Using an Expected Loss Function to Identify Best High Schools for Recruitment Sonia M. Bartolomei-Suárez1 , David González-Barreto2 and Antonio A. González-Quevedo 3 Abstract - An objective of the strategic plan of the University of Puerto Rico Mayagüez (UPRM) is to identify and attract the best possible prospective students from high schools to the College of Engineering. To address this objective a good first step is to identify the high schools that produce, over a period of years, the students that better executed within our institution. The student performance (SP) at undergraduate level is currently available in databases on the institutional research office. In this work, the SP is combined through indicators to develop an index per high school based on the performance of their students in UPRM College of Engineering. The performance index (PI) is based on the concept of the expected loss function. In this function the actual performance for each indicator is compared against an expected or targeted value. The PI includes the distance between the actual and the targeted performance for all defined indicators, thus the objective is to minimize this index. The better schools will results in indexes that are very low, indicating very good SP for their respective students. The PI is a tool that can be used both by the UPRM admission office and by high schools to do benchmarking among them. This paper presents a case study for the high schools that supply students to the UPRM engineering college for a period of six years. The defined indicators for the case study includes: graduation GPA, average time to degree, and graduation rate. Index Terms – Prospective performance index, loss function. students, recruitment, INTRODUCTION value of the IGS is 400. The weight of the GPA is 50%, while the weight for each of the two aptitude tests is 25%. Each academic department or program determines each year the minimum value of the IGS for the entering students. In general terms, no other measurement is used to admit a student in the first year of university studies. For the engineer class of 2004-2005, the minimum IGS fluctuated from to 313 for Surveying to 342 for Computer Engineering. PERFORMANCE OF OUR ENGINEERING STUDENTS IN THEIR HIGH SCHOOLS This study presents the best high schools, private and public, from the perspective of the student performance at the University of Puerto Rico at Mayagüez. The high schools that were included in the study have sent more than 50 students who have graduated from our School of Engineering in the past ten years (1995-2005). This study was generated using data obtained from the Office of Institutional Research and Planning of our university. The 15 public high schools that have the greatest number of engineering graduates in the past ten years are shown in Figure 1. The top three schools: CROEM (397 students), Patria Latorre (182 students) and Eugenio María de Hostos (158 students) are in our geographic region, the Western part of Puerto Rico. As a matter of fact, eleven of the fifteen public high schools are located in our geographic region. Only two of the fifteen schools are located in the capital city of San Juan, which is the largest city in Puerto Rico. These schools are the University Gardens High School (146 students) and the High School of the University of Puerto Rico (108 students). CROEM, Mayagüez 397 Patria Latorre, San Sebastian 182 Eugenio María de Hostos, Mayagüez 156 Efrain Sánchez Hidalgo, Moca 149 University Gardens, Río Piedras 146 Blanca Malaret, Sabana Grande 143 Luis Muñoz Marin, Yauco Escuelas Públicas A study of our entering student profile demonstrates that a large number of them come from the Western part of the island of Puerto Rico, our geographic region. (1) The school of engineering is interested in attracting good students from all the geographic areas of Puerto Rico. With this goal in mind, this study was developed to identify the best schools in the island based on the performance of the engineering students in our university. 