An Automatic Method for Structuring and Recommending Exercises

In Light of Case-based Reasoning, Knowledge Representation and Error Mediation

Carlos Andr

e Zavadinack

, Fabiano Silva

, Alexandre I. Direne

and Alexander Kutzke

Department of Informatics, Universidade Federal do Paran

a, Caixa Postal 19.081 – 81.531-980, Curitiba-PR, Brazil

Sector of Technological and Professional Education, Universidade Federal do Paran

a, Curitiba-PR, Brazil

Keywords:

Case-based Reasoning, Error Mediation, Knowledge Representation, Educational Informatics.

Abstract:

Case-based Reasoning (CBR) is a method for solving problems with similar retained solutions. CBR demands

a knowledge representation that allows the reasoner to ﬁnd similar cases by a query and the similarity rate

is given by a distance in hierarchical tree structure, an ontology. The main goal of this research is to use

CBR as a pedagogical tool supported by three pillars: Case-based reasoning, Knowledge representation and

Error Mediation in Education. It is considered that the error has a role of importance in the pedagogical

development, so it has to be mediated. The error mediation is used as a rule for a quantitative classiﬁcation

of exercises, it takes into account how many times an exercise have been uncorrected answered, the distance

between exercises gives the similarity between them. This kind of automatically classiﬁcation for exercises in

a educational support systems is one of the main contributions of this research. This work suggests that the

CBR cycle is useful in the designing of a tool for automatic creation of exams.

1 INTRODUCTION

In the last decades, researches and tools have been

developed aiming to improve educational support sys-

tems. Distance Learning is a type of educational sup-

port system that could be helped by those researches.

Automatic creation of exercises, introduced by Fis-

cher (Fischer and Steinmetz, 2000), could make dis-

tance learning systems reliable and credible. Using a

reasoner that could, automatically, generate assorted

exercise lists for various students is a solution that

looks very helpful because, e.g., it can avoid stu-

dents sharing exercise lists with their colleagues, what

could improve the evaluation reliability.

Generating assorted exercise lists is a trivial ac-

tivity, a simple algorithm could set groups by some

parameters. But to ﬁnd out a way that certiﬁes the

similarity between exercises lists and generates lists

with dynamics variables could be helpful. Artiﬁcial

Intelligence (AI) with its techniques and methodolo-

gies has been providing substantial contributions for

educational systems. An AI methodology that seems

helpful for the task of suggesting exercise lists is the

Case-based Reasoning (CBR). Case-based Reasoning

is a methodology which solves new problems reusing

past experience, taking into account similarity be-

tween singular elements in a complex range to ﬁnd

out solutions. This work relies on a quantitative way

in an hierarchically organisation of the elements.

According to Kutzke and Direne (Kutzke and Di-

rene, 2015), error is “an integral part of the teaching

and learning process”. Among the future directions

pointed by their research, we highlight: analysis of

error recommendation in the learning and knowledge

process; research and design of a tool for an automatic

creation of exams and collected data analysis; a data

structuring that takes into consideration the error is a

useful contribution. We suggest that a CBR system

could be a tool for a an automatic creation of exams.

This paper shows a research that aims to experi-

ment CBR as a method for recommendation of learn-

ing objects, speciﬁcally, exercise lists. Two appli-

cations were used for the experiment, one is a CBR

framework named myCBR 3

(Hundt et al., 2014);

and the other is FARMA-ALG (Kutzke and Direne,

2015), an application for computer programming edu-

cation, where the data for the present tests were taken

from. Brieﬂy, there are data with sets of questions and

answers from FARMA-ALG, that data were struc-

tured in an ontology that is the knowledge representa-

tion used in myCBR 3.

The results point that a structured data as in an on-

http://mycbr-project.net/

Zavadinack, C., Silva, F., Direne, A. and Kutzke, A.

An Automatic Method for Structuring and Recommending Exercises - In Light of Case-based Reasoning, Knowledge Representation and Error Mediation.

