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This article was downloaded by: [University of New Mexico]On: 22 November 2014, At: 00:15Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK
European Journal of EngineeringEducationPublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/ceee20
Teaching and learning conceptions inEngineering Education: an innovativeapproach on MathematicsMario Neto Borges a , Maria Do Carmo Narciso Silva Goncalves b &Flavio Macedo Cunha ca Electrical Engineering Department, Federal University, Sao JoaoDel Rei—UFSJ, Brazilb Biomedical Engineering Department, Federal University of SaoJoao Del Rei, Brazilc Catholic University of Minas Gerais—PUC/MG, BrazilPublished online: 08 Dec 2010.
To cite this article: Mario Neto Borges , Maria Do Carmo Narciso Silva Goncalves & FlavioMacedo Cunha (2003) Teaching and learning conceptions in Engineering Education: an innovativeapproach on Mathematics, European Journal of Engineering Education, 28:4, 523-534, DOI:10.1080/0304379032000101791
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Teaching and learning conceptions in Engineering Education:
an innovative approach on Mathematics
MARIO NETO BORGES{*, MARIA DO CARMONARCISO SILVA GONC ALVES z and FLAVIO MACEDOCUNHA§
A worldwide problem in Engineering education is the high rates of students’ failureand drop out particularly at the beginning of the course. This is related to theprocess by which students learn Mathematics. An innovative methodology ofteaching calculus was developed and it is presented in this paper. The approach,based on both course modularisation and the error theory, is student centred. Itfosters student/lecturer commitment and emphasizes continuous assessment of theprocess. Knowledge, in this work, is regarded as a construction and reconstructionprocess based on phenomenological and hermeneutic concepts. Survey resultsdemonstrated the effectiveness of the applied methodology.
1. IntroductionIn order to approach the topic of teaching/learning process this paper takes into
account two important issues: on the one hand, the assessment of theories on howknowledge process takes place and, on the other hand, people’s conception aboutknowledge itself. This debate takes place within the epistemological field given thatthe focus is on knowledge as a way of understanding the lecturers’ pedagogical prac-tices. First and foremost this paper recalls the traditional studies that discussed the actof knowing as a relation between the subject who knows and the object of knowledge.This relation has its roots in the debate between rationalism and empirism which,despite being overcome in the philosophical field, still lingers on as a background forpedagogical practices in many schools that keep considering knowledge as being situ-ated in one of the poles either in the subject or in the object. These views having beensurpassed by the theories based on phenomenology and hermeneutics which in turn,despite presenting different approaches one another, make possible a complementaryunderstanding of the teaching/learning process. These theories consider that know-ledge takes place as an interaction process involving the subject and the object.Last but not least, as regards the conceptions about knowledge, the issue is whetherit is an insight or a construction. Rational and empirical assumptions lead to the firstconception whereas phenomenology leads to an understanding that knowledge is aconstruction process or, if a hermeneutic approach is taken, knowledge is seen as
{ Electrical Engineering Department, Federal University, Sao Joao Del Rei—UFSJ, Brazil.z Biomedical Engineering Department, Federal University of Sao Joao Del Rei, Brazil.§ Catholic University of Minas Gerais—PUC/MG, Brazil.* To whom correspondence should be addressed. e-mail: [email protected]
European Journal of Engineering EducationISSN 0303-3797 print/ISSN 1469-5898 online # 2003 Taylor & Francis Ltd
http://www.tandf.co.uk/journalsDOI: 10.1080/0304379032000101791
European Journal of Engineering Education
Vol. 28, No. 4, December 2003, 523–534
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a reconstruction process. This paper tries to shed light on those issues, finding on thema conceptual basis for underpinning pedagogical practices and alternative methodo-logies applied to the teaching/learning process.
As an example of a practical and successful experience, which took into accountsuch issues, this paper presents the case developed in the Engineering course at theFederal University of Sao Joao Del Rei (UFSJ) in Brazil. The experience as well asthe results show how teaching/learning is approached—in actual Engineeringcourses—based on the concept of knowledge as a construction/reconstruction process.
2. Knowledge approach in the rationalism and empirism conceptionsAccording to Cortella (1999), one of the crucial aspects of pedagogical practice is
the conception about knowledge. In that sense it is necessary to consider the followingquestion: ‘is knowledge acquisition a process that involves discovery or construction?’This topic is approached by considering knowledge as a process which sets up a rela-tion between the cognitive subject and the known object.