140 Miguel Meléndez Muñoz, Cayey 127 Lola Rodríguez de Tió, San Germán 126 Benito Cerezo, Aguadilla 112 Luis Muñoz Marin, Añasco 112 Dr. Carlos González, Aguada DESCRIPTION OF ADMISSION CRITERIA 109 Secundaria UPR, Río Piedras 108 Domingo Aponte Collazo, Lares 106 Ramón José Dávila, Coamo The admission index, which is called the IGS, is composed of the high school grade point average, the verbal aptitude test score and the mathematics aptitude test score from the College Board Entrance Examination. The highest possible 106 0 50 100 150 200 250 300 350 Cantidad de Estudiantes FIGURE 1 FIRST 15 PUBLIC HIGH SCHOOLS WITH 50 OR MORE GRADUATES AT UPRM FOR THE COLLEGE OF ENGINEERING (YEARS 1995-2005). 1 Sonia M. Bartolomei-Suárez, Associate Dean of Academic Affairs, School of Engineering, University of Puerto Rico, Mayagüez, [email protected] David González-Barreto, Associate Professor, Industrial Engineering Department, University of Puerto Rico, Mayagüez, [email protected] 3 Antonio González-Quevedo , Professor, Civil Engineering and Surveying Department, University of Puerto Rico, Mayagüez, [email protected] 2 Coimbra, Portugal September 3 – 7, 2007 International Conference on Engineering Education – ICEE 2007 400 450 The top 15 private high schools that send more than 50 students to the College of Engineering at UPRM who graduate are shown in Figure 2. The top private high school is Notre Dame in the city of Caguas with 262 graduates. In second place is Immaculate Conception High School in Mayagüez with 182 graduates, followed by Colegio San José in San Juan with 145 graduates. Eight of the 15 schools are located in the metropolitan area of San Juan. Notre Dame High School, Caguas 262 Academia de la Inmaculada Concepción, Mayagüez 182 Colegio San José, Río Piedras Colegio Ponceño 145 Colegio San Ignacio, Río Piedras 122 Academia San José, Guaynabo Academia Discípulos de Cristo, Bayamón 121 Colegio San Antonio, Río Piedras Colegio San Antonio, Río Piedras 117 Colegio Marista, Guaynabo 96 343 342 Notre Dame High School, Caguas 340 Colegio San José, Río Piedras 340 90 Colegio Santo Tomás de Aquino, Bayamón 340 Colegio San Agustín, Cabo Rojo 90 Academia de la Inmaculada Concepción, Mayagüez 340 Academia Santa María, Ponce 88 Cupeyville School, Río Piedras 340 Colegio San Antonio Abad, Humacao 88 Colegio María Auxiliadora, Carolina 87 Colegio San Carlos, Aguadilla 86 Colegio Evagélico Capitán Correa, Arecibo 82 Carvin School, Carolina 77 0 50 100 150 200 250 300 Vocacional Antonio Lucchetti, Arecibo 340 Leonídes Morales Rodríguez, Lajas 340 Emilio R. Delgado, Corozal 339 337 337 Domingo Aponte Collazo, Lares 337 Juan Quirindongo Morell, Vega Baja 336 337 338 339 340 341 342 337 Ponce High School, Ponce 336 Asunción Rodríguez, Guayanilla 336 Juan Antonio Corretjer, Ciales 333 339 338 336 334 335 336 337 338 339 340 341 343 The top fifteen public high schools with the shortest time to graduate with a bachelor’s of science degrees in engineering from 1991-2006 are shown in Figure 5. The top school in this category is the UPR High School in San Juan with 5.59 years. In second place is Ana J. Candelas School in Cidra with 5.65 years. In third place there is a tied with 5.79 years for Ramón José Dávila in Coamo with Patria Latorre School in San Sebastián. Among the fifteen top public high schools in this category, two are from the metropolitan area of San Juan, five are from the Western region, three are from the Southern region, four are from the Central region, and one from the Eastern region. 