DOI: 10.5220/0006318903550362

In Proceedings of the 9th International Conference on Computer Supported Education (CSEDU 2017) - Volume 1, pages 355-362

ISBN: 978-989-758-239-4

355

tology is a requirement for a good use of knowledge

base in a CBR system. An automatic and quantita-

tive way for exercise classiﬁcation was made taking

into consideration the students’ mistakes, and we be-

lieve that it may be helpful for learning tools. Also,

we provide a validation to prove the utility of a CBR

automatic tool for exams creation.

For presenting how the research is developed, this

paper is organised as follows. The ﬁrst section in-

troduces the Case-Based Reasoning and myCBR - a

CBR system chosen for the present research. Sec-

tion 3 is about the role of error mediation and show

FARMA-ALG, a framework for teaching computer

programming. The section 4 brings how the raised

data from FARMA-ALG are structured. The experi-

ment and its results are shown in section 5. Finally,

section 6 relates the conclusions, contributions from

the research and future directions.

2 CASE-BASED REASONING

Case-based reasoning is a methodology introduced by

Kolodner (Kolodner, 1992) and Schank (R.Schank,

1989). CBR is a problem solver based on past experi-

ences, named cases. According to Kolodner (Kolod-

ner, 1992), the meaning of the therm case in CBR is

a contextualised piece of knowledge representing an

experience that teaches a fundamental lesson for the

reasoner achieving a settled goal. Aamodt and Plaza

(Aamodt and Plaza, 1994) introduced the CBR cycle,

a reasoning model (Figure 1). CBR cycle consists of

four tasks: Retrieve, Reuse, Revise and Retain.

CASE BASE

Problem

RETRIEVE

REVISE

RETAIN

Updated

Proposed

Solution

Figure 1: CBR cycle by Aamodt and Plaza (Aamodt and

Plaza, 1994).

The retrieve process is the matching of features in

a settled case, a query with the case features brings

similar cases in the case base. The case retrieved and

the query are compared, an adaptation of the case for

each feature happens in the reuse task. The revision

task is the time that an expert (machine or human) will

check if the reuse works. If it works, then a new case

is retained.

Richter (Richter, 2003) introduced that it is possi-

ble to identify knowledge in CBR with four containers

(Hundt et al., 2014):

Vocabulary deﬁnes attributes and their allowed

values.

Cases are the descriptions of past episodes of ex-

perience, represented in an ordered pair (problem,

solution). The cases are stored in a Case Base

(CB).

Similarity Measures are functions to calculate the

similarity between individual attribute values.

Adaptation Knowledge are represented by rules

that can be applied as solution of retrieved cases.

The attribute-value representation consists in a

name A; a ﬁnite set DOM(A) with a set of values from

A; and a variable x

. The values allowed are deter-

mined in reason of each context, assuming numerical

or symbolical values.

The retrieving is a simple operation for CBs and

data bases. But, while in the data base a query

matches an exact data, at CBR systems the query

presents a problem and would retrieve a solution in an

inexact match with the problems in the CB. For both

of them, the tree structure plays a major role to struc-

ture data and cases for an efﬁcient retrieve (Richter,

2003).

Formally, Cimiano (Cimiano, 2006) deﬁnes Sim-

ilarity Measure as a function sim: sim : R

× R

→

{0, 1} with the following properties:

∀v

, v

∈ R

, sim(v

, v

) = 0 ⇔ v

· v

= 0

∀v

, v

∈ R

, sim(v

, v

) > 0 ⇔ v

· v

> 0

∀v ∈ R

, sim(v,v) = 1.

The ﬁrst condition means that the similarity be-

tween two elements is zero if there are no common

features. Thus, the sim is greater than zero in case

they have at least one common feature. The last prop-

erty afﬁrms that a vector is maximally similar to itself.

In a data structured tree, the similarity between

two attributes is given by their distance. A Distance

measure is a function dist : R

× R

→ R

with

the following property: ∀v dist(v,v) = 0, means that

the distance of a vector to himself is 0. The trans-

formation of distance to similarity and the opposite

way needs to fulﬁl the following conditions (Cimiano,

2006):

dist(x, y) = +∞ ↔ sim(x, y) = 0

CSEDU 2017 - 9th International Conference on Computer Supported Education

356

dist(x, y) = 0 ↔ sim(x, y) = 1.