The rational/empirical model brings the idea of knowledge as a discovery process,that is, a conception according to which truth and knowledge are hidden somewherewaiting for someone able to get there and discover them. This is a point of view thatdoes not consider how the knowledge acquisition process takes place. In this case isknowledge (truth) in the subject or in the object? In order to answer this question itis necessary to consider the point of view of both philosophical theories which discussthis problem: rationalism and empirism.
For rationalism the source of knowledge is in the subject who knows as a result ofone’s deductive reasoning ability. In this conception the subject brings possibilitiesof self-knowledge and self-learning which manifest themselves on the object of know-ledge (innate). In other words, intellectual development happens in-out, dependsessentially on the subject, not on the environment, and refers to a subjective process.It is also argued that in the knowledge acquisition process the subject plays an activerole and acts on the object of knowledge. The object itself is neutral and static andonly receives the action from the subject.
According to the rationalist conception, the learning process consists of emphasi-zing those theoretical models in which value is given to what a subject thinks of reality.It considers memorization, intellectualism, deductive reasoning and ideas about thingsas valuable issues.
On their turn, the empiricists believe all knowledge comes from experience.Knowledge consists of an environmental act on the subject. External stimulus wouldbe caught by the human senses which receive data or information coming from theobject as if the object had the ability to transfer its essence to the subject, thus present-ing reality as it is to the subject. The subject is passive, contemplative, being influ-enced and indoctrinated by the truths which come from the object. As opposed tothat, the object is active and leads the act of knowledge. The mind, in this case, is ablank sheet where data and information of the external world will be recorded.
The focus of this learning process conception lies on knowledge resulting fromexperimental and measurable data. Knowledge validation is based on the scientificmethod applied—a model intrinsically linked to positivism. The active role playedby the student is stressed and knowledge is acquired by action and experience. In otherwords, the phenomenon to be learned is in front of the subject, meaning the idea of theobvious fact.
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In the Cartesian conception consciousness may reach truth by pure self-intuition,without the need to consider a relation with language and tradition. Nevertheless, theidea that the subject has of the world does not come exclusively from inside as if itwould be part of the subject’s nature. The subject’s conceptions, language, values (thatare already available when the subject is born and that are learnt by living in the world)by which the world is thought, result from a social process, that is, they are not privateitems of the subject, but rather inter-subjective.
In the empiricist conception ‘the blank sheet theory offers a poor and simplisticexplanation of consciousness, without addressing the complexity of its ways and itsintentions’ (Gomes 1983). It is not possible to experience an empty consciousness andmore difficult yet to know its pure impression, giving that reflecting assumes a ready-made consciousness. In fact, the subject approaches facts, experience, and texts, byalways bringing a previous comprehension. The facts faced by the subject becomemeaningful depending on the subject’s previous knowledge of the world.
Kant tried to address this controversy between Rationalism and Empirism by advo-cating that thinking and experience are both sources of knowledge (Hessen 1987).Following Kant’s reasoning, in every knowledge act the ways of the spirit have a priorintervention as a condition for experience to take place. In other words, knowledgeprecedes experience; nevertheless thinking is what gives it a shape. On the other hand,experience is what actually provides the object of knowledge. The object, which is per-ceived by the human senses, is organized by thought since the previous elements ofreason make this organization possible—this is a phenomenon that happens in thespace and time of cognitive consciousness. In Kant’s words, ‘to know is to know some-thing’ (Pascal 1996). Human knowledge refers to the world of phenomena, not beingpossible to know the object itself. Kant’s contribution to epistemology made it possibleto introduce the concept of knowledge as a construction, since it considers that mindchanges from a passive agent to act modelling, classifying and organizing the world.The later development of phenomenology takes into account this principle, accordingto which to know is to know something.
3. Knowledge construction and reconstruction: a phenomenological andhermeneutical approach
Phenomenology and hermeneutics enabled the observation that knowledge sets upa relation between the subject who knows and the object known, and therefore fromsuch relation truth and wisdom emerge. Knowledge (truth) is neither in the subjectonly (rationalism) nor in the object only (empiricism) but rather in the interactionbetween them, that is, the knowledge that springs up from the relation between thesubject who knows and the object of knowledge. Both subject and object are activeparts of the process.