338 Patria Latorre, San Sebastían 339 PERFORMANCE OF THE STUDENTS AT THE COLLEGE OF ENGINEERING 340 337 339 Colegio Evagélico Capitán Correa, Arecibo It can be concluded that the first four charts show high school students characteristics as they enter the university. In the next section, the student performance in the College of Engineering will be analyzed. 339 Luis Muñoz Marin, Añasco 339 Colegio San José, Caguas FIGURE 4 PRIVATE HIGH SCHOOLS WITH THE HIGHEST IGS FOR GRADUATES OF THE SCHOOL OF ENGINEERING WITHIN 1995-2005 341 Ramón José Dávila, Coamo Eladio Tirado López, Aguada Academia Santa María, Ponce IGS 341 Secundaria UPR, Río Piedras Carmen Belén Veiga, Juana Díaz 339 335 The top 15 public high schools with the highest admission index (IGS) for students of the College of Engineering at UPRM from 1995-2005 whom graduate are shown in Figure 3. The top public high schools are Antonio Luchetti Vocational School in Arecibo followed by the UPR High School (both with the same IGS of 341 points). Following these two schools are Ramón José Dávila in Coamo, Leonides Morales Rodríguez in Lajas and Emilio R. Delgado in Corozal with an average IGS of 340. These fifteen top public high schools are distributed throughout Puerto Rico. Carmen Bozello de Huyke, Arroyo 340 Carvin School, Carolina Colegio San Conrado, Ponce FIGURE 2 FIRST 15 PRIVATE HIGH SCHOOLS WITH 50 OR MORE GRADUATES AT UPRM FOR THE COLLEGE OF ENGINEERING (YEARS 1995-2005) University Gardens, Río Piedras Colegio Marista, Guaynabo Colegio San Antonio Abad, Humacao Cantidad de Estudiantes Escuelas Públicas 343 American Military, Guaynabo Escuelas Privadas E scu ela s P riva da s The top 15 private high schools with the highest admission index (IGS) for students of the College of Engineering at UPRM from 1995-2005 whom graduate are shown in are shown in Figure 4. The top two schools are tied with and IGS of 343 and they are Colegio Ponceño in the city of Ponce and San José Academy in the city of Guaynabo. Following is Colegio San Antonio with an average IGS of 342. The cities represented in these 15 schools are Caguas (3), Ponce (3), Guaynabo (2), San Juan (2), and Bayamón, Mayagüez, Carolina, Arecibo, Humacao all with one school. 342 IGS FIGURE 3 PUBLIC HIGH SCHOOLS WITH THE HIGHEST IGS FOR GRADUATES OF THE SCHOOL OF ENGINEERING WITHIN 1995-2005 Coimbra, Portugal September 3 – 7, 2007 International Conference on Engineering Education – ICEE 2007 344 RIO PIEDRAS-SECUNDARIA UPR 5.65 CIDRA-ACADEMICA ANA J CANDELAS COAMO-RAMON JOSE DAVILA 5.79 SAN SEBASTIAN-PATRIA LATORRE 5.79 HUMACAO-ANA ROQUE 5.83 5.87 ARROYO-CARMEN BOZELLO DE HUYKE E s c u e la s P ú b lic a s Domingo Aponte Collazo School in Lares with an average GPA of 3.07. Among the 15 public high schools with the highest UPRM graduation GPA, two are from the metropolitan area of San Juan, eight are from the Western region, two are from the Southern region, two are from the Central region, and one from the Eastern region. 5.59 RIO PIEDRAS-SECUNDARIA UPR OROCOVIS-JOSE ROJAS CORTES 5.97 SAN GERMAN-LOLA RODZ DE TIO CAYEY-MIGUEL MELENDEZ MUNOZ 5.97 LARES-DOMINGO APONTE COLLAZO JUANA DIAZ-CARMEN BELEN VEIGA 3.22 3.13 3.07 COAMO-RAMON JOSE DAVILA 5.97 3.06 SAN SEBASTIAN-PATRIA LATORRE AGUADILLA-BENITO CEREZO 3.05 6.00 3.05 MAYAGUEZ-JOSE DE DIEGO LARES-DOMINGO APONTE COLLAZO Escuelas Públicas 6.00 AIBONITO-DR JOSE N. GANDARA 6.03 RIO PIEDRAS-UNIVERSITY GARDENS 6.04 YAUCO-LUIS MUNOZ MARIN HUMACAO-ANA ROQUE 6.09 SAN GERMAN-LOLA RODZ DE TIO 3.04 AGUADILLA-BENITO CEREZO 3.04 RIO PIEDRAS-UNIVERSITY GARDENS 3.04 ANASCO-LUIS MUNOZ MARIN 3.04 MAYAGUEZ-CROEM 6.12 3.03 CAYEY-MIGUEL MELENDEZ MUNOZ 5.30 5.40 5.50 5.60 5.70 5.80 5.90 6.00 6.10 3.02 6.20 Tiempo Promedio FIGURE 5 TOP 15 PUBLIC HIGH SCHOOLS WITH THE LOWEST AVERAGE TIME TO COMPLETE THE BACHELOR’S DEGREE IN ENGINEERING (1991-2006) SABANA GRANDE-BLANCA MALARET 3.01 AIBONITO-DR JOSE N. GANDARA 3.01 ARROYO-CARMEN BOZELLO DE HUYKE 3.00 2.85 2.90 2.95 3.00 3.05 3.10 3.15 3.20 3.25 