Three CBR systems was studied during the re-

search: TUUURBINE, jColibri and myCBR. TUU-

URBINE

is a generic CBR engine for the seman-

tic net able to reason on knowledge stored in RDF

(Resource Description Framework)

format (Gaillard

et al., 2014). We used TUUURBINE in our ﬁrst at-

tempt, but a technical unsolved problem didn’t en-

able its usage

. One of the most signiﬁcant CBR

systems developed is jColibri

, presented in (D

ıaz-

Agudo et al., 2007) and (Recio-Garc

ıa et al., 2013),

a free software with more than 10000 downloads.

jColibri and myCBR are compared in (Atanassov and

Antonov, 2012), where they bring the conclusion that

jColibri is a framework for complex operations, with

multiple data bases, requesting a strongly program-

ming knowledge and time for developing an appli-

cation with it. In light of (Atanassov and Antonov,

2012), myCBR is recommended for non-complex ap-

plications and not recommended for applications with

a great amount of attributes. The experiment in the

present research counts with only ﬁve attributes, and,

in face of that, we decided for myCBR. There is a

brief report about its properties and its knowledge

modelling in the subsection 2.1.

2.1 MyCBR 3

MyCBR

is a CBR framework developed through a

partnership between DFKI

and UWL

. MyCBR 3 is

the latest version known, and it comprehends three

knowledge containers: vocabulary, similarity mea-

sures and case base. The adaptation task and its

rules are not available in the last version, although in

(Hundt et al., 2014) is mentioned that a version would

be soon available with those properties.

Developed in Java, myCBR 3 Workbench has a

friendly interface that allows users modelling the

knowledge by a set of attributes and its own set of val-

ues. The cases are sets of allowed attributes, the case

base can be fed by the interface or by the exportation

of .csv ﬁles. Vocabulary in myCBR 3 is given by at-

tributes with allowed values by the types: symbols,

boolean, float, integer and string.

Similarity measure functions (SMF) are given

within concepts and attribute values. SMFs can

http://tuuurbine.loria.fr/

http://www.w3.org/standards/techs/rdf

TUUURBINE’s web service didn’t work properly and

we had to interrupt its using.

http://gaia.fdi.ucm.es/research/colibri

http://mycbr-project.net/

http://www.dfki.de/web

http://www.uwl.ac.uk/

be edited by advanced similarity mode, table editor

mode and taxonomy editor mode. The advanced sim-

ilarity mode is recommended for values of the types

integer and float. The table editor mode is the de-

fault edition mode, the relations could be settled by

the interval [0,1] where the main diagonal are the sim-

ilarities between the same values sim(x, x) = 1. In the

taxonomy edition mode, settled by the hierarchy, only

the symbol type is allowed.

The retrieve window is composed of a query with

predetermined ﬁelds that can be ﬁlled in only with the

allowed attribute values. User can also ﬁll in with un-

known (

unknown ) and undeﬁned ( undefined )

values. The result search correspondent elements

with a similarity function and, therefore, among the

cases. The retrieved cases are shown in an ordered

list by similarity rate.

3 THE ROLE OF ERROR

MEDIATION IN TEACHING

AND LEARNING COMPUTER

PROGRAMMING

In this study we consider error an answer that is not in

accord with the expectation for who made the ques-

tion. Kutzke and Direne (Kutzke and Direne, 2015)

bring that, according to the Cultural-Historical Psy-

chology, the relevance of error in the learning and

teaching process merges in given differences between

the development of scientiﬁc and spontaneous con-

cepts. According to Kutzke’s and Direne, error has to

be mediated within the scientiﬁc concepts, making it

an object of learning task, a part of concept assimi-

lation process. The role of error mediation is an es-

sential problem for the Kutzke research, it presents

a demand for tools that help teachers in the students

errors analysis.