Phenomenology considers important the description of phenomena which appearto consciousness. Phenomenology theory ‘searches to describe the intentional actsof consciousness and of the objects addressed’ (Capalbo 1983). Oliveira (1996), refer-ring to Husserl’s studies, stresses that consciousness as intentionality is fundamentallyaimed at something. This argument contrasts with the one which advocates that it ispossible a pure consciousness. On the other hand, it does not exist an object itself, theobject only exists for the subject who gives it a meaning. This argument is opposed tothe empirism for which the object has a prior meaning.
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Hermeneutics argues that the knowledge act entails a previous comprehension, acultural memory—language, theories, myths, points of view—and therefore, they draftan interpretation of the text or fact which is faced. This sketch may be reasonablyadequate requiring a later analysis of the text and context. Each interpretation happensunder the light of what is known and what is known may change as interpretation isbeing processed. The Hermeneutics considers the historical process as a principle forhuman being comprehension. The search for truth and understanding takes placewithin a tradition to which all individuals are subject and which makes understandingpossible. This tradition is an aspect that determines and makes possible each and everyunderstanding.
Thus, in phenomenology understanding means the acquisition of a way of beingwhich appears to the subject, whereas understanding in hermeneutics considers thehuman being, the world, as possible symbols of interpretation. Both of these concep-tions are opposed to the classical conceptions from rationalism and empirism.
Therefore, the issue of knowledge is not satisfactorily approached neither byrationalism nor empiricism, that is, the construction of reality cannot be carried outby systematic deduction neither is reality a fact that appears ready in front of the cog-nitive subject. Moreover, it is within the phenomenological-hermeneutic frameworkthat one finds ‘the possibility for human beings to be critically placed in the knowledgecontext’ (Siebeneichler 1983).
It is also relevant to refer to the point of view of Demo (2000) who contrasts thenotion of construction with that of reconstruction of knowledge. In the first, realitywould be caught by the perception and mental system which interprets it in a construc-tive way. The latter is a hermeneutic view according to which ‘we learn from what wehave learnt, know from what is known, perceive reality within a certain previous con-text’. Demo privileges the second notion although he considers this as an unproductivedebate. This paper does not aim at probing deeper into the question as it considers thetwo as complementary approaches in the sense that what prevails, in both situations, isthe argument in favour of a subject’s autonomy through the learning process. As aresult, this paper argues that the teaching/learning process may be seen as a pheno-menon of construction/reconstruction of knowledge.
In this conception students play an active role in the learning process by bringingtheir own history, experience, initiative and autonomy. The context and the momentin which learning is developed are vital in this process in which participants interactwith a new situation (a text, a theory, an experiment). In this approach knowledge isgenerated through the interaction between the subject and the object in a way that bothsubject-object and subject-world are integrated in knowledge dynamics.
4. The innovative approach on teaching and learning calculusThe Federal University of Sao Joao Del Rei—UFSJ is a peculiar institution of
higher education given that all its undergraduate courses offer classes at night. Mostof its students work and travel every single day searching for knowledge and qualifi-cations. Those students have demonstrated low performance levels related to theirachievements in the Engineering subjects and, as a result, failure and drop out ratesare considerably high.
This problem in engineering subjects, especially calculus, has being an importantissue for UFSJ, as much as it is for other national and international institutions (Regoand Fossa 1998). Several reasons for the problem have been listed and most of the
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times the students have been blamed. Because of that, some institutions in Brazil(Silva et al. 1998) have carried out surveys aiming at diagnosing the general teachingand learning conditions in night Engineering courses.
The work presented in this paper aimed at drawing the students profile in order tosuggest an alternative methodology to improve the students’ learning quality and per-formance. The methodology developed is based on the teaching/learning process asknowledge construction/reconstruction. This innovative methodology was tested inseven groups (from seven different semesters) at UFSJ. The groups were characterisedas follows: students were interested in Engineering; although they had difficulty inlearning Mathematics they liked it; they were enrolled in five subjects each semester(average); they did not plan their studying time and often asked for help.
