda, Delen, and Turban, 2014, p.

56). Prescriptive analytics concerns the determination

of the best course of action, providing a decision or a

recommendation (Sharda et al., 2014; Turban,

Sharda, Aroson, and Liang, 2007).

Adaptive learning systems present some

challenges as well as some potential advantages when

compared with traditional systems. As challenges we

can identify the following ones: i) content can be too

A2E 2017 - Special Session on Analytics in Educational Environments

632

easy, which can demotivate the students, or too hard,

which can be frustrating; ii) students can have

different prior knowledge; iii) the costs of education

can make hard for the students to access the systems

(Oxman and Wong, 2014). As potential advantages,

we can identify the following ones: i) reduce the

number of students that give up: ii) achieve outcomes

more effectively; iii) achieve outcomes faster; iv)

help faculty to focus.

Several applications of adaptive systems are

known in educational contexts with success, from

elementary and secondary to higher education levels

(Brusilovsky and Peylo, 2003; Guo, Palmer-Brown,

Lee, and Cai, 2014; Hamann, Saul, and Wuttke, 2015;

Kara and Sevem, 2013; Oxman and Wong, 2014;

Paramythis and Loidl-Reisinger, 2004; Tsai, Lee,

HSU, and Chang, 2012).

An important aspect of the process relates to the

use of standardized data collection and result

reporting methods to allow interoperability with other

applications, namely Learning Management Systems.

The two major specifications supporting this process

are SCORM (Shareable Content Object Reference

Model) and xAPi (also known as TinCan API).

SCORM is a collection of specifications

developed by ADL (Advanced Distributed Learning)

for e-learning systems through the web. Among other

things, SCORM defines the rules of communication

between educational content (in the form of Learning

Objects - LO) and the host application, usually in the

form of a LMS. In this way, it is possible to

standardize the way in which the educational contents

relate to the systems that support them and allow the

LOs to be independent of these systems (Rustici

Software, 2016).

In general terms, xAPI is a free, open source

technical specification for the implementation of a

global architecture including the definition of a

Learning Record Store (LRS) and 4 complementary

APIs. xAPi was conceived with a much more open

view of the learning process. In fact, learning is

acknowledged as happening everywhere, not just in

the digital world of an LMS and is often self-managed

by the student. This has entailed a change in the way

learning systems are organized so that it is necessary

to monitor and integrate the different learning

experiences and data gathered from these various

sources. Thus, xAPI is agnostic about the type of

learning content being used and allows flexible

monitoring of learning activities and experiences

regardless of the model, including formal e-learning

courses, performance systems, group learning, social

or even informal learning scenarios (Rustici

Software, 2016).

xAPI allows following and assessing micro-

behaviors, states and contexts of learning experiences

such as (ADLnet, 2016):

• Reading an article or interacting with an e-book

• Watching a video lesson

• Using a simulation

• Running a mobile application

• Talking to a tutor

• Acquiring physiological data, such as heart beats

• Evaluating team performance in a serious game

• Recording real-world performance in an

operational context

In fact, the flexibility of xAPI is so great that it

can be used in contexts that would not seem relevant

before. For instance, Long et al used the specification

to collect military sniper performance data in order to

create an adaptive training system (Long, et al.,

2016). Several other studies contributed to the

development of the specification and its application

in different settings.

Berg et al analyzed the experience of the

application of xAPI in several projects including the

use of LRSs (Berg, Scheffel, Drachsler, Ternier, &

Specht, 2016). The main conclusion was that the lack

of a unique source of validation could lead to the

appearance of inconsistent implementations and the

consequent abandonment of the specification.

Bakharia et al evaluated the use of the specification in

conjunction with a specific tool, the Connected

Learning Analytics Toolkit, in order to verify if it

would contribute in any way to facilitate the

collection of the necessary information for this

process (Bakharia, Kitto, Pardo, & Gasevic, 2016).

The main conclusion was precisely the need to

complete the existing specification. Another proposal

to extend the specification was made by De Nies et al

who proposed the W3C PROV model in order to

improve the interoperability of systems using xAPI

(2016). Traore also identified some limitations of the

specification when implementing it in the SOFAD

authoring system (2016).

Vidal et al proposed a semantic approach to the

analysis of the specification through a representative

ontology that in the future may contribute to the

verification of the conformity of a given application

model of the xAPI (2015).

Manso-Vázquez et al proposed a model to

improve student / trainee monitoring in self-learning

processes (2015). The model was based on xAPI and

somehow demonstrated the extensibility of the

specification as new applications emerge. However,

this extension may imply the aggravation of the

problem detected by Berg.

