Internacional Conference on Engineering and Computer Education, IEEE-

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Internacional Conference on Engineering and Computer Education, IEEE-ICECE’05, 14-16 noviembre 2005, MADRID

THE CHALLENGING-PROBLEM METHOD: HOW TO DRIVE THE LEARNING-TEACHING PROCESS FROM REAL-WORLD PROBLEMS TO

THEIR SOLUTIONS THROUGH ENGINEERING SKILLS

Estanis Oyarbide

¹

1 Estanis Oyarbide, Dpto. de Ing. Electrónica y Comunicaciones, Universidad de Zaragoza, Maria de Luna 1, 50018 Zaragoza, Spain, [email protected]

Abstract ⎯ This paper explains a practical innovative learning-teaching experience in the field of Electronics. The process has been carried out in a standard classroom configuration, i.e., more than fifty students per group, fixed chairs and tables, a slide projector and a blackboard. Face to the classical teaching approach (a.device’s theory, b.training problems, c.application problems, d.related concepts), it is proven that “standard” students would be actually motivated if: a)they understand any real problem to be solved, b)they are able to employ previously acquired skills and contents to solve part of the problem, c)this way they reach, by themselves, the border of the problem where the need of a new, concrete and unknown device, tool or paradigm is stated, d)at the end the teacher must simply explain the new and desired device or concept, including the related theory, training problems and laboratory practice.

The paper shows a practical case related to Analog Electronics.

Index Terms ⎯ Challenging-Problem Method, Cognitive Learning, Problem Based Learning, Electronics Learning

I

NTRODUCTION

The construction of the European Higher Education Space has pushed a big amount of work towards the optimal learning-teaching process (LTP). As a result, most of the concerned agents have focused their interest on Cognitive- type LTP face to the more classical Conductive-type LTP. In the frame of these discussions, several important concepts as the leaded or guided discovering process and the net-type knowledge concept have been established: any subject can be reached from many different points provided the adequate question is made by the student (not by the teacher) and that someone guides the student towards the new subject, tool or concept. The key issue of this LTP is not only the fact that students reach a subject by themselves, but also that for doing so the student improves other required skills or competencies.

In the field of engineering education, Problem (Project) Based Learning (PBL) [1] and Cooperative Learning methods (e.g. Case-Method) are commonly employed when a Cognitive-type LTP has to be implanted [2]-[3]. One of the problems of the PBL or similar active learning-teaching theory is the need of a big amount of human and material resources. This fact is limiting the generalization of strict

PBL strategies and states an interesting question: how can we apply the PBL method in a University mainly characterized by large student groups and rigid classroom configuration? And moreover, how can we do so by keeping the budget at a reasonable level?

This paper shows an adaptation of the PBL, the so called Challenging-Problem Method (CPM). This method has been applied in classically configured universities since 1999, and it has shown to be an efficient approach to the Cognitive-type LTP.

First, the paper describes the context, objectives and constraints of this experience. Secondly, motivation and CPM implantation strategy are explained. Next, a practical implantation example is given, finalizing by CPM implantation results and conclusions.

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^ONTEXT

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OBJECTIVES AND CONSTRAINTS The CPM has been applied in the University of Mondragón and in the University of Zaragoza. Fundamental Electronics and Power Electronics related to engineering careers have been the involved subjects. In all the cases it has been an individual (not institutional) attempt towards a better LTP, and so on, habitual restrictions related to the classical education approach had to be considered: a) up to 80 or 100 students per group, b) classical time scheduling, i.e., 40 theory hours in large classrooms and 14 hours in laboratory sessions.

The main objectives of the CPM are not new, as they are usually stated in almost any LTP:

• The student must be able to manage in new scenarios related to previously non-studied problems

• Student must be able to establish a structured analysis approach face to any new requirement

• Student must improve its autonomy, self-confidence and critical spirit

• Student must exploit previously acquired contents and capacities (recovery goal)

There are important environmental constraints:

• The process has to be implanted in a standard large classroom configuration, i.e., more than fifty students per group, fixed chairs and tables, a slide projector and a blackboard

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Internacional Conference on Engineering and Computer Education, ICECE’05, 14-16 noviembre 2005, MADRID

• The amount of preparation work must not explode, i.e., the teacher must be able to design the course (notes, slides, etc...) within the initially forecasted time

C

HALLENGING

-P

ROBLEM

M

ETHOD

Motivation

The main question which pushed us towards a new LTP is the anti-natural approach of the classical teaching chain:

device’s theory → training problems → application problems → related concepts

Usually only the best students are able to follow the explanations along the first theoretical phase. They simply do not understand where the teacher wants to lead them and

“...for what all these formulas and numbers serve...”. In fact, the index of any subject is, itself, a source of troubles for a standard student: how can a student understand the goal of a course if the index is full of terms he or she has never seen before? If we take the example of Analog Electronics, most of related program indexes talks about semiconductors, diodes, transistors, and others instead of battery chargers, AM receivers, audio circuits, etc...