Kutzke and Direne (Kutzke and Direne, 2015)

bring the speciﬁcities of computer programming

teaching and learning. Learning computer program-

ming raises that “the student needs to appropriate

himself of signs and speciﬁc operations of this area

in a superior way. It is demanded, thus, to form scien-

tiﬁc concepts” (Vygotski

ı et al., 2012) apud (Kutzke

and Direne, 2015). It has to be an empirical appre-

hension of reality in computer programming learn-

ing, even the concept assimilation in its ﬁnished form,

“the error is certainly part of the process of scien-

tiﬁc concept formation (...) and must be mediated”

(Kutzke and Direne, 2015). Thus, the access to error

records is needed and useful, so it is the relation be-

tween the errors. Kutzke and Direne, in terms of that,

An Automatic Method for Structuring and Recommending Exercises - In Light of Case-based Reasoning, Knowledge Representation and

Error Mediation

357

consider that an instrument for the manipulation of

this relationship would help teachers’ reﬂection about

students’ errors.

3.1 FARMA-ALG

FARMA-ALG was developed for helping teachers

and students in teaching and learning computer pro-

gramming. Speciﬁcally, FARMA-ALG uses error

mediation as a main role in the process of knowledge

acquiring. Each question is a computer program-

ming problem, FARMA-ALG compiles andchecks if

the answer is correct or not by the comparison of in-

puts and outputs. FARMA-ALG is well presented in

(Kutzke and Direne, 2015), there are some of main

application’s functions:

Answers’ Similarities Computation is the simi-

larity function determined by the expected output

and the output obtained, according to test case and

answer’s source code.

Search of Answers is facilitated using keywords

and meta-data such as name of the student, class,

time interval etc.

Timeline View where it is possible for teachers

and students to access the answers on a timeline

representation.

Similarity Graph is a functionality of viewing

and manipulating answer records, where is pos-

sible to observe and interact with stored answer

records.

FARMA-ALG is able to recommend to the teacher

answer records and exercises that would be of high

pedagogical relevance for a speciﬁc group of students

through, a semi-automatic recovery of potentially rel-

evant answers. An exercise in FARMA-ALG is a set,

basically, with: title, content, identiﬁers, creation time

and programming language(s). For instance:

{"Title": "is_Palindrome?"}

{"Content": "A palindrome is a word, phrase,

number, or other sequence of characters

which reads the same backward or forward,

such as madam or kayak. Write and compile

a program that finds out if a sequence of

characters is a palindrome or not."}

{"Language": "Pascal, C" }

{"lo_id": c950ded46e4d9e530d61 }

The student gives the answer by coding a program

that the FARMA-ALG evaluates. Each question has

test models of input and output to check automatically

if an answer is correct or not.

Kutzke’s research was made with 80 students and

23 exercises, 3723 answers were collected. The data

was collected and its structure was given by an ontol-

ogy, the next section brings how part of that ontology

was made for the present experiment.

4 STRUCTURED DATA FOR AN

ERROR MEDIATION

This section aims to explain how the amount of data

that came from FARMA-ALG are exported for a con-

ceptual and hierarchical ontology. First of all, an ap-

proach about ontologies in the subsection 4.1. The

exportation is explained at the Subsection 4.2, it is a

quantitative way for error mediation, this is the con-

ception of the Knowledge Base (KB) to be used in a

CBR system.

4.1 Ontologies

According to Cimiano (Cimiano, 2006), “the term

Ontology comes from the Greek ontologia and means

the study of being”. Aristotle (384 - 322 BC) shaped

the logical background of ontologies, brought notions

of category and subsumption. In Computer Science,

accord to Gruber (Gruber, 1995), ontology assumes

the meaning as a formal speciﬁcations from a concep-

tualisation, or a representation of conceptual models

in a certain domain.

Ontologies allow a general indexation schema that

comprehends the knowledge through the similarity

between the concepts. Usually, specialists are the

humans responsible the creation of an ontology. An

ontology representation is given by the individuals,

classes and concepts showed in the nodes and the

edges could assume values giving relation between

the objects.