Survey results demonstrated that the more students fail in calculus the more diffi-cult it becomes to learn the subject. Successive failure leads students into questioningnot their appreciation of Mathematics, but their course option. In general, as they flunka subject, students tend to fail in others. Low performance leads to lack of interest.When asked to identify the reasons for their own failure students always say they lackstudy time at home since they have to work.
This study has identified the reasons for students’ low performance during theteaching and learning process. External influence factors deriving from the social eco-nomic background are: daytime work, living in another town, lack of time to study andabsence or late arrival for night classes. Intrinsic factors deriving from psychological(emotional and cognitive) difficulties are: lack of underpinning knowledge, difficultyin learning mathematics and cumulative failure at the beginning of the course.
In this scenario, in 1992 an innovative methodology of teaching and learningcalculus was developed and implemented in Engineering courses at UFSJ aiming atminimising the educational problems caused by failure and drop out.
4.1. Applied methodology
The pedagogical innovation proposed to promote change in this scenario was basedon the concept of knowledge as a construction/reconstruction process. From experi-ence in the classroom and reflections upon the students’ failure to achieve the expectedlearning outcomes (Otter 1992), some guidelines were defined such as: teaching pro-cess planned for real students rather than for ideal ones; lecturer and students commit-ment to achieve the learning outcomes; learning time flexibility; mistake, understoodas both a condition to learn and a way of identifying students knowledge and, as a con-sequence, a way of re-structuring teaching; continuous evaluation of the teaching/learning process (formative assessment).
4.1.1. Course planningConsidering the philosophical basis described above, two approaches were adopted
for this proposal. The first one considered the lecturer-subject and the student-object ofknowledge. In this case it is necessary to know the student to be prepared as a wayof supporting the pedagogical practice. This relation must be present throughout theprocess and it is a central issue in course planning. It is important to emphasize thatthe object only exists for the subject that gives it a meaning. And what is the meaningof the student to the lecturer?
In order to address this concern it was necessary to stress the relevance of thecourse planning. It was set up as a co-operative agreement aiming at fostering partner-ship between lecturer and students for the sake of students’ success. Course planning
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was presented and a previous and consensual set of rules and regulations was drawnup. In this opportunity a friendly relation with the students was demonstrated in orderto build positive expectation that may build a favourable teaching/learning environ-ment. The next step was a questionnaire applied to the students as a way of keepingin touch with them and starting the formative assessment.
The second approach considered the student-subject facing the object of know-ledge. In this case the student was considered having a cultural memory which wouldbe changed and improved during the course and must be taken into account whendeciding the teaching/learning strategies. This approach supports the needs for theformative assessment components right from the beginning and throughout the course.It is important to stress that throughout this assessment procedure the relationshiplecturer-subject and student-object of knowledge was exercised.
A preliminary test was applied, comprising simple questions and involvingfundamental concepts considering that it would verify previous learning as the basisfor planning the teaching/learning strategies for the next steps, therefore puttingcourse planning in practice. As far as a permanent formative assessment is concerned,it was a way of keeping students continuously involved and questioned so as to leadthem to the construction/reconstruction of knowledge by exploring the error logic(Hoffmann 1993).
During interaction between lecturer (subject) and student (object) teaching/learningstrategies were chosen from the ones described below:
– group work, supervised by the lecturer, aiming at working with students aspersons, assessing students individually, motivating them to learn and develop-ing co-operative learning while promoting a physical and affective relationship;
– work on the blackboard, as a way to develop both self-reliance and the abilityto solve problems by interacting with the whole group which, in turn, makesthem learn how to listen, reflect and work on the error;
– homework, so as to reinforce and fix the concepts and principles learned aswell as to practice self-discipline, allowing students to review and formalisethe acquired knowledge by giving them the opportunity to question the studiedcontent;
– lecture, the lecturer leads the group aiming at motivating them to start impor-tant topics and inviting them to exercise analysis and synthesis of a particularunit focusing their attention to the difficult points so as to promote analysis andreflection;
– self-assessment, to make students reflect upon their mistakes and, as a result,develop the ability to perform critical analysis and having positive attitudes;
– re-assessment, aiming at giving students the opportunity to review the topic inwhich they did not succeed in demonstrating the learning outcomes for a sec-ond chance summative assessment—hopefully successful;
– informal conversation, with the objective of establishing a personal relation-ship thus enabling a closer contact between lecturer and students and thereforea demonstration of personal interests from both sides;
– simulations, by using a software package.