Usually, classical Analog Electronics LTP begins as follow: first, after a “review” chapter, semiconductors’

theory is explained, next, the PN junction theory is treated and finally the diode is presented. In the classroom it takes several hours to travel along the next typical sequence:

solid-state semiconductors → diodes → rectifiers → DC supply → actual DC supply needs (battery chargers, radio supply, etc...)

As it can be observed, the student crosses a large

“desert” equivalent to the 75% of the learning-teaching time in which he or she does not know “...what we are looking for...” or “...for what we are doing all this stuff...”. A more comprehensive sequence would be:

battery charger need, radio supply need... → DC supply need → rectifier need → rectifier topology → rectifier attempt with conventional switch → fast switch need: static switch → solid-state semiconductors → diodes

Challenging Problem Method implantation strategy The previously explained sequence can be easily implemented if the CPM is employed. When a new concept, paradigm or tool has to be learned, next steps have to be followed:

• First, a Challenging Problem (CP) is stated. This CP must be related to an actual scenario in such a way that a new concept, paradigm or tool should be required in the resolution

• Discussion groups of 4 or 5 students are organized (a group per table-array, for example)

• These groups must develop the CP during a time (from 5 to 60 minutes, depending on the CP). They must propose and evaluate several possible solutions using exclusively their own knowledge and capacities

• After this internal discussion-time, a brain-storming session is organized. For doing so each group selects a speaker. The teacher writes or draws on the blackboard all the proposed solutions

• Once all the proposed solutions are listed, they are analyzed in a general classroom session. Students must evaluate the suitability of each proposed solution, retaining the right ideas and rejecting the deficient ones.

During this phase the teacher must act as a simple guide, stimulating and leading the students towards the right way

• As a result of this process, students have reached, by themselves, the proximity of the solution, i.e., the proximity of a new concept, paradigm or tool which would make possible the entire solution. They “feel” the need of a new and clearly bounded topic

After a CP session:

• Student has identified the utility of a desired new concept, paradigm or tool

• Student has evaluated his or her initial abilities and deficiencies regarding the topic

• Student locates his or her own knowledge and capacities in contrast with the rest of the group. This is one of the key issues of the CPM: this is the group, i.e., the colleagues of the student, not the teacher, who has been able to reach the border of the subject

• And definitively, students “feel” the need of learning, and they activate a ready “memory box” in their minds

At the end the teacher must simply explain the new and desired device or concept, including the related theory and training problems. This is the fastest phase of the CPM. It is important to explain “why” the resolution is carried out instead of “how” it is carried out. If the “why” is learned, it can be reutilized in many other different problems, contrary to the “how”, which normally only serves in topologically similar problems (if we refer to the problem’s topology as the set of related variables, equations and constraints).

Because of that, it is interesting to avoid formulas and related summarizing-tables, which push students towards a conductive-type methodology of problem’s classification, reinforcing the “how” instead of the “why”.

It has been always pointed out that, for a given time, PBL and similar active methodologies are not capable of processing the same amount of contents as the conductive- type classical learning-teaching approach does. It has to be admitted that CPM spends more time than the classical approach does in synthesis problems, but this over-time is

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Internacional Conference on Engineering and Computer Education, ICECE’05, 14-16 noviembre 2005, MADRID

compensated by the fast theoretical exposition. As students have been previously motivated, they are able to follow fast theoretical explanations about the new topic. In any case it has to be remembered that it is hard to improve cognitive- type skills out of the classroom, contrary to contents’

knowledge, which can be easily improved by students by their own, using the appropriate lecture note-book.