4.2 Quantitative Error Mediation by

Ontology

The FARMA-ALG data model contains relevant

classes for a teaching framework, such as: answers,

users, teams, comments, questions, etc. The similar-

ity between answers is given in the error mediation

by the teacher, a qualitative way for relation between

questions, answers and students. The FARMA-ALG

data was generated in JSON

(Java Script Object No-

tation), a dictionary structure

. This data was ex-

ported for a OWL semantic, as seen on the Figure 2.

http://rfc7159.net/rfc7159

A dictionary is a data structure that contains, basically,

key and its value.

CSEDU 2017 - 9th International Conference on Computer Supported Education

358

Figure 2: Ontology of Learning Objects.

The root class is Learning Objects and its sub-

classes are: users and exercises. The exercises class is

subdivided in contents and taxonomy. The class Con-

tent contains pairs with titles of the exercises and its

contents. The class Taxonomy is detailed bellow, at

the Figure 3.

Figure 3: Ontology representing the Taxonomy class.

Taxonomy is a class determined to discern the ex-

ercises (or questions) according to subject and difﬁ-

culty. Subject is about the conceptual content that

exercises are in the learning of computer program-

ming, e.g., conditional, iteration, data structures, etc.

The subject tags were determined by the teachers as

they had created the exercises. Exercises, as instances

for the subject class could be assigned for more than

one concept, for example, an exercise tagged as con-

ditional could also be tagged as iteration. Difﬁculty

is a class that subdivided exercises between corrects

and errors up to the answers. The same exercise could

appear in a subclass of corrects and in a subclass of

errors, but must not appear in different subclasses of

errors.

Differently from the subject class, the taxon-

omy class is a dynamic class. The questions in

classes errors and corrects are divided in levels by

the times each one had been correctly or wrongly an-

swered. The assignment is binary, “correct”(True) or

“wrong”(False), in this ﬁrst experiment approach, i.e,

currently, there is no fuzzy classiﬁcation. This exer-

cises approximation by errors is given automatically

and quantitatively, complementing the qualitative way

in the Kutzke’s work.

A Python

program was designed for the exer-

cises classiﬁcation. There are two subsections for the

error classiﬁcation, after an average number of errors,

a ﬁrst cut is given: High and Low. In the High class,

there are the exercises with more than the average of

errors, thus the Low class has the exercises with the

lesser average or errors. The second cut subdivided

High and Low classes in the same way. The sec-

ond cut, in the same way, subdivided High and Low

classes. After that, there are four disjunctive classes

(see Figure 4): High high, High low, Low high and

Low low. With n exercises, it is reasonable to use four

levels, but the ontology could be more complex and

bigger as bigger is the input data. Section 5 brings

details about the data.

Figure 4: Ontology representing the Error class and its sub-

classes.

Formally, in the ontology O of error there is a set

C of concepts C := {High, Low, High high, High low,

Low high, Low low}. The set R of relations R := { is-

SubClassOf, isInstanceOf } and the set A of attributes

A := { title, content }. Relations and attributes are as-

signed, formally, as follows:

(isSubClassO f ) = {(High, Erred), (Low, Erred), ...,

(Low low, Low)}

(isInstanceO f ) = {(Id, High high), (Id, High high)}

(title) = (Id, string)

(content) = (Id, string)

The Knowledge Base is formed by the ontology

of error (Figure 4). The experimental KB conception

is an automatic and quantitative method that uses the

https://www.python.org/

An Automatic Method for Structuring and Recommending Exercises - In Light of Case-based Reasoning, Knowledge Representation and

Error Mediation

359

error mediation topic for the classiﬁcation. This clas-

siﬁcation method, performed as an assistant tool, can

be easily joined to an educational tool as FARMA-

ALG. This tool was developed aiming to improve the

error mediation in the FARMA-ALG. The question is

classiﬁed every time it is answered. For example, if a

question is not correctly answered, its total number of

errors is incremented and the place of the questions in

the tree may change.

5 EXPERIMENT AND RESULTS

The data structured, as seen in the previous section,

are added to the myCBR’s knowledge containers.

The vocabulary is composed by the exercise titles.

The distances in the Error ontology (Figure 4) con-

sequently give the similarity functions. The Kutzke’s

experiment (Kutzke and Direne, 2015) brings an

amount of 23 questions that were used to make the

vocabulary container. The Case Base is a set of exer-

cise lists with those questions.