In a similar approach, Poonam et al used xAPI as

a support architecture to capture and monitor user

Collecting and Analysing Learners Data to Support the Adaptive Engine of OPERA, a Learning System for Mathematics

633

interactions and store them in an LRS (2016). In a

more comprehensive approach, Amrieh et al used the

specification to capture student interaction with an e-

learning platform and tried to correlate this factor

with the student performance (2015). They concluded

that there is, in fact, a strong correlation between the

two. In a similar perspective, but for a completely

different audience, Murphy et al used the

specification to monitor the performance and

efficiency of military training (similar to the Long

approach) and thus demonstrated the usefulness of the

specification (2016). Kazanidis et al presented ProPer

which combines technologies from both Adaptive

Educational Hypermedia Systems (AEHS) and

SCORM compliant LMS. To help teachers and

students alike to locate possible weaknesses it

monitors and visualizes user progress through

instruction. To motivate students to continue with

their study an immediate feedback and comparative

techniques are presented. (2009).

Looking at this compilation of studies, it is safe to

say that technology seems to be ripe and fitted to the

objectives of OPERA.

2.2 OPERA Model

OPERA is an adaptive learning system that addresses

the topic of operations with real numbers. The

application goals were defined as:

• Flexibility with an adaptable learning

environment designed to consider the student's

performance;

• Accessibility to course materials at any time and

from anywhere;

• Merging to the individual needs of the student.

The OPERA strategy is based on an adaptive

model in which students solve exercises through a

progression scheme adjusted to their level of

knowledge and performing skills. The system

supports the learners’ individual needs, assuming

specific tutoring strategies for efficient and effective

learning. The students’ individual needs assessed are

cognitive as problem solving and independent

reasoning; personal as self-guidance, time

management, self-assessment; and affective as

development of positive attitudes through attaining

goals.

The core of the OPERA strategy is based on the

continuous collection of information on a particular

student´s performance while solving problems and

challenges. The student model is continually being

updated throughout the session and a corresponding

adapted progression (difficulty and themes) scheme

is provided. The model combines domain specific

information discriminating all the expected

knowledge to be acquired, by topic, and domain

independent information which, in this case, is related

to the personal skills (also identified in the literature

as personal traits) to be acquired/already developed.

For instance, some of the challenges are identified as

contributing to critical analysis, problem solving,

time management, etc. The way students solve (or

not) those challenges contribute to the identification

of their personal traits in the model.

The progression model also provides hints and

other automatic feedback following the students’

knowledge status. For instance, the student is linked

to oriented video-tutorials, which students watch

when they have doubts about the exercises they are

solving. The construction of knowledge is done in an

efficient and motivating way, differently from the

traditional classroom, much more attractive and

engaging since it always requires the student

interactivity.

Students become independent, proactive and

'learn by doing'. Student-knowledge is created by a

constructive process, oriented and articulated

according to the students' understanding and fulfilling

the guiding role that should be carried out by the

teacher.

2.3 OPERA Contents

The “OPERA – OPErations with ReAl numbers”

project contains four main topics, namely, rational

numbers, real numbers, absolute value and intervals,

each topic being divided into several subtopics. The

choice of this theme is due to the fact that, although it

is one of the basic subjects in mathematics, it always

generates difficulties. Table 1 presents a summary of

the subject contents evaluated in the OPERA model.

Table 1: Summary of topics and subtopics evaluated in the

OPERA model.

Topics Subtopics

Operations with

rational numbers

 Addition

 Multiplication

 Potentiation

 Number expressions

Operations with real

numbers

 Addition

 Multiplication

 Potentiation

 Number expressions

Absolute value  Operations

Interval operations

 Intersection

 Union

 Complementation

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Table 2 outlines the essential mathematical skills and

competences that a student will acquire at the end of

each topic.

Table 2: Summary of learning outcomes in the OPERA

model.

Topics Learning outcomes

Operations

with rational

numbers

Perform calculations involving

operations (addition, multiplication,

and potentiation) with rational

numbers.

Solve problems with rational numbers

that involve addition, multiplication,

and potentiation.

Operations

with real

numbers

Perform calculations involving

operations (addition, multiplication,

and potentiation) with irrational

numbers.

Solve problems with irrational

numbers that involve addition,

multiplication and potentiation

operations.

Absolute

value

Solve problems involving the absolute

value of real numbers.

Interval

operations

Determine sets that result from

operations with intervals of real

numbers.

3 OPERA ADAPTIVE SYSTEM

The OPERA system adapts the learning experience to

the user's abilities by reorganizing the content

presentation sequence (questions) according to the

given answers. The user's model is therefore

behavioural, since it does not have any pre-existing

information about the user when the user first

accesses the system. This model is updated according

to the questions answered by the student.