Learning assessment

As it is well known students are focused in the optimization of their assessment performance. So it would be hard to keep their interest during any LTP if the assessment is not aligned with the intended learning outcomes [4]-[5]. In the other hand, assessment must be carried out keeping at a reasonable level the time that the lecturer must expend in this task. In the frame of large- classrooms under CPM learning strategy, the so called constructive alignment [4] can be achieved if:

• An individual examination is carried out

• Along the examination students must propose a solution to a CP, and so on, their synthesis skill is evaluated

• In another section of the examination, a CP together with several possible solutions are given. Student must evaluate the suitability of each solution, in such a way that critical skill can be assessed

• Conceptual and low-level concrete training problems are also included in the examination

• The examination can be partitioned in several modules, in such a way that in some of them student can employ any document, e.g., lecture-notes. This point is important as far as otherwise most of students would focus their effort memorizing contents, classifying problems by topology and understanding the “how”

instead of the “why”

• Practical sessions must also be evaluated

CPM

APPLICATION EXAMPLE

: DC

^POWER

SOURCE

Any introductory course in Analog Electronics can be organized in two main chapters: Electronic Energy Management and Electronic Information Management (it has to be noted that we use the word “information” instead of “signal” in the title, as the last one is a concept which must be learned along the course).

We are going to give a CPM implementation example related to the Electronic Energy Management. The first part of the index is presented in Table I. As it can be observed, the starting point is the CP1 (section 1.1.1.) related to a battery charger (Figure 1). The word “diode” appears first at the end of point 1.2.5. After some discussions and following the explained CP methodology, the group reaches the transformer plus rectifier topology of Figure 2 (the load can be replaced by a resistor R_L). Any student can understand that the load must be directly branched to the input when a

positive voltage is applied, whereas it must be inversely connected to it when input voltage becomes negative. For doing so four simple switches are needed. It must to be noted that students have reached by themselves this stage of the problem, exploiting their own previous knowledge and capacities, without any need of electronics.

TABLE I

FIRST PART OF THE INDEX OF ELECTRONIC ENERGY MANAGEMENT 1. ELECTRONIC ENERGY MANAGEMENT: DC SUPPLY

1.1. Battery charger

1.1.1. CP1: “We need to charge a small DC battery at home. Provided that the only available energy is an AC power line supply, an AC/DC conversion stage is needed. Design the topology of a device capable of doing so. For that, consider the simplest DC voltage definition, i.e., a voltage with small or large variations but that never inverses its polarity”

1.1.2. CP2: “Provided switches are needed, and in order to evaluate the speed of operation, compute the switch-on and switch-off times of an electro-mechanic relay”

1.1.3. The need of a static switch device. Basic ideas 1.2. Looking for a static-switch

1.2.1. Conductors and semiconductors.

1.2.2. Current conduction in an intrinsic semiconductor. Covalent XXX model

1.2.3. Doping and conduction on an extrinsic semiconductor: P-type and N-type

1.2.4. Influence of the temperature 1.2.5. PN junction and operating modes

• PN junction in equilibrium state: currents, voltages and junction behavior

• Direct polarization: conduction, forward current

• Reverse polarization: blocking, leakage current

• Notation. The Diode

• Diode switching

1.2.6. CP3: “Based on the topology developed along the CP1, replace electro-mechanic switches by diodes, taking into account their polarity”

FIGURE 1.

CP1: BATTERY CHARGER

FIGURE 2.

SOLUTION APPROACH TO THE CP1: TRANSFORMER PLUS RECTIFIER TOPOLOGY

vi vo RL

S1

S2 S4 S3

“DC power supply”

vi vo

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Internacional Conference on Engineering and Computer Education, ICECE’05, 14-16 noviembre 2005, MADRID

Once student has developed the way in which an alternative current is converted to direct current, practical implementation of rectifier can be analyzed. Fist of all, a second CP is stated (section 1.1.2.), forcing students to compute the switch-on and switch-off times of an electro- mechanic relay (Figure 3).

FIGURE 3.

ELECTROMECHANIC SWITCH OF CP2

The resulting switching time values are around 10msec, in such a way that students realize that it is not possible to build a rectifier with conventional switches operated by mobile elements: a faster (static) switch is needed.

After these two CPs, student knows the topology of a rectifier and feels the need of a static switch. At this point, most of students wants to learn how it is possible to get faster speed static switches, and so on, semiconductor’s theory and diode’s operating principle can be easily explained. As it has been noted before, this theoretical phase (from section 1.2.1. to section 1.2.5) is fast, and once the students know the existence of the diode and how it works, it is easy to locate four of them in the previously developed rectifier topology (CP3 of section 1.2.6)

CPM

ASSESSMENT

The assessment of any new LTP approach requires the selection of adequate indicators, in such a way that the

“classical” process can be easily compared to the “new” one.