4.1.2. Pedagogical resourcesIn order for these actions to take place, texts were produced for each unit, designed
by dividing the content of the course into modules with their set of learning outcomes.
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Group work were set up, aiming at allowing students to: learn at their on pace; acquireknowledge; face their difficulties in understanding the content; have an active partici-pation; get acquainted to specific vocabularies and promote communication betweenstudents and lecturer. These modules comprised relevant information such as the learn-ing outcomes, previous knowledge required, assessment procedure and the teaching/learning strategies, besides making students work on the content.
Use of a suitable software package which promoted interaction by creating linksbetween the textbook and the lecturer material with a collection of selected exercises.The lecturer’s text and didactic material allowed a partnership between students andlecturer throughout the knowledge construction. Having raised questions as a startingpoint, solutions were presented step by step. The collection of exercises allowed stu-dents to reflect on, review, fix and study relevant content at their own pace. Throughoutsolution of exercises, definitions and factual knowledge could be accessed by softwarelinks. Exercises were selected according to the learning outcomes to be demonstrated.At the end of each learning section students had the opportunity to be led to use thesoftware in order to prepare them to explore and create a very large series of exercises.
4.1.3. Process developmentIn order to implement the methodology several activities were designed to be
developed with the students inside the classroom as well as outside, aiming at fosteringthe interaction lecturer-student-knowledge as described below.
Defining activities. Formative assessment is a continuous process focused onstudents’ performance (including students ups and downs) that allowed flexibility tothe teaching plan. Therefore, the lecturer set up a goal to be achieved by students in aweek time, not in an imposed way but drawing students attention to their rights andduties. Those students who did not achieve the goals were given an extra time—theweekend. In such a way it was possible to program homework.
Interacting with the groups. Having defined the activities and having the learningmaterial available, students groups were set and started working. As they read anddiscussed a text in groups, students were allowed to interact with one another, thusbuilding a democratic relationship in which all of them had responsibilities. Given thatpersonal relationship is a continuous process and lecturers are involved, the studentshad to find resources and means to develop effective actions (Ribeiro 1986). Primed bythe group enquiries, the lecturer interacted with the students as many times as neededto reach a satisfactory answer (Vasconcellos 1998). Students should feel stimulatedand capable of noticing that the lecturer believed them and was committed to theiractivities and their lives.
Inviting students to the blackboard. Inviting students to the blackboard in order tosolve an exercise proved effective. Letting them work on the exercise, if there was anydifficulty the lecturer asked other students to help—somewhat fostering interactionbetween classmates and leading the selected student to the right answer. On the onehand the lecturer rebuilds and organises knowledge and on the other hand students, bythe interaction with the lecturer, become critical learners (Hoffmann 1993). Sometimesthe lecturer allowed a wrong answer or solution. In order for the mistake to be usedas source of knowledge an effective verification to understand its origin and structureis necessary (Luckesi 1997). Then the student was encouraged to start again by a set of
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questions which was followed by the right solution allowing the student to recognisethe mistake and to correct it. It was also an opportunity for the whole classroom towatch, reflect and work on the error.
Working together with students during learning activities. Sometimes it is necessaryto gather the group together in order to co-ordinate and reorganise the proposedactivities. The meeting should be used to present information, review topics or focusstudents attention on specific topics (Ribeiro 1986). In such group activities, thelecturer took advantage of presenting the text to be used extra class for reviewing andmaking up for classes missed when needed.
If the group had content difficulty or problems with the approach adopted, one ofthe following alternatives was used depending on the level of difficulty: either the lec-turer explained the question involving students in the understanding of the content; orthe lecturer asked for a stronger student to explain and to solve the problem at theblackboard.
When the group had finished the proposed activities it was necessary to consolidatethe proposed goal in order to start another one. By questioning the students, the deve-loped activity was reviewed and then a summary was prepared emphasising the funda-mental aspects and adding related information.
When the group ended up the module, the objective was to review relevant content.Given that knowledge construction comprises analysis and synthesis (Vasconcellos1994), the module was checked on the whole and the remaining doubts were explainedand solved in a way that promoted students development and stimulated abilities suchas reasoning, organisation and clarification of knowledge.