GPA Promedio The top fifteen private high schools with the shortest time to graduate with a bachelor’s of science degrees in engineering from 1991-2006 are shown in Figure 6. The shortest time belongs to Colegio San Antonio Abad in Humacao with 5.48 years. In second place is Colegio San Conrado in Ponce with 5.52 years and in third place is Colegio Espiritú Santo in San Juan with 5.55 years. Among the fifteen top private high schools in this category, six are from the metropolitan area of San Juan, three are from the Western region, three are from the Southern region, two are from the Central region, and one from the Eastern region. HUMACAO-COL SAN ANTONIO ABAD 5.52 RIO PIEDRAS-COL ESPIRITU SANTO 5.55 PONCE-COL PONCENO 5.62 CAGUAS-COL SAN JOSE 5.66 RIO PIEDRAS-COL SAN ANTONIO 5.66 AGUADILLA-COL SAN CARLOS 5.67 SAN GERMAN-COL SAN JOSE 5.70 RIO PIEDRAS-COL SAN IGNACIO 5.75 CAGUAS-NOTRE DAME HIGH SCHOOL RIO PIEDRAS-COL ESPIRITU SANTO 5.76 MAYAGUEZ-ACAD LA INMACULADA 5.78 GUAYNABO-COL SAGRADOS CORAZONES 5.40 5.50 5.60 5.70 5.80 5.90 Tiempo Promedio FIGURE 6 TOP 15 PRIVATE HIGH SCHOOLS WITH THE LOWEST AVERAGE TIME TO COMPLETE THE BACHELOR’S DEGREE IN ENGINEERING (1991-2006) 3.20 3.19 RIO PIEDRAS-COL SAN ANTONIO 3.15 SAN GERMAN-COL SAN JOSE 5.90 5.30 3.21 HUMACAO-COL SAN ANTONIO ABAD 5.88 PONCE-ACAD SANTA MARIA 3.21 PONCE-COL SAN CONRADO 5.87 CAROLINA-CARVIN SCHOOL 3.22 MAYAGUEZ-ACAD LA INMACULADA 5.80 RIO PIEDRAS-COL SAN JOSE 3.23 AGUADILLA-COL SAN CARLOS 6.00 Escuelas Privadas Escuelas Privadas The top seventeen private high schools that showed the highest UPRM graduation grade point average (GPA) for students who entered the Faculty of Engineering and graduated from it (1991-2006) are shown in Figure 8. The top private school in this category is Colegio Espiritú Santo in San Juan with an average GPA of 3.23. In second place for this category is Colegio San Carlos in Aguadilla tied with Immaculate Conception Academy in Mayagüez with an average UPRM graduation GPA of 3.21. Among the 17 private high schools with the highest UPRM graduation GPA, six are from the metropolitan area of San Juan, five are from the Western region, three are from the Southern region, two are from the Central region, and one from the Eastern region. 5.48 PONCE-COL SAN CONRADO 5.20 FIGURE 7 TOP FIFTEEN PUBLIC SCHOOLS WITH HIGHEST UPRM GRADUATION GRADE POINT AVERAGE (GPA)FOR STUDENTS FROM PUBLIC HIGH SCHOOLS WHO ENTERED THE FACULTY OF ENGINEERING (1991-2006) 3.12 CAGUAS-COL SAN JOSE 3.09 GUAYNABO-COL SAGRADOS CORAZONES CAGUAS-NOTRE DAME HIGH SCHOOL 3.08 CAROLINA-CARVIN SCHOOL 3.07 PONCE-ACAD SANTA MARIA 3.06 ISABELA-COL SAN ANTONIO 3.05 CABO ROJO-COL SAN AGUSTIN The top fifteen public high schools that showed the highest UPRM graduation grade point average (GPA) for students who entered the Faculty of Engineering and graduated from it (1991-2006) are shown in Figure 7. In first place is the UPR High School with an average GPA of 3.22. In second place is Lola Rodríguez de Tió School in San Germán with an average GPA of 3.13 and in third place is 3.04 PONCE-COL PONCENO 3.04 GUAYNABO-AMERICAN MILITARY 3.04 CAROLINA-COL MARIA AUXILIADORA 2.90 3.04 2.95 3.00 3.05 3.10 3.15 3.20 GPA Promedio FIGURE 8 TOP SEVENTEEN PRIVATE SCHOOLS WITH HIGHEST UPRM GRADUATION GRADE POINT AVERAGE (GPA)FOR STUDENTS FROM PRIVATE HIGH SCHOOLS WHO ENTERED THE FACULTY OF ENGINEERING (1991-2006) Coimbra, Portugal September 3 – 7, 2007 International Conference on Engineering Education – ICEE 2007 3.25 PONCE-COL SAN CONRADO 93.02 90.18 MAYAGUEZ-ACAD LA INMACULADA PONCE-ACAD SANTA MARIA 82.50 BAYAMON-COL DE LA SALLE 82.22 CABO ROJO-COL SAN AGUSTIN 81.16 RIO PIEDRAS-COL SAN IGNACIO Escuelas Privadas The top fifteen public high schools with the highest UPRM graduation rates for students who entered the Schools of Engineering in the cohorts of 1991-1997 are shown in Figure 9. The first public high school in this category is Patria Latorre School in San Sebastián with a graduation rate of 83.56%. In second place is the UPR High School in San Juan with a graduation rate of 82.46%. In third place is Efraín Sánchez Hidalgo School in Moca with a graduation rate of 80%. Among the top fifteen public high schools with highest graduation rates, two are from the metropolitan area of San Juan, nine are from the Western region, one is from the Southern region, two are from the Central region, and one from the Eastern region. 