There are two possible scenarios:

• Both the “new” and the “old” LTP seek for the same learning goals (contents and skills) and the same grading policy is applied

• The “new” and the “old” LTP seek for different learning goals (similar contents but different skills) and so on different grading policy is applied

The first case is the simplest one. As the grading policy evaluates the consecution of the same goals, the resulting scores would be useful as comparison indicators.

Unfortunately our case belongs to the second scenario:

previously non considered complementary skills have been introduced in this LTP, leading to different grading policies and, so on, to non comparable student-scores.

At the end of each lecture period students of the University of Zaragoza are asked for filling a form per each subject and lecturer. At this form they are requested to answer to several questions regarding the LTP of each course. Results of these questionnaires are available to lecturers and complemented with multiple statistics about the same questions regarding other groups, subjects or both them. This data can be useful in LTP comparison tasks if several precautions are taken: in order to avoid exogenous influences, only statistics related to questions which have been answered by the same students’ group at the same year can be used for comparison tasks.

We are going to show CPM application results related to the subject Principles of Electronics, which is inserted at the second year of Computing Engineering grade of the University of Zaragoza. This is quite a challenging case, as this subject often falls out of the area of interest of most of students in computing. Moreover, there is not any other subject related to analog electronics along this five years- long career. We have studied four different cases (case 1 to case 4) related to data from four different groups. Results have been separately grouped in four tables (Table I to Table IV). Each line of the tables is related to a question. The first column of the table collects the average score of the answers to our CPM experience, related to the subject Principles of Electronics. We can denote it as “our score”. The second column collects the average score of the answers related to all the subjects in which the group has been implied along the same academic year. We can denote it as the “group’s score”. All the scores are rated from 1 to 5, in such a way that the maximum score variation is 4.

TABLE I

CASE 1:MORNING GROUP,2003-2004 YEAR difference (relative) difference (absolute) Group’s score Principles of Electronics

subject difficulty 4.26 4.02 6% 8%

1 (low) to 5 (high) importance of the subject

in students’ formation 3.28 3.73 -11% -16%

use of teaching tools and

resources 3.71 3.3 10% 18%

clarity and organization of

explanations 3.7 3.32 10% 16%

efficiency transferring

concepts 3.56 3.2 9% 16%

amenity 3.69 2.91 20% 41%

reinforcement of dialogue 4.08 3.14 24% 44%

1 (very deficient) to 5 (excellent)

reinforcement of students’

motivation against the subject

3.97 3.12 21% 40%

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Internacional Conference on Engineering and Computer Education, ICECE’05, 14-16 noviembre 2005, MADRID

The third column computes the normalized absolute difference between the first two columns as:

( )

100

( )

%

4

' ×

=Our score−Groupsscore abs

Difference

The fourth column computes the normalized relative difference of the same two values as:

( )

100

( )

%

1 '

' ×

−

= −

score s Group

score s Group score

rel Our Difference

The first two lines of the tables analyze students’

perception about the relevance of the subject in their career and the level of difficulty of the topics contained in it. These questions are not correlated with the LTP methodology in such a way that the information contained in them can be used in order to know initial students’ predisposition around the subject. As it can be observed in all cases students think that Principles of Electronics is more difficult than the rest of the subjects and that it is less relevant than other subjects in their formation as Computing Engineers. As it has been previously forecasted, the experimented scenario is quite a challenging case if a new LTP has to be validated.

Looking to the LTP evaluation, it can be observed that the average score of Principles of Electronics under the CPM is always better than the average score of the rest of the subjects. As it can be expected the “use of teaching tools and resources” is better in all the cases (from 16% to 18%

higher).

TABLE II

CASE 2:AFTERNOON GROUP,2003-2004 YEAR difference (relative) difference (absolute) Group’s score Principles of Electronics

resources 3.64 3.24 10% 18%

concepts 3.58 3.29 7% 13%

amenity 3.42 3.07 9% 17%

3.67 3.3 9% 16%

The “clarity and organization of explanations” is one of the key-items of CPM evaluation, as this new method employs a non-conventional sequence of explanation.

Nevertheless, students think that the “clarity and organization of explanations” is higher (from 16% to 28%) than the average of other “conventional”-type LTP. Students also think that the “efficiency transferring concepts” is better than other LTPs (from 13% to 31%).