In this methodology there were activities planned to be accomplished outside theclassroom, in which case the homework was seen as a way to promote students colla-boration through their own knowledge construction. That is, a way of fostering stu-dents reflection, formulating their questions, organising their difficulties andsynthesising knowledge to be discussed with the lecturer (Vasconcellos 1998).Having been set up at the last class of each week the homework should be carried outindividually and handed in next class. After collecting the homework its marking pro-cess allowed lecturer to have a personal contact with each individual student. Thelearning mistakes identified are the starting point for moving ahead and vital to over-come learning difficulties (Luckesi 1997).
Therefore, marked homework is taken back to students—immediately—during thefollowing class so that students may have a feedback of their knowledge and under-standing about the topic studied (Vasconcelos 1995). Mistakes were pointed out andindividual suggestions presented at the same time. Similar mistakes were discussedduring the class with the whole group. Student who had difficulty in that specific topicwere invited to do some of those exercises. Depending on the number of mistakes andtheir importance the student individually was invited to redo the exercise.Alternatively, as an extra-classroom activity, students could take advantage of the col-lection of exercises available in proper software as a process of self-instruction.
4.1.4. Student assessmentAt the end of the module several lists of exercises have been done and marked.
Having carried out the review and explained all the questions, the learning outcomeswere assessed through individual tests. The intention here is not to get a grade but tolearn (Vasconcelos 1995).
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The next class, immediately after the lecturer had marked the test, studentsreceived the test in a way that they know neither the right answer nor the grade.Led by the lecturer students marked their own test and should allocate grades A, B,C or D according to what they think was correct. A was for getting it exactly right,B was for getting it right yet having few mistakes, C was for those who had problemssolving the exercises but somewhat demonstrate the learning outcomes and D for thosewho failed. During this process, and as a way to demonstrate control of the results, thelecturer posed questions to students who had failed in some topics.
After self-assessment had been carried out the tests were returned so that the lecturercould contrast the marking procedure by comparing the lecturer’s own results with thoseproduced by the students. Finally both lecturer and student decided each individual finalgrade for that particular module. During this process specific difficulties and mistakes ifany were listed and activities planned—tailor made—for each student in particular. Anextra-time, previously defined, was given for carrying out remedial activities and a newassessment was booked. By the same token, during this time student took advantage ofthe software package for further practice and consolidation.
In this proposed approach, formative assessment was a lecturer decision to makesure that all students could learn at their own pace. In that sense, reassessment shouldtake place as soon as possible. However, it was necessary to ensure that students stillhad the opportunity to: overcome their difficulties, demonstrate learning outcomes andsucceed in getting approval in that module and, as a result, move on to the nextmodule. Grade D in any module implied student failure in the subject. This was statedin the course plan, discussed and approved at the very beginning of the course.
An important point to be stressed in this approach is that the possibility to even-tually succeed in each module and, at the end, in the whole subject made studentsappreciate the subject and developed motivation. The idea should be inculcated thattheir learning process depended very much upon dedication and persistence, since theywere given enough time and appropriate learning conditions.
At the end of the course each student was asked to carry out a self-assessment.After that, lecturer and student together analysed the student performance in allmodules, including student development, maturity, knowledge, abilities, learning out-comes achievement and self-assessment as bases for the final mark.
4.2. Results
Improvement in students’ performance reducing high rates of failure and drop outwas confirmed by comparing the results obtained in calculus from two different
Figure 1. Results before the methodology.
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groups. Results from the first group were collected between 1987 and 1991—beforethe proposed methodology had been applied. Results from the second group were col-lected between 1992 and 1998—after the methodology was implemented. In the lattergroup a study was carried out contrasting classes in which students undertook theproposed methodology and those in which they did not.
The results were: between 1987 and 1991, 24 classes comprising 1023 studentswere assessed, from these data base 239 students dropped out, 462 failed and 322passed. That means 23.4%, 45.1% and 31.5% respectively. In other words 68.5% didnot succeed as opposed to a success rate of only 31.5%. This can be seen in figure 1.
On the other hand from 1992 to 1998, 27 classes underwent the usual assessmentprocess. From these classes 2 were selected to undertake the new methodology. On thewhole, from 949 students enrolled, 206 (21.7%) students dropped out, 305 (32.15%)failed and 438 (46.15%) passed as shown in figure 2. An improvement can beobserved by comparing with figure 1.