3.1 Opera Interface

In Figure 1, we can see the welcome screen, with the

theme to be studied and a button to start the course.

Figure 1: OPERA Input screen.

OPERA presents a hierarchical approach to the

issues, according to the thematic areas (Figure 2). The

number of difficulty levels in each topic is set by

default to two, but can be changed. All these

definitions (questions, groups of questions,

progression schemes) can be changed according to

different courses and audiences. A progression

scheme is directly connected to the topic, which

means that it can include questions from different

modules.

Figure 2: Thematic organization of OPERA.

A progression scheme is defined as a sequence of

steps that the student has to do. The number of

exercises, the correct number of answers that the

student has to give, and the maximum amount of time

allowed define each step.

The questions can be numeric, multiple choice,

true/false or graphic. The questions are randomly

chosen from those available in the database. The

sequence can be set so according to the student

behaviour at a given time: for example, if the student

correctly solves all the questions at a given step/level

Collecting and Analysing Learners Data to Support the Adaptive Engine of OPERA, a Learning System for Mathematics

635

in a short period of time, he can level up when

compared to a student who had completed this same

step with fewer right answers and over a longer period

of time. In a given step, the behaviour of the

progression scheme in function of the student's failure

can be configured as: the student can repeat the step,

be re-assigned to the previous step or additional

information to study can be provided. Instructions are

displayed on the screen so student understands how it

will work (Figure 3).

Figure 3: Presentation of the OPERA model.

Summing up, learning will be essentially done

through the resolution of exercises (Figure 4). The

questions can be formulated in a formal way or in a

realistic way trying to facilitate the transfer of

acquired knowledge (Figure 5).

Figure 4: Example of an OPERA question.

Figure 5: Formal OPERA question.

As the student is answering (or not) the questions,

the application identifies their difficulties and

proposes them the information needed to deepen the

subjects addressed there. The heuristics used are

relatively simple, but they allow approaching the use

of the application to the real needs of the students.

Some examples of rules used:

• An immediate resolution of a simple exercise

allows moving immediately to a complex

exercise. Its immediate resolution allows to

move to the next module;

• If the student completes two consecutive

modules without errors, moves directly to the

difficult level of the next module. As long as he

doesn’t make any mistakes, always moves to the

difficult levels of the following modules;

• Two consecutive mistakes at a simple level

results in a suggestion that student should access

video-lessons;

• Two consecutive mistakes on the difficult level

brings back to the simple level.

Figure 6: Video-presentation lesson of the real numbers

module.

A2E 2017 - Special Session on Analytics in Educational Environments

636

The information will be available in the format of

video lessons, print documents or consolidation

exercises (Figure 6). Note that, after a wrong answer,

OPERA also immediately provides detailed feedback

on the error and on the correct resolution.

The student can use the documents available or

watch the proposed video-lessons to consolidate the

knowledge worked. These activities aim to strengthen

and consolidate learning.

At the end, students will be able to take a global

test containing several questions related to the course

syllabus. After this a feedback is given to inform the

student about the performance achieved.

3.2 Technical Requirements

In terms of development, the tools used were

Panopto, Camtasia Studio, Articulate Storyline and

Javascript. This conjugation allowed to create a

multiplatform learning object (runs on mobile

devices, web environments and, natively, on

Windows systems).

In addition, OPERA is produced in accordance

with the SCORM and xAPI specifications, which

allows its integration into Learning Management

Systems (LMS) in such a way that the results obtained

by the students can be part of a formal learning

evaluation process. SCORM is used for the packaging

of the learning object and the interoperability with the

LMS, allowing the transfer of data to the host grading

system. xAPI is used to standardize the collection and

storage of the discourse learning analytics data and

therefore also supports the student model.

4 CONCLUSIONS

In this paper we have presented the learning system

“OPERA – OPErations with ReAl numbers”.

OPERA mainly intends to identify the subjects in

which the students have more difficulties, and thus

help them to have a better perception of their own

level of knowledge. As the students' difficulties are

identified, the application provides them with the

necessary tools to overcome these difficulties

(through video lessons, print documents or

consolidation exercises). It makes the learning more

efficient and more motivating. OPERA is therefore a

rule-based adaptive learning system following an

adaptation model.

Extensive testing will take place in the next few

months but preliminary results indicate that the

system can provide results close to the original

objectives.

ACKNOWLEDGEMENTS

Part of this work has been supported by the Porto

Polytechnic (P.Porto) through the PIPED award.

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