80.33 ARECIBO-COL EVANG CAPITAN CORREA 78.05 78.05 HUMACAO-COL SAN ANTONIO ABAD CAGUAS-NOTRE DAME HIGH SCHOOL 76.26 RIO PIEDRAS-COL SAN ANTONIO 75.56 RIO PIEDRAS-COL SAN JOSE 73.58 68.29 BAYAMON-ACAD DISCIPULOS DE CRISTO GUAYNABO-AMERICAN MILITARY SAN SEBASTIAN-PATRIA LATORRE 66.67 83.56 CAROLINA-COL MARIA AUXILIADORA RIO PIEDRAS-SECUNDARIA UPR 0.00 MOCA-EFRAIN SANCHEZ HIDALGO YAUCO-LUIS MUNOZ MARIN Escu elas Púb licas 10.00 20.00 30.00 80.00 COAMO-RAMON JOSE DAVILA 72.73 72.09 RIO PIEDRAS-UNIVERSITY GARDENS 50.00 60.00 70.00 80.00 90.00 100.00 FIGURE 10 TOP FOURTEEN PRIVATE HIGH SCHOOLS WITH THE HIGHEST UPRM 73.21 MAYAGUEZ-EUGENIO M DE HOSTOS 40.00 Tasa Graduación 76.06 AGUADILLA-BENITO CEREZO GRADUATION RATES FOR STUDENTS WHO ENTERED THE SCHOOL OF ENGINEERING IN THE COHORTS OF 1991-1997 71.67 MAYAGUEZ-CROEM 70.59 HUMACAO-ANA ROQUE 70.00 OROCOVIS-JOSE ROJAS CORTES 68.97 CIDRA-ACADEMICA ANA J CANDELAS 68.63 SAN GERMAN-LOLA RODZ DE TIO The previous six charts are related to time to graduate, graduation grade point average and graduation rate. These three indicators will be combined in the next section to develop a performance index (PI) that will allow ratings of these high schools. 68.33 SABANA GRANDE-BLANCA MALARET 65.00 LARES-DOMINGO APONTE COLLAZO 0.00 58.70 82.46 64.91 10.00 20.00 30.00 40.00 50.00 60.00 70.00 PERFORMANCE INDEX USING QUADRATIC LOSS FUNCTION 80.00 90.00 Tasa de Graduación FIGURE 9 TOP FIFTEEN PUBLIC HIGH SCHOOLS WITH THE HIGHEST UPRM GRADUATION RATES FOR STUDENTS WHO ENTERED THE SCHOOL OF ENGINEERING IN THE COHORTS OF 1991-1997 The top fourteen private high schools with the highest UPRM graduation rates for students who entered the Schools of Engineering in the cohorts of 1991-1997 are shown in Figure 10. In first place in this category is Colegio San Conrado in Ponce with a graduation rate of 93.02%. In second place is Immaculate Conception Academy in Mayagüez with a graduation rate of 90.18% and in third place is Santa María Academy in Ponce with a graduation rate of 82.50%. Among these fourteen private schools with highest UPRM graduation rates, seven are from the metropolitan area of San Juan, one is from the Western region, two are from the Southern region, one is from the Central region, and one from the Eastern region. The concept of quadratic loss function has been proposed by Phadke [2] to approximate quality losses. One can develop a performance index (PI) to compare high schools through the execution of their students at the high level institutions. The quadratic loss function is given by Loss(y) = k (y – T)2 (1) where k is a proportionality constant and T is the target value for the y characteristic. Usually in quality control applications a tolerance ∆ is defined such that if the y characteristic is within T + ∆ (two sided tolerance) the characteristic is acceptable. The quadratic loss function in (1) penalizes the behaviors that deviate from the target T. A challenge with (1) is the definition of constant k. ArtilesLeón [3] defined this value to assure that the loss function is insensitive to the system of units used to measure the quality characteristic y. For the two sided tolerance problem this definition becomes: 2 k = 2∆ 2 (2) Using k in (2) results in a “standardized” loss function. Since the standardized version of