5.1 Knowledge Containers

Each question in the exercise list is an attribute:

questions = {question

, ..., question

}. All the at-

tributes have the 23 exercises for the vocabulary set:

question

= {Birthday, 1 rad Cosine, ..., Tempera-

ture converting}. All the values are of type Symbol in

myCBR. The similarity or distance in the vocabulary

set brings an important contribution in this research.

The distance between the questions would be helpful

to generate similar exercise lists that are given for a

same class. A list of questions is structured in a bal-

anced way, i.e. with questions from a varied levels of

difﬁculty and subject.

Each attribute has the same similarity function

given by a default table, as seen at section 2.1. The

structured graph gives the distance between an ele-

ment and another. Those distances are used to ﬁll in

the table of the similarity function. The distance d be-

tween two elements x and y in the ontology is given

by the sum of the weights w in the path, given by the

formula:

d(x, y) =

∑

i=1

where i is the given value by each time an edge is

crossed, starting with 1 untill the last node, i.e. the y

node. For instance, from x to y there are four nodes

(we don’t count the x as one of them), then n = 4.

The weight w

is given in each edge. For the present

knowledge, each edge has the weight of 0.125. Triv-

ially, it takes into account how many nodes had been

Table 1: A sample Table with an example of the similarity

function determined by the ontology in the Figure 5.

Temp. Conv. Rep. Nums. Prime F.

Temp. Conv. 1 0.75 0.5

Rep. Nums. 0.75 1 0.5

Prime F. 0.5 0.5 1

visited and multiplies by the weight. As w has a

unique value, the distance can be represented by:

d(x, y) = #visited nodes × w.

To ﬁnd the similarity sim between two elements x

and y, it could be possible to use a simple transforma-

tion functions, recommended by (Cimiano, 2006):

sim(x, y) = k − d(x, y)

where k is an appropriate constant. For the present

KB in this research, k = 1. To ﬁnd the similar-

ity between the questions ‘Prime Factors’ and ‘Birth-

day’ as in Figure 5: if the distance d is given by

d(’Prime Factors’, ’Birthday’) = 0.25, then the simi-

larity is given by sim(’Prime Factors’, ’Birthday’) =

1 - 0.25 = 0.75.

Figure 5: Part of ontology structured with weights between

elements and classes.

Table 1 shows a few examples of how the de-

fault similarity function is settled for myCBR. The

distance d between the exercises “Prime Factors” and

“Repeated Numbers” as seen in Figure 5 is given by,

d(’Prime Factors’, ’Repeated Numbers’) = 0.5, then

the sim(’Prime Factors’, ’Repeated Numbers’) = 0.5.

This similarity rate is given twice in the table, at the

3rd row with the 2nd column and at the 2nd row with

the 3rd column.

The experimental queries were composed accord-

ing to three parameters as critical success factors:

Balance is a boolean variable, it is considered bal-

anced an exercise list in which at least three exer-

cises are elements from different subclasses in L.

Amount of F values in a query.

CSEDU 2017 - 9th International Conference on Computer Supported Education

360

Figure 6: An query example from Group 1 in myCBR.

Figure 7: A retrieve example from the Group 4 in myCBR.

Unknown values in the query.

The Case Base for the experiment is composed of

2000 exercise lists, each list is a case. It is deter-

mined a set F = {‘

E k-alternante’, ‘Co-seno de 1 ra-

diano’, ‘Matriz de Vandermonde’, ‘

E palindromo?’}.

There are four values in the set F, each one is picked

from the levels subclasses L = {High high, High low,

Low high, Low low} at the ontology to provide bal-

anced lists. F is included randomly in each list of

case base, i.e. all the cases in the case base have the

F elements. That was made because the order of the

elements is relevant for myCBR.