TABLE III

CASE 3:MORNING GROUP,2002-2003 YEAR difference (relative) difference (absolute) Group’s score Principles of Electronics

in students’ formation 3 3.69 -17% -26%

resources 3.57 3.22 9% 16%

concepts 3.81 3.14 17% 31%

amenity 3.58 2.92 17% 34%

3.7 3.06 16% 31%

TABLE IV

CASE 4:AFTERNOON GROUP,2002-2003 YEAR difference (relative) difference (absolute) Group’s score Principles of Electronics

1 (low) to 5 (high)

importance of the subject

resources 3.7 3.28 11% 18%

concepts 3.83 3.29 14% 24%

amenity 3.47 3.13 9% 16%

3.7 3.22 12% 22%

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Internacional Conference on Engineering and Computer Education, ICECE’05, 14-16 noviembre 2005, MADRID

Regarding the classroom “working clime” most of students think that CPM based environment is better than others (from 16% to 41% better in “amenity”). Two of the goals of the CPM are the improvement of students’

motivation and the reinforcement of the dialogue at the classroom. Looking at the results collected at the last two lines of each table we can conclude that the two objectives have been achieved. Students feel that dialogue in the CPM based-subject is better than in other subjects (from 19% to 44% of improvement) and that their motivation face to Principles of Electronics is much higher than in other subjects (from 16% to 40% of increase in motivation).

Taking into account that students consider that this subject is harder than the others (first line of the tables) and that it is not as important as the others (second line of tables), the fact that their motivation is higher with this subject than with the others is an encouraging result: clearly, CPM allows to increase students’ motivation and to reinforce the dialogue (maximum improvement score), together to other “collateral” improvements.

Regarding other objectives of the LTP, it has to be noted that, after the course, most of students have lost their

“white sheet panic complex”, i.e., they have reinforce their self-confidence and creativity level face to synthesis problems, one of the key skills of an engineer. In the same way, and thanks to all the discussion and brain-storming sessions, the critical spirit has also been reinforced.

Taking into account that new skills are being tested, overall results of students at their examination are quite good. Figure 4 shows the distribution of the examination scores related to the Cases 1 and 2. The horizontal axis sets intervals of one point along the score values (from a minimum of 0 to a maximum of 10). Each bar reflects the percentage of examination’s scores in each interval. As it can be observed results are quite satisfactory and 65% of students pass the examination at their first attempt, getting a quite constant distribution at high score values.

Nevertheless, data from several years of experience will be necessary in order to get accurate conclusions from the analysis of students’ score values.

FIGURE 4

PERCENTAGE OF EXAMINATION SCORES IN EACH SCORE INTERVAL

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ONCLUSION

A practical cognitive-type LTP approach has been presented.

One of the characteristic of this approach is that it can be implanted keeping the preexisting human and material resources.

Previous to any theoretical dissertation, students are stimulated and leaded towards the border of the related topic by an adequate Challenging Problem. Thanks to this stimulating effort, theoretical dissertation phase becomes easier and faster. Students are forced to reutilize their own previously acquired skills and knowledge, in such a way that self confidence is reinforced. Thanks to brain-storming sessions followed by discussion sessions students improves their critical spirit.

The CPM can process almost the same amount of contents as the conductive-type classical learning-teaching approach does. There are two main problems related to this LTP. First, it takes several hours to the students to understand the CPM mechanism, as it usually becomes the first non-conductive type learning process for most of them.

Second, there would be some topics for which it becomes difficult to find out an appropriate challenging problem.

Student’s evaluation of the CPM leads to satisfactory conclusions related to several LTP outcomes, as the motivation reinforcement, classroom amenity and the efficiency transferring concepts. More data from future years will be necessary in order to establish a suitable analysis of students’ examination scores.

We can conclude that the overall outcome is highly positive.

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EFERENCES

[1] Donald Woods, “Problem-based Learning, especially in the context of large classes”, http://chemeng.mcmaster.ca/pbl/pbl.htm, McMaster University, 2005

[2] Clark, D., C., "High-Risk Teaching", The Teaching Professor, Vol, No 8., October 1994, pp.1-2

[3] “Teaching & learning support: Principles of effective university teaching”,

http://www.tedi.uq.edu.au/teaching/toolbox/tlprincipals.html, The University of Queensland, Australia, last modified in January 2005 [4] Biggs, J., “Teaching for quality learning at university”, SRHE & Open

University Press, 2003

[5] Houghton, W., “How can Learning and Teaching Theory assist Engineering Academics?”,

http://www.engsc.ac.uk/er/theory/index.asp, Engineering Subject Centre, University of Exeter, 2005

0 5 10 15 20 25

1 2 3 4 5 6 7 8 9 10

Student’s score value

%

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