However, specifically for the 2 selected classes comprising 106 students in whichthey undertook the new methodology the results were much more significant. Theperformance of these particular students soared and only 18 (17%) of them gave upthe course, 12 (11%) failed and 76 (72%) passed. This relevant result can be seenin figure 3. This demonstrates that the previous scenario can be dramatically changedby the use of the proposed methodology.
5. ConclusionThe methodology herein described demonstrates that the high rate of student
failure and drop out can be dramatically changed. Having the student’s low perfor-mance as a starting point the following issues were considered in this work: students
Figure 2. Results for mixed classes.
Figure 3. Results for students under the proposed methodology.
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background and attitude, no flexibility of the curriculum content, lack of reading andstudying habits, bad results during the assessment procedures and the assessmentmethodology itself—based only on summative assessment.
The effort to change led to the practical development of an alternative pedagogicalapproach based on the conception that knowledge is a construction/reconstructionprocess that, in turn, is study centred, focused on lecturer/students commitment, errorlogic and continuous assessment (including formative assessment). It was demon-strated that it is possible to achieve positive results in students’ performance whenlearning calculus in Engineering courses by using the methodology which takes intoaccount the principles and concepts discussed in this paper.
Solution for the addressed problem is a result of political attitudes and technicalcompetence. A political commitment which provides relevant educational changesin both course and students as a result of deep transformations coming from educa-tional conceptions.
Therefore, the concept of knowledge being a construction/reconstruction process,when applied to the calculus subject at UFSJ, demonstrated, in practice, that significantimprovement in teaching/learning strategies can be achieved given that learning is nolonger seen as a knowledge reproduction, in which case the role played by lecturersand students, together with the knowledge approach, may vary from the traditionalmodel. Knowledge is not an innate feature; it is not situated in the subject pole neitherin the object pole and cannot be transmitted. Within this conception the student is not apassive person who receives the knowledge and, by the same token, the lecturer is nota knowledge transmitter. In the applied methodology it is clear that learning calculusbecame more effective as a result of the interaction between lecturer-students, havingthe object of knowledge as a reference. Moreover, knowledge as a continuous con-struction/reconstruction process embraces a set of dynamic procedures which makepossible relevant advances in the teaching/learning process.
ReferencesCAPALBO, C., 1983, Phenomenology and Hermeneutics: Selection of Texts (in Portuguese) (Rio de
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(in Portuguese), 2nd edn (Sao Paulo: Cortez/Instituto Paulo Freire).DEMO, P., 2000, To Know and to Learn: Wisdom of Limits and Challenges (in Portuguese) (Porto
Alegre: Artes Medicas Sul).GOMES, F. A., 1983, From the empirism to the phenomenology. In C. CAPALBO (ed.),
Phenomenology and Hermeneutics: Selection of Texts (in Portuguese), (Rio de Janeiro:Ambito Cultural), Chap. 6, pp. 96–121.
HESSEN, J., 1987, Theory of Knowledge (in Portuguese), 8th edn (Coimbra: Armenio Amado).HOFFMANN, J. M. L., 1993, Alternative Assessment: A Building Practice from Nursery to University
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Authors biographiesMario Neto Borges is an Associate Professor at the Electrical Engineering Department at
the Federal University of Sao Joao Del Rei—UFSJ, Brazil, currently, the Rector of
the University. He has 25 years experience in higher education. He received his MSc in
Electrical Machines at Federal University of Minas Gerais—UFMG Brazil in 1985 and his
PhD in Education at the University of Huddersfield UK in 1994. His research interests are
in knowledge-based systems and curriculum development for engineering courses.
Maria do Carmo Narciso Silva Goncalves is an Associate Professor at the Biomedical
Engineering Department at the Federal University of Sao Joao Del Rei, Brazil, currently the
Vice-rector. She has over 26 years experience in higher education. She received her MSc in
Mathematics at UFMG Brazil in 1992. Her research interests are in mathematics and engineer-
ing education.
Flavio Macedo Cunha is an Associate Professor at the Catholic University of Minas Gerais—
PUC/MG, Brazil. He received his MSc in Technological Education at the Federal Centre for
Technological Education—CEFET/MG in 1999. He has over 20 years experience in higher
education. His research interests are in vocational education, philosophy and engineering
education.
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