An amount of 30 queries were made in six dif-

ferent groups. Each group has a quantity of queries,

quantity of elements of the set F, the presence of

an unknown value ( unknown ) and unbalanced

queries. An unbalanced query is a list with exercises

of a same level, what is very important to observe

because in a trustworthy CBR system for this con-

text would not ﬁnd cases with a high similarity. The

groups were divided:

Group 1: 12 queries with no elements of F;

Group 2: 3 queries with one element of F;

Group 3: 3 queries with 4 elements of F;

Group 4: 8 with an unknown value ( unknow );

Group 5: 4 queries where all the exercises are in-

stances of a same subclass in the difﬁculty level.

A query in myCBR is predetermined as the features

structure in the vocabulary container, as seen in the

Figure 6.

A list of cases in order of similarity is given at

myCBR retrieve, the Figure 7 presents a sample of

the cases retrieved, the darker the cell, the bigger is

the rate of similarity. A table ordered by the highest

similarity for each group of retrieving is given in the

Table 2. Obviously, the more elements of F are in the

Table 2: Table ordering the groups of queries by the simi-

larity rate in the retrieving.

Highest

Sim.Rate

Group 3 0.89

Group 2 0.77

Group 1 0.77

Group 4 0.73

Group 5 0.63

query, the bigger is the similarity rate. In the Group

1, myCBR retrieved results with a similarity rate of

0.77, it is good considering the fact that there is no

element of F in the query. And this proves the my-

CBR capacity in retrieving distincts exercise lists by

the similarity.

Relevant points were veriﬁed in this research: case

retrieving, knowledge representation and similarity

relation between elements. There is no adaptation on

myCBR 3, what is a another point that could be veri-

ﬁed for the stated research.

6 CONCLUSION

This work considers that ﬁnding creative solutions for

structuring and retrieving learning objects in learning

tools are relevant for educational informatics. Case-

based reasoning method seems useful as an exercise

lists retriever. CBR systems can be used in educa-

tional solutions as learning object recommender and

automatic creation of exercises. In this research, the

context is the computer programming teaching, but it

can be applied to others disciplines.

Another important point explored in the present

work is the quantitative error mediation by an auto-

matic classiﬁcation of exercises. That is a creative

and role of error way to classify how hard may an

exercise be, that shows the importance of error in ed-

ucation. This dynamic way would help to understand

how an exercise can be harder than another in a dever-

siﬁed class of students. Example, a distance learning

system is used for teaching Math. The teacher’s class

brings 300 exercises. They are divided in: basic oper-

ations, geometry, algebra, etc. Different exercise lists

are given for the students. After they have answered

this lists, the exercises are classiﬁed up to the difﬁ-

culty. This classiﬁcation are used in the test elabora-

tion for that class. And a certain quantity of different

exams can be automatically generated and applied.

This research were developed in the context of the

project ”Pesquisa de redes sociais em nuvem voltadas

par objetos educacionais” of the Brazilian Ministry

An Automatic Method for Structuring and Recommending Exercises - In Light of Case-based Reasoning, Knowledge Representation and

Error Mediation

361

of Education at the C3SL

laboratory of the Federal

University of Paran

a. The learning objects generated

can be integrated with the digital repository of this

project.

6.1 Contributions

It is possible making myCBR a tool that automati-

cally creates, distinct exams for distinct students. This

work suggests that the CBR cycle is useful in the de-

signing of a tool for automatic creation of exams. An-

other relevant contribution is, in light of error media-

tion, an automatic creation of a knowledge base that

considers how many times a question has been mis-

takenly answered by a group of students.

6.2 Future Directions

Studies that experiment reasoning methods for auto-

matic creation of exams seem to be very useful. To

trust the CBR as an interesting method for that, an

adaptation task should be tested.

In the current representation knowledge area,

greater repertories of programming exercises will be

welcomed, because a big amount of data can be struc-

tured in a more complex ontology, what helps the va-

riety of lists and also makes retrieves better with more

accuracy at the similarity.

Adding other variables such as the chronological

way that the questions had been solved, the user level

and a fuzzy classiﬁcation of errors will be very help-

ful for a better exercise list build and its recommen-

dations.

ACKNOWLEDGEMENTS

We would like to acknowledge the Brazilian Fund-

ing Agency (CAPES) for the ﬁnancial support of this

work.

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