the loss function is dimensionless if several quality characteristics are considered their correspondent loss functions can be added. In our case study, the quality characteristics or critical indicators that we are considering are: the average Coimbra, Portugal September 3 – 7, 2007 International Conference on Engineering Education – ICEE 2007 time to degree, the average graduation GPA and graduation rates for the high schools under consideration. These characteristics are not suited for the two sided tolerance approach. The first one, average time to degree, can be described better as an smaller-the-better characteristic, while the other two average GPA, and graduation rate of a higherthe-better characteristic form. Expanding the standardized concepts to one-sided tolerance characteristics the following two equations can be derived for smaller-the-better (3) and higher-the-better (4). 2 y ∆2 ∆2 SLoss ( y ) = 2 y SLoss ( y ) = (3) (4) A total standardized loss (TSLoss) for our case study can be defined as: TSLoss = y12 ∆22 ∆23 + + ∆21 y 22 y 32 exploring the following indicators, average GPA math courses, average GPA science courses, average GPA language courses, attempted credits, among others. A limitation of the described performance index is that it does not take into account the correlations among the critical indicators variables considered. Future work should consider techniques such as the Mahalanobis Distance to incorporate such relationships. ACKNOWLEDGMENT The authors want to acknowledge the effort by Leo I Vélez and Irmannette Torres from the Office of Institutional Research and Planning of the University of Puerto Rico at Mayagüez for providing and validating the data used in this study. REFERENCES [1] González-Barreto, D. and González-Quevedo, A.,“Attracting a More Diverse Student Population to the School of Engineering of the University of Puerto Rico at Mayagüez”, Proceedings of the 9th International Conference on Engineering Education. July 23-28, 2006. San Juan, PR, pp. R4E21, R4B25. [2] Phadke, M. S., Quality Engineering using Robust Design, PrenticeHall, Englewood Cliffs, NJ, 1989 (5) where yi, and ∆i corresponds to the characteristic and tolerance for the critical indicators. The TSLoss in (5) could be generalized to m characteristics and can combine one and two sided tolerance characteristics. TLoss can be viewed as a performance indicator for high schools as represented by their students execution The lower performance index the better the students performance at the university, the better the high school. Applying (5) to institutional research data for high schools that provide the largest number of students to our engineering college for the last 10 years the following estimates in Table 1 are obtained. . [3] Artiles-León, N., “A Pragmatic Approach to Multiple-Response Problems using Loss Functions”, Quality Engineering, 9,2, 19961997, pp. 213-220. TABLE 1 RATINGS OF HIGH SCHOOLS BASED ON PERFORMANCE OF INDEX High School Colegio San Conrado, Ponce Academia de la Inmaculada Concepción, Mayagüez Secundaria UPR, Río Piedras Colegio San Antonio Abad, Humacao Patria Latorre, San Sebastian Academia Santa María, Ponce Colegio San Antonio, Río Piedras Notre Dame High School, Caguas Ramón José Dávila, Coamo Benito Cerezo, Aguadilla University Gardens, Río Piedras Ana Roque, Humacao Lola Rodríguez de Tió, San Germán Domingo Aponte Collazo, Lares Performance Index 3.250182 3.376351 3.569336 3.737924 3.74815 3.796827 3.893357 3.995966 4.195212 4.237077 4.326681 4.376365 4.440817 4.711063 FINDINGS AND CONCLUSIONS FUTURE WORK The suggested performance index, based on the TSLoss, should include additional critical indicators. We suggest Coimbra, Portugal September 3 – 7, 2007 International Conference on Engineering Education – ICEE 2007
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